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mr_homm
Hi hexa,

Continuing the analysis, I was stalled for a while because the calculation looked very long. Fortunately I have thought of a method of streamlining the calculation so that it is really very easy to do. That is especially fortunate because I found still another calculation error! This is getting embarrassing. I've been very busy and doing these calculations a few minutes at a time, when I'm already sleepy. Sorry. First I'll outline the streamlined calculation idea, then correct my previous error, then finish the complete calculation.

The basic idea is that the error is always orthogonal to the ideal behavior. For instance, if the LP is non ideal, it lets through a little bit of light that is not aligned with the LP axis. However, all of this extra light must be plane polarized perpendicular to the LP axis. To prove this, suppose it was not perpendicular. Then you could resolve it into a perpendicular and parallel component. But the parallel component is already accounted for, because this part is what is supposed to get through in the ideal LP. Therefore, it cannot be part of the error, so the error consists entirely of light polarized perpendicular to the LP filter axis. But changing the direction of the polarization from vertical to horizontal before the light hits the first QWP reverses the filter from RCP to LCP, according to the instructions for building the filter that I posted earlier.

If you look at the error of QWP(pi/4+b,0), again only the part of the error that produces a state perpendicular to the ideal filter output is real, since any parallel part of the error would already have been include in the ideal behavior. The state perpendicular to RCP is LCP, so the error in the QWP produces a small amount of the opposite circular polarization. Ao again the polarization is changed from RCP to LCP in the error term.

If you look at the error in the angular position of each QWP relative to its own LP, the error is in the rotation matrix term R(Θ). Again, a small error in a rotation matrix is the same as adding a small component turned 90 degrees further counterclockwise than the ideal output of the matrix. You can see this easily by differentiating R(Θ) w.r.t. Θ. Sines and Cosines will switch places and there will be some sign changes. If you then apply the trig identities -sin(Θ) = cos(Θ+pi/2) and cos(Θ) = sin(Θ+pi/2), you find that (d/dΘ)R(Θ) = R(Θ+pi/2). This is the angle that controls the orientation of the QWP relative to the preceding LP. Adding pi/2 to this angle reverses the orientation of the QWP axis relative to the LP axis, which once again changes RCP light into LCP light in the error term.

It is important to notice that this is true even if the errors are not small. Even large errors must produce output that is orthogonal to the ideal component's output, because that is the only other possibility in a 2 dimensional state space. for the case of the LP, the error due to non-ideal filtering is ADDED to the light that would have come through the ideal filter, so a non-ideal LP looks like 1*LP(V) + a*LP(H). As for the errors in the angular position or phase delay of the QWP, these errors DIVERT light into the error, rather than letting additional light through, so the state remains normalized. In other words, if an ideal QWP(pi/4,0) has an output of magnitude 1, then a non-ideal QWP(pi/4,e) must have an output (1*QWP(pi/4,0) + e*QWP(pi/4,pi/2))/√(1+e^2). Also, a non-ideal QWP(pi/4+b,0) must have an output (1*QWP(pi/4,0) + b*QWP(-pi/4,0))/√(1+b^2).

Now I'll correct my previous error and then I'll show how the streamlined calculation works on the corrected formula. When I first wrote down my matrix formula, I said,
QUOTE
To account for rotating the filter, you should put a rotation matrix on both sides of it: LP(a,Θ) = R(Θ)LP(a,H)R(-Θ). This is like rotating the light by -Θ, then applying the L(H), then rotating the result by +Θ, which puts it back where it was. The effect is the same as rotating the filter by +Θ, so this is the math for rotating filters.

This was correct. Note that the matrix on the right is R(-Θ). However, when I wrote out my formula, I wrote
QUOTE (->
 QUOTE To account for rotating the filter, you should put a rotation matrix on both sides of it: LP(a,Θ) = R(Θ)LP(a,H)R(-Θ). This is like rotating the light by -Θ, then applying the L(H), then rotating the result by +Θ, which puts it back where it was. The effect is the same as rotating the filter by +Θ, so this is the math for rotating filters.

This was correct. Note that the matrix on the right is R(-Θ). However, when I wrote out my formula, I wrote
LP(a2,Θ5)QWP(b3,TΘ)QWP(b2,Θ3)LP(a1,0) = R(Θ5)LP(a2,0)R(-Θ5)R(Θ4)QWP(b3,0)R(-Θ4)R(Θ3)QWP(b2,0)R(Θ3)LP(a1,0) = LP(a2,0)R(Θ4-Θ5)QWP(b3,0)R(Θ3-Θ4)QWP(b2,0)R(Θ3)LP(a1,0).

Note that I forgot the minus sign on the copy of R(Θ3) just to the right of QWP(b2,0). It should be R(-Θ3).

In the stremlined calculation, though, I don't even need to look at all these detailed matrices, just notice three basic facts:
1) errors produce states orthogonal to the ideal ones (already shown above).
2)any of the three erros a1, b1, or e1 will change the first filter from a RCP filter to an LCP filter, and similarly for a2, b2, and e2 changing the second filter. (already shown above).
3) A rotation matrix R(Θ) affects a circularly polarized beam as follows:
R(Θ)|R> = exp(iΘ)|R> and R(Θ)|L> = exp(iΘ)|L> (shown in a previous post).

With these three facts, I can now compute easily the complete error terms, NOT assuming the errors are small, as follows: each error switches each filter between RCP and LCP, so combinations of errors will switch the filter type multiple times. Therefore, the first non-ideal RCP filter behaves like [1*RCP + (a1 + b1 +e1)*LCP + (a1*b1 + b1*e1 + e1*a1)*RCP + (a1*b1*e1)*LCP]/√[(1+b1^2)(1+e1^2)] = [(1 + a1*b1 + b1*e1 + e1*a1)*RCP + (a1 + b1 + e1 + a1*b1*e1)*LCP]/√[(1+b1^2)(1+e1^2)]. Now I can just collect together these constants and name them A and B, to get A*RCP + B*LCP. Therefore, when acting on unpolarized light, the output of the first filter state will be A*|R> + B*|L>. If the filter is pretty good, than A is nearly 1 and B is small.

The second non-ideal RCP filter can be treated in ALMOST the same way, but you have to remember that we are only looking at the filter as far as the last LP, since the final QWP does not affect the light color or intensity. The part of the second RCP filter that we are looking at will pass through incident |R> light, but turn it into |H> light. The a2,b2 and e2 errors will cause it to accept |L> light instead, but since the a2 error is in the final LP, it will cause the filter to put out |V> light instead.

Therefore, the second filter will perform as follows:
[(1 + a2*b2 + b2*e2 + e2*a2)*RCP + (a2 + b2 + e2 + a2*b2*e2)*LCP]/√[(1+b1^2)(1+e1^2)] with the added effect than any term that contains an a2 factor will put out light in the state |V> and the other terms will put out light in the state |H>. This means that the second filter will turn |R> light into (1 + b1*e1)/√[(1+b1^2)(1+e1^2)]*|H> + a1*(b1 + e1)/√[(1+b1^2)(1+e1^2)]*|V> = C*|H> + D*|V> by collecting constants. If the filter is pretty good, than C is nearly 1 and D is small.

Similarly, it will turn |L> light into
(b1 + e1)/√[(1+b1^2)(1+e1^2)]*|H> + a1*(1 + b1*e1)/√[(1+b1^2)(1+e1^2)]*|V> = E*|H> + F*|V>. If the filter is pretty good, then E and F are both small.

Therefore when unpolarized light hits the first filter, the output of that filter will be 1/√2 * (A*|R> +B*|L>), the rotation matrix converts into 1/√2 * (A*exp(iΘ)|R> +B*exp(-iΘ)|L>). The second filter will turn this into 1/√2 * (A*exp(iΘ)*(C*|H> + D*|V>) +B*exp(-iΘ)(E*|H> + F*|V>)) = 1/√2 * [(AC*exp(iΘ)+BE*exp(-iΘ))|H> + (AD*exp(iΘ)+BF*exp(-iΘ))|V>] = |O>, where O stands for Output.

The intensity of this light will be <O|O> = 1/2*[(AC*exp(-iΘ)+BE*exp(iΘ))(AC*exp(iΘ)+BE*exp(-iΘ))<H|H> + (AD*exp(-iΘ)+BF*exp(iΘ))(AD*exp(iΘ)+BF*exp(-iΘ))<V|V>], remembering that <O| has complex conjugate coefficients, and that <V|H> = 0 and <V|V> = <H|H> = 1.

This simplifies to 1/2[(AC)^2 + (BE)^2 + 2ACBEcos(2Θ) + (AD^2 + (BF)^2 + ADBFcos(2Θ)] = 1/2[(AC-BE)^2 + (AD-BF)^2 + 4(ACBE+ 4ADBF)cos^2(Θ)]. Since A and C are large and the rest of the constants are small, this exact formula reduces to approximately AC/2*[1+BEcos^2(Θ)]. The exact values of all the constants can be traced back to the original error terms in the descriptions of the non-ideal filter components, so if these can be measured, you can predict the exact light output of two non-ideal RCP filters.

What if the second filter is LCP instead? This is very simple. The description of the first filter is unchanged, and for the second filter, you just switch the |R> and |L> terms in the description of the second filter 5 paragraphs ago. This in effect simply switches the constants C with E, and switches D with F. Therefore, the filter output is 1/2[(AE-BC)^2 + (AF-BD)^2 + 4(AEBC+ 4AFBD)cos^2(Θ)]. Since A and C are the only llarge terms, this exact formula reduces to approximately 1/2[(AE-BC)^2 + (AE)^2 + 4(AEBC)cos^2(Θ)]. All of these terms involve one small quantity, so the total light should be small, and has a constant part and a part that varies like cos^2(Θ). The sign of the cos term could be either + or -, so there could be a max or a min at Θ=0, depending on the way in which the filters are non-ideal.

This shows that non-ideal filter components could fully account for the lack or rotation invariance in your experiment. Since no filter is likely to be perfectly ideal, (nothing in this world is perfect), this is exactly the kind of experimental result you should expect according to both QM and classical physics. Remember, in this type of experiment both QM and classical Electromagnetism agree in their predictions, so if your experiment contradicted QM it would also contradict classical EM, which is one of the most thoroughly tested theories ever. In other words, I consider it extremely unlikely that these results are due to anything other than minor imperfections in your filters. To take the experiment to the next stage, I would try to think of ways to set it up so that the non-ideal nature of the filters canceled out by symmetry to produce a very nearly ideal result. Off hand, I don't know how to do this.

Now that I've finally finished this very long calculation (made longer my several errors of mine), I'm ready to look at your further questions in my next post.

Hope this helps!

--Stuart Anderson
mr_homm
Don't worry, I'm just posting to correct a typo. This does not affect anything in the conclusion of my previous post. I forgot a minus sign in how the rotation matrix affects |R> and |L> states. Where I wrote
QUOTE
R(Θ)|R> = exp(iΘ)|R> and R(Θ)|L> = exp(iΘ)|L> (shown in a previous post).

the second formula should have (-iΘ). In other words, the corrected formulas are:
R(Θ)|R> = exp(iΘ)|R> and R(Θ)|L> = exp(-iΘ)|L>. The difference is because in RCP light, the E field rotates in a clockwise helix, like the thread on a screw, and in LCP light it twists the other way. Rotating a screw CCW is equivalent to pushing it forward, but rotating a reverse screw CCW pulls it backward.

These correct formulas are the ones that I used in all my later calculations, so all the calculations after this point in my previous post are still correct. Sorry for any confusion!

In a day or so I'll post again addressing hexa's more recent queries.

--Stuart Anderson
hexa
Hi Mr Homm,

In addition to the question that I have raised in my posting on 2 Oct. 06, I would like to seek some clarification on the relative position between the filters that goes towards the construction of the Right or Left Circular Polarizer.

We will use the following convention that we have defined for this discussion:
a] the x & y axes are used to define the orientation of the linear polarizers; and
b] the z axis is used to define the position of each filter from the source of light.

Using this convention, we will state the position of the two circular polarizers as follows:
Circular polarizer 1
i) QWP1a=z1
ii) x-linear polarizer = z2
iii) QWP1b=z3

Circular polarizer 2
iv) QWP2a=z4
v) x-linear polarizer=z5
vi) QWP2b=z6

Questions:
1) Is it correct to assume that the variation in the displacement between one QWP and the next linear polarizer does not alter the property of the circular polarizer?
In other words, does it make any difference if we vary the position of z1, z2 and z3?

2) Is it true that a photon that passes through a True Circular Polarizer will remain in that state indefinitely until its path is impeded by another filter (be it a Linear Polarizer or another Circular polarizer)?
In other words, does it make any difference if we vary the position of z3 and z4.

I would appreciate if you could address the questions that I have raised here as well as those raised in 2 Oct.

Cheers.
mr_homm
Hi hexa,

I can answer your most recent question right now, and then get back to your October 2 post in a little while. The answer is no, the z positions affect nothing. Travel along the z direction changes the phase of the photon, but phase is unobservable, since it cancels out when computing <state|state>. A photon, once put into a state, remains there until some outside interaction disturbs it. This is the QM equivalent of Newton's First Law. Therefore, the locations of the filters on the z axis makes no difference at all to the output state.

More later.....

--Stuart Anderson
hexa
Hi Mr Homm,

Thanks for the clarification.

I will now wait for your explanation pertaining to the issues that I have raised on 2 Oct 06.

Cheers.
mr_homm
Hi Hexa,

I'm finally getting back to your earlier questions. Sorry for the long delay, but my cousin died (we were not very close, but friendly), he told me I would be the executor of his estate, but he left no will, so my relatives and I have been down at his house cleaning it up and looking for documents. It has been a big mess, and now I have even less time than before, but temporarily I have a little time to answer you today.

QUOTE
My primary concern in raising this topic is to determine whether we can distinguish a photon in the x-linearly polarized states from one that is in the y-linearly polarized state as well as one from the Left or the Right circularly polarized state.
In other words, if we were to pass a single photon through a x linear polarizer, the single photon (if it emerges from the linear polarizer) is distinguishable from a photon that passes through a y linear polarizer, a Left or a Right circular polarizer.

QM says yes it is. QM does apply to individual photons and does say that each one is in a distinct polarization state after exiting the filter. Depending on the type of filter, this could be |V>, |H>, |L>, |R>, or something else entirely. It is controlled by how your filter is built.

QUOTE (->
 QUOTE My primary concern in raising this topic is to determine whether we can distinguish a photon in the x-linearly polarized states from one that is in the y-linearly polarized state as well as one from the Left or the Right circularly polarized state.In other words, if we were to pass a single photon through a x linear polarizer, the single photon (if it emerges from the linear polarizer) is distinguishable from a photon that passes through a y linear polarizer, a Left or a Right circular polarizer.

QM says yes it is. QM does apply to individual photons and does say that each one is in a distinct polarization state after exiting the filter. Depending on the type of filter, this could be |V>, |H>, |L>, |R>, or something else entirely. It is controlled by how your filter is built.

From the discussion, you seem to suggest that there is no such physical reality as Quantum Mechanics appears to concern itself with only the Statistical prediction of a GROUP of photons and not whether each individual photon can be described distinctly using the 3-D physical space.

No, QM doesn't necessarily concern itself with the statistical prediction of behavior of groups of particles. That is just an experimental trick WE use to get results faster. The fundamental trouble is that you cannot measure the same photon twice. Once you measure it, your measurement throws it into a new eigenstate, and so if you try to measure it again, you will find the new state, not the original one, so you cannot gain any more information about the original state than what you can get from a single measurement.

For example, QM predicts that if you put a SINGLE photon through a vertical linear polarizer, it will sometimes emerge, sometimes not, depending on the unknown original state. However, if it DOES emerge, it will be in the state |V>. This state has the property that it has 100% probability of passing successfully through a second vertical linear polarizer, 0% for a horizontal one, and 50% for right or left circular polarizers. However, since you can only make ONE measurement on this photon, you can't test all these predictions, only one of them. QM makes similar predictions about single photons that pass through circular polarizers.

Fortunately, one of the basic assumptions of QM (and of classical physics) is reproducibility: If you repeat the experiment with a fresh photon, it will emerge from the first filter in exactly the same state as the original photon. You can then repeat the experiment as many times as you wish, using a single photon each time, and test all the predictions. This is not really much different from the case in classical physics. If you want to prove that something ALWAYS happens, or NEVER happens, it is not enough to test it just once. You must test it many times and see if a consistent pattern appears. If you want to test for alternative outcomes, again you must test many times. This has nothing to do with uncertainty or probability, it is just a fact of life that many tests are required to test universal assertions.

Of course, this process would be very time consuming if you only work with one photon at a time, but there is a way out: use many photons at once. This is not as obvious as it may seem at first, because you have to know that the presence of many photons simultaneously will not affect the results. The reason that this works in QM is that one of the basic features of the theory is that each particle interferes ONLY WITH ITSELF, and not with other particles. This is exactly the opposite of the conclusion you might come to by thinking classically about interfering light waves, but is has to be this way. If each photon interferes only with itself, then the presence of other photons will not affect the outcome of the experiment for each individual photon, and so you can confidently use many photons at once without affecting the results.

This seems somewhat paradoxical, because we usually observe strong light beams, rather than individual photons, and we usually think in terms of the collective behavior of the whole light beam. Classically it looks like we have taken the whole light beam and split it into polarization components, each containing part of its energy, or in the two slit experiment, we have split the whole light beams into two beams, each coming through one slit, which interfere with each other. The paradox is that it is the individual photons' completely INDIVIDUAL behavior that produces the classical illusion of COLLECTIVE behavior. If the photons did interfere with each other (instead of just each photon with itself) then when large numbers of photons were together in a light beam, the interference effects would be stronger when there were more photons. In other words, the SHAPE of the interference pattern would change when the light intensity increased. This violates the principle of superposition for classical electromagnetism, and more importantly, is not observed experimentally.

By the way, this is how we know that QM is a completely LINEAR theory. If large numbers of photons in a light beam obey the classical principle of superposition, then the rules of quantum mechanics must also have the principle of superposition, and ALSO the principle of individual interference. Because of the large numbers of photons in a classical light beam, the classical observation of superposition is a VERY VERY sensitive experiment to test the linearity of QM. If QM were nonlinear or included interference between different particle states, even to a very slight degree, then classical light superposition would be drastically wrong. This tests that QM is linear to many decimal places (at least 11, if I recall). With such experimental results, it would be absurd to assume QM is anything less than 100% EXACTLY linear, or that different states interfere with one another AT ALL.

Now the other question, about whether photon states can be described by the 3d physical space, is completely separate from the statistics vs. individual particle question. I still cannot see why 3d space would be an appropriate choice in general. Most things in classical physics are described by many other properties than their position in 3d space. Why should a photon not be so described? If I want to describe an irregular box, I might have to give its position + 4 or 5 further numbers describing the lengths of its sides, and so forth. This is mathematically equivalent to a point in a multidimensional space. Ultimately, it's just a lot of coordinates, no more or less abstract than the three we are used to, just less familiar. That's my opinion anyway.

I'm out of time for now, so I'll deal with your other questions in my next post, which will (I hope) be later today, not next week!

--Stuart Anderson
mr_homm
Continuing...
QUOTE
From your description of a True Circular Polarizer, you have shown that the critical component of the circular polarizer is the linear polarizer that is sandwiched between the two QWP. It is the ability of the QWP (before the linear polarizer) to polarize the photons passing through it into a linear polarized state that determine the efficacy of the entire circular polarizer to act as an opposing polarizer that will stop the passage of any photon through one circular polarizer followed by another circular polarizer. In such circumstances, the experiments which I have conducted show that the passage of light through a Right followed by a Left circular polarizers is NOT ROTATION invariant.

Yes, the two QWPs do not actually perform a filtering action, since 100% of the light gets through them. However, remember that this sandwich structure is just the most practical way to make a circular polarizer, and that this is a technical limitation of available equipment, not a fundamental fact. It is possible that a material which directly absorbs one circular polarization component will be discovered one day, so that we can have circular polarizers that work just like linear polarizers. I don't see any fundamental reason why this could not happen.

Now about your experimental results, these are exactly as expected since the filters are not ideal. In theory (both classical electromagnetism and QM) if the filters are exactly as prescribed, then the effect should be rotation invariant. Note that this is NOT a quantum effect, but is predicted by classical electromagnetism too. In any reasonably sensitive physics experiment, you always end up measuring some mixture of the intended physical process and artifacts of your equipment. The only way to be sure that what you are seeing is real is to very carefully eliminate equipment effects from the experiment.

Sometimes that means investing in better, more expensive equipment, and other times it means exercising cleverness in the experimental design. Often both are required. Let's take the equipment one piece at a time:

1: the linear polarizers. These are polymer sheets which do a pretty good job of removing one polarization component, but a small fraction of this component WILL get through them, which contaminates your results. These are the a1 and a2 terms in my error analysis from a previous post, which contribute some of the non-rotation-invariance. It is hard to improve these filters very much, but they can be replaced with other linear polarizers. For instance, you can use a large calcite crystal to split unpolarized light into perpendicular linearly polarized beams that run side by side. The split is virtually perfect, withe a1 and a2 so close to zero that they cannot be measured. Since QWPs are usually also made of calcite, this would give an all-calcite experimental setup.

2: the QWPs. These have one basic fault, which is that they only provide a perfect 1/4 wave delay at one exact wavelength, and at different wavelengths they will produce non-rotation-invariant results. The only real way around this is to use monochromatic light at the exact wavelength where the wave delay is 1/4 wavelength. You can get monochromatic light by using a laser, or by using white light and a diffraction grating. The laser will be a very pure monochromatic light, but the frequency is not adjustable. In that case, you may have to start with a QWP which is slightly too thick and hand polish it down to the right thickness so that the delay is exactly 1/4 wavelength. On the other hand, with a diffraction grating, you can use your original QWP without any polishing, but you must select the right frequency out of the diffracted spectrum so that the delay is 1/4 wave. This is much easier, but since you are only using a small fraction of the light, you must start with a quite bright source. That's not really a problem though.

3: the angles. If the angles are not precisely 45 degrees between the LP and the QWP axes, you will again get non-rotation-invariant results. The only way around this is to make the angle adjustable with some kind of very precise fine-tuning mechanism, and then hand adjust it so be precisely 45 degrees. This can best be done by adjusting them with the experiment running, until you can get absolutely no light through in the RCP followed by LCP case. There are 4 angles to adjust, so this will be a long process of twiddling to get it just right. There's really no other good way to make sure the angle is accurate enough.

Varying the experimental equipment is really the only way to separate equipment effects from the effect under study. I'm confident that if you try the experiment with different equipment, you will find that the outcome is much more nearly rotation invariant, and that by varying the equipment (fine tuning) you can show that all the rotation invariance is associated with equipment artefacts.

QUOTE (->
 QUOTE From your description of a True Circular Polarizer, you have shown that the critical component of the circular polarizer is the linear polarizer that is sandwiched between the two QWP. It is the ability of the QWP (before the linear polarizer) to polarize the photons passing through it into a linear polarized state that determine the efficacy of the entire circular polarizer to act as an opposing polarizer that will stop the passage of any photon through one circular polarizer followed by another circular polarizer. In such circumstances, the experiments which I have conducted show that the passage of light through a Right followed by a Left circular polarizers is NOT ROTATION invariant.

Yes, the two QWPs do not actually perform a filtering action, since 100% of the light gets through them. However, remember that this sandwich structure is just the most practical way to make a circular polarizer, and that this is a technical limitation of available equipment, not a fundamental fact. It is possible that a material which directly absorbs one circular polarization component will be discovered one day, so that we can have circular polarizers that work just like linear polarizers. I don't see any fundamental reason why this could not happen.

Now about your experimental results, these are exactly as expected since the filters are not ideal. In theory (both classical electromagnetism and QM) if the filters are exactly as prescribed, then the effect should be rotation invariant. Note that this is NOT a quantum effect, but is predicted by classical electromagnetism too. In any reasonably sensitive physics experiment, you always end up measuring some mixture of the intended physical process and artifacts of your equipment. The only way to be sure that what you are seeing is real is to very carefully eliminate equipment effects from the experiment.

Sometimes that means investing in better, more expensive equipment, and other times it means exercising cleverness in the experimental design. Often both are required. Let's take the equipment one piece at a time:

1: the linear polarizers. These are polymer sheets which do a pretty good job of removing one polarization component, but a small fraction of this component WILL get through them, which contaminates your results. These are the a1 and a2 terms in my error analysis from a previous post, which contribute some of the non-rotation-invariance. It is hard to improve these filters very much, but they can be replaced with other linear polarizers. For instance, you can use a large calcite crystal to split unpolarized light into perpendicular linearly polarized beams that run side by side. The split is virtually perfect, withe a1 and a2 so close to zero that they cannot be measured. Since QWPs are usually also made of calcite, this would give an all-calcite experimental setup.

2: the QWPs. These have one basic fault, which is that they only provide a perfect 1/4 wave delay at one exact wavelength, and at different wavelengths they will produce non-rotation-invariant results. The only real way around this is to use monochromatic light at the exact wavelength where the wave delay is 1/4 wavelength. You can get monochromatic light by using a laser, or by using white light and a diffraction grating. The laser will be a very pure monochromatic light, but the frequency is not adjustable. In that case, you may have to start with a QWP which is slightly too thick and hand polish it down to the right thickness so that the delay is exactly 1/4 wavelength. On the other hand, with a diffraction grating, you can use your original QWP without any polishing, but you must select the right frequency out of the diffracted spectrum so that the delay is 1/4 wave. This is much easier, but since you are only using a small fraction of the light, you must start with a quite bright source. That's not really a problem though.

3: the angles. If the angles are not precisely 45 degrees between the LP and the QWP axes, you will again get non-rotation-invariant results. The only way around this is to make the angle adjustable with some kind of very precise fine-tuning mechanism, and then hand adjust it so be precisely 45 degrees. This can best be done by adjusting them with the experiment running, until you can get absolutely no light through in the RCP followed by LCP case. There are 4 angles to adjust, so this will be a long process of twiddling to get it just right. There's really no other good way to make sure the angle is accurate enough.

Varying the experimental equipment is really the only way to separate equipment effects from the effect under study. I'm confident that if you try the experiment with different equipment, you will find that the outcome is much more nearly rotation invariant, and that by varying the equipment (fine tuning) you can show that all the rotation invariance is associated with equipment artefacts.

Does this mean that it is incorrect for authors of Quantum Mechanics text to suggest that photons can be polarized into one or the other Circular Polarized State and behave strangely in accordance with what QM has predicted?

I think that the textbooks are correct on this point. First, experiments are inconclusive until equipment effects can be sorted out from underlying physics. Second, the rotation invariance is predicted by classical physics too, so if this non-invariance is a real physical effect, it also contradicts many classical results, all of which have been carefully verified experimentally. Third, the structure of QM is mathematically very rigid in certain ways. Superposition is at the basis of the theory, and superposition predicts that ALL particle states can be considered as equally fundamental and can be used as the basis for expressing other states. This means that circular polarization MUST be just as fundamental as linear polarization, and individual photons must be able to be circularly polarized. If any of this is false, then the single most basic feature of QM (superposition, i.e. linearity) would be false. But as I mentioned in my last post, linearity has been tested very, very precisely and QM is exactly linear to as many decimal places as we can measure.

All of these points argue for perfect rotational invariance as the fundamental physical fact, PROVIDED that the filters are perfect (which of course they are not, since no equipment is ever perfect). Well, that's my position on the matter anyway. I'm still interested in discussing this further with you of course; you may change my mind after all, and then I will have learned something new.

--Stuart Anderson
hexa
Hi Mr Homm,

I am sorry to hear the passing of your cousin and that you are saddled with the unenviable task of helping to administer the estate.

Thanks for being so patient in providing the fine details to the questions that I have raised as well as in addressing the bigger picture pertaining to Quantum Mechanics.

While I agree with most of what you have stated, there is one aspect of Quantum Mechanics that continues to trouble me notwithstanding your explanation as well as those provided by other prominent physicists like Richard Feynman in his Lecture on Physics. This is the Superposition principle that you have just stated.

QUOTE

The reason that this works in QM is that one of the basic features of the theory is that each particle interferes ONLY WITH ITSELF, and not with other particles. This is exactly the opposite of the conclusion you might come to by thinking classically about interfering light waves, but is has to be this way. If each photon interferes only with itself, then the presence of other photons will not affect the outcome of the experiment for each individual photon, and so you can confidently use many photons at once without affecting the results.

Before I elaborate my objection, I would like to seek some clarification from you.

QUOTE (->
 QUOTE The reason that this works in QM is that one of the basic features of the theory is that each particle interferes ONLY WITH ITSELF, and not with other particles. This is exactly the opposite of the conclusion you might come to by thinking classically about interfering light waves, but is has to be this way. If each photon interferes only with itself, then the presence of other photons will not affect the outcome of the experiment for each individual photon, and so you can confidently use many photons at once without affecting the results.

Before I elaborate my objection, I would like to seek some clarification from you.

QM says yes it is. QM does apply to individual photons and does say that each one is in a distinct polarization state after exiting the filter.
...........................
...........................
For example, QM predicts that if you put a SINGLE photon through a vertical linear polarizer, it will sometimes emerge, sometimes not, depending on the unknown original state. However, if it DOES emerge, it will be in the state |V>. This state has the property that it has 100% probability of passing successfully through a second vertical linear polarizer, 0% for a horizontal one, and 50% for right or left circular polarizers. However, since you can only make ONE measurement on this photon, you can't test all these predictions, only one of them. QM makes similar predictions about single photons that pass through circular polarizers.

If what you said is true, can we then infer that a photon must have a certain physical axis before and after it has passed through a set of filters?

Let us first assume that each photon has a certain physical axis that we can describe within the physical 3D space. Next, let us further assume that if a photon were to translate along the z-axis, this physical axis would lie on the x-y plane.

Would it be reasonable to assume that each photon in a group of unpolarized photons has an axis pointed randomly at θ: where θ has an angle between 0 deg < θ <360 deg using the convention that we have established earlier.

This would imply that a photon in the lx> state will have angle θ between 0 deg < θ < 45 deg; 135 deg < θ < 225 deg; and 315 < θ < 360 deg.

In the case of a photon in the ly> state, its polarizing axis will have an angle θ in the following range: 45 deg < θ < 135 deg; 225 deg < θ < 315 deg.

Please confirm if such assumption is a reasonable representation of the physical state of any single photon found in either the lx> or ly> state.

Cheers
Confused2
Mr Homm, Hexa et al,
Could I add a rider to hexa's question about photons only interfering with themselves? Using Feynmans wavelength wheel we get peaks and troughs of probability .. for convenience confining the analysis to the most probable path we see a 'wave' with some apparent relationship to a classical EM wave. When looking at interference fringes there are often many of them .. clearly the (say) first 'wave' of one path is meeting not only the first 'wave' of the other path but also the second, third etc. Can the N1 peak of the one path interfere with the N2 peak of the other path (any N)? I have to admit my concept of the 'speed of light' is simply falling apart under the strain. Your assistance would be greatly appreciated.
-C2.
"THEY"
QUOTE (mr_homm+Oct 15 2006, 10:13 AM)
< a SINGLE photon >

I asked this question a long time ago on this forum (different thread) but didn't get a response, so I would like to ask again here if I may... (sorry if it has been addressed previously in this thread, I have had a hard time keeping up lately)

Can we truly measure one photon? If so, how do we know for sure?

Confused2
Hi THEY,

I appreciate you'd like a response from Mr Homm..

but meanwhile
http://www.optica.tn.tudelft.nl/education/photons.asp

And for good measure .. electrons!
http://physicsweb.org/articles/world/15/9/1

Best wishes,
C2.
"THEY"
Thanks C2! I have only read the electron article so far, but will read the optica article today or tonight. Will get back later if I still have questions.

Thanks again!
Confused2
Hi Hexa, Mr Homm, THEY (Maltida?)

Hexa, For what it's worth I think the full 'link' between QM and EM is here .. http://www.physics.ucsb.edu/~mark/MS-QFT-11Feb06.pdf CAUTION .. it's a whole book of 600 pages on Quantum Field Theory .. Maxwell's equations start on page 336 .. my maths doesn't even get me to page 1. Mr Homm is very kindly giving us page 336 without us going through the first 300 pages .. in fairness I think we might have to take Mr Homms's word as gospel .. OR .. do it the hard way. I think it would be possible (though not probable) that one or other of us could learn the maths to sufficient level to understand the logic (though perhaps not apply it). A challenge?

Best wishes,

C2.
hexa
Hi Confused2,

Thanks for providing the links which is absolutely essential for the discussion here.

I am not too sure whether Mr Homm wanted us to take what he said as Gospel Truth. Perhaps Mr Homm would like to clarify this perception.

While I may agree with much of what Mr Homm had shared with us, including his approach in defining what he called a TRUE Circular Polarizer, I continue to have my doubt as to whether a photon can be described as having a Distinct Circular Polarized State, since the photon has to pass through a series of filters.
Is it not a quantum rule that the interaction of a particle with the last filter decide the state vector of the photon emerging from the series of filters?
In the case of a photon passing through a SINGLE linear polarizer, the photon can be described as having an orientation (represented either by its electric axis or magnetic axis) that is aligned Vertically or Horizontally with the axis of the polarizer.

I have drawn the parallel between the polarized states (linear and circular) of a photon with Boltzmann Kinetic Theory of Gas. In the Kinetic Theory of Gas, the macro phenomena of Temperature and Pressure can be understood more fundamentally as the motion of the gas molecules at a given energy state within a confine space.

My question to Mr Homm is whether such similarity exist for the polarized state of photons. THis has led me to ask the question in my previous post ( http://forum.physorg.com/index.php?showtop...ndpost&p=134659 ):

QUOTE

QUOTE (->
 QUOTE Quote Mr Homm:QM says yes it is. QM does apply to individual photons and does say that each one is in a distinct polarization state after exiting the filter.......................................................For example, QM predicts that if you put a SINGLE photon through a vertical linear polarizer, it will sometimes emerge, sometimes not, depending on the unknown original state. However, if it DOES emerge, it will be in the state |V>. This state has the property that it has 100% probability of passing successfully through a second vertical linear polarizer, 0% for a horizontal one, and 50% for right or left circular polarizers. However, since you can only make ONE measurement on this photon, you can't test all these predictions, only one of them. QM makes similar predictions about single photons that pass through circular polarizers. If what you said is true, can we then infer that a photon must have a certain physical axis before and after it has passed through a set of filters? Let us first assume that each photon has a certain physical axis that we can describe within the physical 3D space. Next, let us further assume that if a photon were to translate along the z-axis, this physical axis would lie on the x-y plane. Would it be reasonable to assume that each photon in a group of unpolarized photons has an axis pointed randomly at θ: where θ has an angle between 0 deg < θ <360 deg using the convention that we have established earlier.This would imply that a photon in the lx> state will have angle θ between 0 deg < θ < 45 deg; 135 deg < θ < 225 deg; and 315 < θ < 360 deg.In the case of a photon in the ly> state, its polarizing axis will have an angle θ in the following range: 45 deg < θ < 135 deg; 225 deg < θ < 315 deg.Please confirm if such assumption is a reasonable representation of the physical state of any single photon found in either the lx> or ly> state.

Given his current circumstances, I hope it is not too imposing for Mr Homm to provide his answer to the question in my earlier post.

Cheers.
mr_homm
Taking several posts in order...

First, thanks for the condolences. This event has been very upsetting for us all in my family, and so my mind is not so much on QM right now. Nevertheless, I'll try to answer the queries that have come up so far. After this, I might have to post less often for a while, but I have NOT lost interest, and I will return, just not as regularly, until things straighten out here.

@hexa:

QUOTE
If what you said is true, can we then infer that a photon must have a certain physical axis before and after it has passed through a set of filters?

That depends on what you mean by a physical axis. It looks like you are assuming that the photon is in a linear polarization state. In that case, yes, each individual photon has a physical axis, which is its own private polarization direction.

However, if you assume at the outset that all photons are linearly polarized, you are assuming your conclusion that circular polarization is not a fundamental state. On that basis, the question becomes very difficult to investigate! If you start with the assumption that the individual photon MIGHT be in any of the states identified in classical electromagnetism (i.e. circular, elliptical, plane, etc.) then you can investigate whether that assumption is actually true by showing some kind of logical contradiction in the assumption that an individual photon is in a non-linear polarization state. I'll state up front that I don't think there is any such contradiction.

In this case, specifying an axis is not enough, because to completely describe the polarization, you must also give the degree of ellipticity of the polarization. Therefore, you could say that before passing through the filter, each photon has an axis and an ellipticity. Mathematically, this turns out to be equivalent to saying that each photon is in a state that is a COMPLEX linear combination of |H> and |V>. A REAL linear combination of these states would always generate a linear polarization, so the basic issue as I see it is whether individual photons can be in a state that is a complex, or merely a real, combination of |H> and |V>.

Remember of course, that just because something can be built out of other things , that does not make those things more fundamental. For example, if I choose an xy coordinate system, and also a rotated x'y' coordinate system, then I can build the unit vectors x' and y' out of x and y, but I can ALSO build the x and y unit vectors out of x' and y', so neither is mathematically more fundamental. Therefore, building the photon state out of |H> and |V> does not prove that these states are more fundamental; in fact any state can be built out of ANY two other states, so at least in a mathematical sense, all polarization states are equally fundamental. Therefore, the math doesn't give any reason to think that the linear states are more fundamental than the circular states, so there is no theoretical expectation that this would be so. If linear states really are more fundamental, some kind of physical experiment will be required to prove this, but first you need to define in exactly what way a "fundamental" state would be expected to behave differently from a "non-fundamental" state, so that you would know what your experiment is supposed to look for. I think this is where you are headed with your non-rotationally invariant observations.

Anyway, that's the long answer. The short answer is, yes, every photon has an axis before hitting the filter, but the angle of that axis is a complex number, not a real number.

QUOTE (->
 QUOTE If what you said is true, can we then infer that a photon must have a certain physical axis before and after it has passed through a set of filters?

That depends on what you mean by a physical axis. It looks like you are assuming that the photon is in a linear polarization state. In that case, yes, each individual photon has a physical axis, which is its own private polarization direction.

However, if you assume at the outset that all photons are linearly polarized, you are assuming your conclusion that circular polarization is not a fundamental state. On that basis, the question becomes very difficult to investigate! If you start with the assumption that the individual photon MIGHT be in any of the states identified in classical electromagnetism (i.e. circular, elliptical, plane, etc.) then you can investigate whether that assumption is actually true by showing some kind of logical contradiction in the assumption that an individual photon is in a non-linear polarization state. I'll state up front that I don't think there is any such contradiction.

In this case, specifying an axis is not enough, because to completely describe the polarization, you must also give the degree of ellipticity of the polarization. Therefore, you could say that before passing through the filter, each photon has an axis and an ellipticity. Mathematically, this turns out to be equivalent to saying that each photon is in a state that is a COMPLEX linear combination of |H> and |V>. A REAL linear combination of these states would always generate a linear polarization, so the basic issue as I see it is whether individual photons can be in a state that is a complex, or merely a real, combination of |H> and |V>.

Remember of course, that just because something can be built out of other things , that does not make those things more fundamental. For example, if I choose an xy coordinate system, and also a rotated x'y' coordinate system, then I can build the unit vectors x' and y' out of x and y, but I can ALSO build the x and y unit vectors out of x' and y', so neither is mathematically more fundamental. Therefore, building the photon state out of |H> and |V> does not prove that these states are more fundamental; in fact any state can be built out of ANY two other states, so at least in a mathematical sense, all polarization states are equally fundamental. Therefore, the math doesn't give any reason to think that the linear states are more fundamental than the circular states, so there is no theoretical expectation that this would be so. If linear states really are more fundamental, some kind of physical experiment will be required to prove this, but first you need to define in exactly what way a "fundamental" state would be expected to behave differently from a "non-fundamental" state, so that you would know what your experiment is supposed to look for. I think this is where you are headed with your non-rotationally invariant observations.

Anyway, that's the long answer. The short answer is, yes, every photon has an axis before hitting the filter, but the angle of that axis is a complex number, not a real number.

Let us first assume that each photon has a certain physical axis that we can describe within the physical 3D space. Next, let us further assume that if a photon were to translate along the z-axis, this physical axis would lie on the x-y plane.

OK, this makes perfect sense to me, with the caveat that it is the complex xy plane.

QUOTE
Would it be reasonable to assume that each photon in a group of unpolarized photons has an axis pointed randomly at θ: where θ has an angle between 0 deg < θ <360 deg using the convention that we have established earlier.

This would imply that a photon in the lx> state will have angle θ between 0 deg < θ < 45 deg; 135 deg < θ < 225 deg; and 315 < θ < 360 deg.

In the case of a photon in the ly> state, its polarizing axis will have an angle θ in the following range: 45 deg < θ < 135 deg; 225 deg < θ < 315 deg.

Yes, this is reasonable, but again, the axis alone is not enough information. If you give the degree of ellipticity as well, then this is fine; alternatively, you could use the complex angle. The trouble is that there simply isn't enough information in a single real number to do the job of describing polarization, because the state depends on TWO parameters, angle and ellipticity.

Also, a photon in the |X> state would have an angle of EXACTLY 0 or 180 deg, not just in the ranges you mentioned, and similarly the |Y> state has an angle of EXACTLY +/- 90 deg.

@Confused2
QUOTE (->
 QUOTE Would it be reasonable to assume that each photon in a group of unpolarized photons has an axis pointed randomly at θ: where θ has an angle between 0 deg < θ <360 deg using the convention that we have established earlier.This would imply that a photon in the lx> state will have angle θ between 0 deg < θ < 45 deg; 135 deg < θ < 225 deg; and 315 < θ < 360 deg.In the case of a photon in the ly> state, its polarizing axis will have an angle θ in the following range: 45 deg < θ < 135 deg; 225 deg < θ < 315 deg.

Yes, this is reasonable, but again, the axis alone is not enough information. If you give the degree of ellipticity as well, then this is fine; alternatively, you could use the complex angle. The trouble is that there simply isn't enough information in a single real number to do the job of describing polarization, because the state depends on TWO parameters, angle and ellipticity.

Also, a photon in the |X> state would have an angle of EXACTLY 0 or 180 deg, not just in the ranges you mentioned, and similarly the |Y> state has an angle of EXACTLY +/- 90 deg.

@Confused2
Could I add a rider to hexa's question about photons only interfering with themselves? Using Feynmans wavelength wheel we get peaks and troughs of probability .. for convenience confining the analysis to the most probable path we see a 'wave' with some apparent relationship to a classical EM wave. When looking at interference fringes there are often many of them .. clearly the (say) first 'wave' of one path is meeting not only the first 'wave' of the other path but also the second, third etc. Can the N1 peak of the one path interfere with the N2 peak of the other path (any N)? I have to admit my concept of the 'speed of light' is simply falling apart under the strain. Your assistance would be greatly appreciated.

Yes, these different peaks can all interfere with each other. However, there is no problem with the speed of light here. Consider the case where light originates from a source S, and the N1 peak interferes with the N2 peak at a point P. This means simply that the N1 and N2 peaks reach P at the same time, by different paths. The reason that these different peaks are interfering is that the alternate paths from S to P are different lengths. The light travels both paths at speed c, but the extra length causes a delay in arrival via one path, compared to the other, which causes peak N1 and N2 to arrive at the same time even though they left the source at different times. So it is a case of multiple paths, constant speed, not constant path, multiple speeds. The speed of light is still safe!

@THEY
QUOTE
Can we truly measure one photon? If so, how do we know for sure?

The link that Confused2 gave has a very good explanation of this. In fact there are several ways. First, a photomultiplier tube (rather old fashioned these days) can detect a single photon and amplify it to a visible flash. It does this by using the photon to knock loose an electron from a charged plate. There is a strong electric field between this and a second plate, which causes the electron to accelerate and hit the second plate with much more energy, knocking loose several electrons, which are accelerated toward a third plate, knocking loose still more, and so on. A photomultiplier often has 5 or 6 plates, and can produce a cascade of millions of electrons at the end from a single photon.

On the other hand, the retinal cells of your eye are sensitive enough to detect just 2 or 3 photons hitting them at once, so biology is ALMOST good enough to see individual photons in the visible spectrum. More sensitive than the retina is the CCD camera. This is the basic unit used in all digital cameras today, but the original device was designed for taking photographs through astronomical telescopes. Of course, in astronomy, capturing every single photon is important, because you want to see extremely dim, distant objects. Because the exposure times for some astronomical photographs are several DAYS, just to get enough photons for a picture, you can see that photons are coming in one or two at a time. Astronomical cameras can make pictures with light that has a photon flux of less than 1 photon per second, which I consider truly amazing. They can do this because a CCD is sensitive enough that each pixel can react to a single photon, changing the pixel from black to white. The CCD (charge-coupled device) uses a collection of suspended electric charges which discharge when triggered by a photon. It's like a shout causing an avalanche -- the effect is huge in magnitude compared to the cause.

So, yes, you can detect individual photons. In fact, in the link Confused2 provided, that is exactly what the student experimenters are doing.

I've got to stop now, as I am out of time. I will catch up with the rest of the discussion in my next post.

--Stuart Anderson
hexa
Hi Mr Homm,

QUOTE

That depends on what you mean by a physical axis. It looks like you are assuming that the photon is in a linear polarization state. In that case, yes, each individual photon has a physical axis, which is its own private polarization direction.

However, if you assume at the outset that all photons are linearly polarized, you are assuming your conclusion that circular polarization is not a fundamental state. On that basis, the question becomes very difficult to investigate! If you start with the assumption that the individual photon MIGHT be in any of the states identified in classical electromagnetism (i.e. circular, elliptical, plane, etc.) then you can investigate whether that assumption is actually true by showing some kind of logical contradiction in the assumption that an individual photon is in a non-linear polarization state. I'll state up front that I don't think there is any such contradiction.

The answer is No. The Linear polarized state of an array of photons is not the most fundamental state of a photon. What I am asserting is that every photon translating along the z-axis has a physical axis defined by the angle θ on the Real x-y Cartesian plane. A linear polarizer can be described by another physical axis defined by another angle σ.
If the linear polarizer is placed at an angle σ = 0 (or 180) degree, the photons passing through it will have an array of angles given by [ 0 deg < θ < 45 deg; 135 deg < θ < 225 deg; and 315 < θ < 360 deg.] The x-linearly polarized state, l x> IS NOT represented by photon with one unique angle as suggested by your statement:
QUOTE (->
 QUOTE That depends on what you mean by a physical axis. It looks like you are assuming that the photon is in a linear polarization state. In that case, yes, each individual photon has a physical axis, which is its own private polarization direction. However, if you assume at the outset that all photons are linearly polarized, you are assuming your conclusion that circular polarization is not a fundamental state. On that basis, the question becomes very difficult to investigate! If you start with the assumption that the individual photon MIGHT be in any of the states identified in classical electromagnetism (i.e. circular, elliptical, plane, etc.) then you can investigate whether that assumption is actually true by showing some kind of logical contradiction in the assumption that an individual photon is in a non-linear polarization state. I'll state up front that I don't think there is any such contradiction.

The answer is No. The Linear polarized state of an array of photons is not the most fundamental state of a photon. What I am asserting is that every photon translating along the z-axis has a physical axis defined by the angle θ on the Real x-y Cartesian plane. A linear polarizer can be described by another physical axis defined by another angle σ.
If the linear polarizer is placed at an angle σ = 0 (or 180) degree, the photons passing through it will have an array of angles given by [ 0 deg < θ < 45 deg; 135 deg < θ < 225 deg; and 315 < θ < 360 deg.] The x-linearly polarized state, l x> IS NOT represented by photon with one unique angle as suggested by your statement:

Also, a photon in the |X> state would have an angle of EXACTLY 0 or 180 deg, not just in the ranges you mentioned, and similarly the |Y> state has an angle of EXACTLY +/- 90 deg.

Hence, a photon with an angle θ=10 deg. may be found in the x-linear polarized state (defined by the angle σ = 0 deg.) as well as in another linear polarized state where σ = 20 deg. But that same photon will not be found in the y-linear polarized state where σ = 90 deg. or σ = 100 deg.

Next, I noticed that you have qualified your acceptance of my hypothesis with the caveat that it could only be used in the context of a complex angle (whatever it means).
QUOTE

Yes, this is reasonable, but again, the axis alone is not enough information. If you give the degree of ellipticity as well, then this is fine; alternatively, you could use the complex angle. The trouble is that there simply isn't enough information in a single real number to do the job of describing polarization, because the state depends on TWO parameters, angle and ellipticity.
…………………………………………………..
OK, this makes perfect sense to me, with the caveat that it is the complex xy plane.
……………………………………………………
Anyway, that's the long answer. The short answer is, yes, every photon has an axis before hitting the filter, but the angle of that axis is a complex number, not a real number.

You are correct to add the caveat before we can mathematically account for the probability intensity of light passing through two linear polarizers inclined at an angle δ to one another. This is the classical Experimental Malus Law based on the cosine square of the angle δ between the two linear polarizers.
Currently, there is no rational basis in physics to explain why the probability intensity obeys the cosine square and not any other trigonomical function.
In short, it remains incomprehensible as to why the Quantum Law of Physics cannot be expresses using some rational macro analogue or Real Numbers; and that it must be represented as an IMAGINERY COMPLEX Number within the mathematical framework of Quantum Mechanics.
The Superposition Principle of Quantum Mechanics (based on the Copenhagen Interpretation) has a more serious problem than just the use of complex numbers. It violates one of the Cardinal Principle of Science—DETERMINISM. This has led to the speculation that Causality or Locality may be violated in Nature.
This has two very serious implications. Either we are living in a very very strange physical world where our physical existence can just vanish suddenly into thin air without leaving any traces whatsoever; or that the fundamental postulates of Quantum Mechanics is Wrong.
I am more incline to believe that that the fundamental postulate of Quantum Mechanics is wrong, notwithstanding its success, since nothing in the Macroworld suggest that any of the Cardinal Principle can be violated.

Continuing with my hypothesis, please allow me to describe the molecular arrangement of a linear polarizer, a QWP and a Circular Polarizer.

Linear Polarizer:
A linear polarizer with its polarizing axis aligned along the x-axis (0 or 180 deg) will have the molecules principally aligned along this axis. However, the molecules continue to fluctuate about this principal axis. Similarly, a linear polarizer with its axis aligned along the y-axis (+90 or –90 deg) will have the molecules aligned primarily along the y-axis with fluctuation about this other principal axis.

Quarter Wave Plate:
In the case of a QWP (which can be made from a calcite crystal), the molecules are aligned along two principal axes (not necessarily orthogonal to one another). There are two types of QWP. The Right QWP will rotate the orientation of an incoming photons (described by its physical axis) by giving it a clockwise rotation. For example, an incoming photon may have an angle of 80 degree but it will leave the Right QWP with an angle of 70 degree or more.
The Left QWP will rotate the photon in the counter-clockwise direction. This would mean that if the incoming photon has an angle of 20 degree, it will leave the Left QWP with an angle of say 30 degree or more and not an angle that is less than 20 degree.
Notwithstanding the rotational effect of one set of molecules, we must not ignore the action of another set of molecules that makes up the QWP.
In essence, this can be used to explain the presence of the Ordinary and Extraordinary ray passing through a Calcite Crystal.

Circular Polarizer:
If a Circular Polarizer uses a Right QWP after a Linear polarizer, then the composite filters will behave as a Right Circular Polarizer. If we use a Left QWP, the Circular polarizer will behave as a Left Circular Polarizer.

Using the hypotheses above, let us attempt to analyse the behavior of A PHOTON passing through say a x-linear polarizer:
1) The incoming photon may have an orientation of say 20 deg.
On interaction with the x-linear polarizer, it may be transmitted with an angle of 10 deg or 30 deg or any angle θ between 0 deg < θ < 45 deg and perhaps 315 deg < θ < 360 deg;
2) The incoming photon may have an orientation of say 330 deg.
On interaction with the linear polarizer, it may be transmitted with an angle of 340 deg or 350 deg or any angle θ between 315 deg < θ < 360 deg and perhaps 0 deg < θ < 45 deg
3) However, a photon that has an orientation of say 50 deg. or 300 deg. will be prevented from transmitting through the x-linear polarizer.

In short, the photons with angle θ between 0 deg < θ < 45 deg; 135 deg < θ < 225 deg; and 315 < θ < 360 deg. will be manifested as photons in the x-linearly polarized state.
Whereas the photons with angle θ between 45 deg < θ < 135 deg and 225 deg < θ < 315 deg. will be manifested as photons in the y-linearly polarized state.

From this description, you can see that a photon found with a specific orientation or angle θ at one linear polarized state can also be the same photon found in another linear polarized state.

With this hypothesis, you can see that in so far as the photons falls within the permissible range of the linear polarizer, the photons will continue to be transmitted through any numbers of x-linear polarizers.

In conclusion, does this hypothesis not explain the QM predictions:

1) l <x l Mx l x>l^2 = 1
2) l <y l My l x>l^2 = 0

Please comment on this propositions before I proceed to discuss the Circular Polarized state of A SINGLE photon and whether such a state in fact exist.

Cheers.
hexa
Hi Mr Homm, Confused2, They, Maltida, Gtrax, Dr Brettmann, Schneibster, etc,

While we are waiting for Mr Homm to find time to share his view with us, I am curious to hear from all of you your opinion with regards to the prospect that the counterintuitive approach of Quantum Mechanics, couch in unimaginable complex mathematics, which Confused2 said that he had difficulty even to get past page 1 of this text ( http://www.physics.ucsb.edu/~mark/MS-QFT-11Feb06.pdf ) could now be understood more simply with the assumption that every photon is a Physical particle with Real Physical Axis passing through a linear polarizer that again can be described by another Real Physical Axis.

In the meantime, I find this post ( http://forum.physorg.com/index.php?showtop...ndpost&p=136909 ) by Gtrax quite amusing that perhaps sum up much of the problem with contemporary physics:
QUOTE

1/(1-v^/c^2)

We may have found mathematical models that have proved useful in calculating our way about all manner of useful stuff, but that does not mean it even begins to approach reality, and we should be extremely suspicious of stuff that requires the rulers to conveniently change size, time to change rate, and mass to increase in a mysterious way in exact accord to a Lorenz transformatiion.

There was a time before, when, not able to see the wood for the trees, we had Phlogiston, which possessed negative weight to explain the gain in mass of substances when heated. Tycho Brahe believed planets moved in epicycles to explain their retrograde motion, but he had excellent tables and could predict things, not knowing his epicycles were good approximations to relative views of the heavens moving in ellipses. He had a right to believe in epicycles - the evidence was there.

We keep doing it! We invent every kind of fictional abstraction, and it is useful stuff! "Displacement Current" that does not apparently involve any displacement of any electrons, Quarks that would do just nicely - until we need one "charmed" to make the equations come out right. We go the whole way when we get into String Theory. We demonstrate that we can make mathematical models that require mighty intellects to comprehend, yet could still be an effort hopelessly misdirected!

Jeez - ever since omega minus...why am i such a skeptic hardhead?

Cheers.
Montec
Hi Hexa
If I remember my collage laser course correctly:
Linear polarized light's axis of polarization remains the same as the polarized light travels through space.
Circular polarized light's axis of polarization rotates as the polarized light travels through space. The direction of rotation defines CCW or CW Circular/Elliptical polarization.

Confused2
Hi Hexa,

In response to your invitation to share opinions..

Of EM radiation .. it is either infinitely divisible or some sort of 'granule' will become apparent.. the 'granule' (photon) seems to be apparent whether we like it or not. We readily observe that one beam of light appears able to pass through another without modification and we are drawn to the conclusion that an individual photon can only interfere constructively or destructively with itself. It is in the nature of 'interference' that the path taken by the photon becomes hard to describe (and understand). I am under the impression that it is not easy to define the precise properties of a photon such that Maxwell's equations and QED can be seen to be manifestations of one and the same thing. I am content with the words "It can be shown..".

Of possible universes .. there may be ones where the speed of light is infinite .. we seem to be in one where the speed of light is finite .. hence Lorentz transforms .. 'relativity' takes takes this one stage further by removing any assumption about the existence of an 'Aether'.

-C2.
hexa
Hi Gtrax,

I don’t think you need to be apologetic about what you have said.
Dissatisfaction provides the impetus for progress.
Beside, you are not the only one disagreeing. Many prominent scientists Einstein, de Broglie, Schrodinger, Steven Weinberg, etc are also dissatisfied with the prevailing Quantum Theories.
Similarly, not everyone agrees with Einstein on his Theories of Relativity.
Another erudite member in this forum like the prolific Good Elf is also dissatisfied. However, I must qualify that I may not totally agree with his Model on what constitute the fundamentals of Nature. See this humorous posting from him ( http://forum.physorg.com/index.php?showtop...indpost&p=41468 ):
QUOTE

……..this post is aimed generally at the question of mass and is not a criticism of anyone in particular (living or dead). …….The Higgs is a bewildering concept to me as well as a "nonsense". I have seen all those really dumb ideas on the Higgs and how to explain it to Politicians... etc. Very unimpressive. It shows me that some Physicists haven't got a clue how to explain anything. Even CERN has dealt with "the unwashed masses" (no pun intended) as if they are total idiots...
Higgs at CERN
Here are "all" the dumb explanations for the Higgs that are in common circulation...
The Waldegrave Higgs Challenge
Have a read and this would all be very funny except it is supposed to be science. The scientist won a "frigg'in" prize for that! ….And all you guys and gals are the dumb local yokels showing off your prize pigs and turnips. Now that I have shown less than reverence for these ideas we can begin to ask serious questions instead of bowing in admiration at the Emperor's New Clothes.

Science would not have come this far had we blindly accepted Democritus proposition that everything is made of atom but probe no further; or that light is as what Maxwell had described. We would have continued to believe in the fallacy of the aether had it not been the effort of two scientists (Michelson & Morley) who firmly believe in its existence and ironically stood by it until his (Morley) death.

Hi Montec,

QUOTE (->
 QUOTE ……..this post is aimed generally at the question of mass and is not a criticism of anyone in particular (living or dead). …….The Higgs is a bewildering concept to me as well as a "nonsense". I have seen all those really dumb ideas on the Higgs and how to explain it to Politicians... etc. Very unimpressive. It shows me that some Physicists haven't got a clue how to explain anything. Even CERN has dealt with "the unwashed masses" (no pun intended) as if they are total idiots...Higgs at CERNHere are "all" the dumb explanations for the Higgs that are in common circulation...The Waldegrave Higgs ChallengeHave a read and this would all be very funny except it is supposed to be science. The scientist won a "frigg'in" prize for that! ….And all you guys and gals are the dumb local yokels showing off your prize pigs and turnips. Now that I have shown less than reverence for these ideas we can begin to ask serious questions instead of bowing in admiration at the Emperor's New Clothes.

Science would not have come this far had we blindly accepted Democritus proposition that everything is made of atom but probe no further; or that light is as what Maxwell had described. We would have continued to believe in the fallacy of the aether had it not been the effort of two scientists (Michelson & Morley) who firmly believe in its existence and ironically stood by it until his (Morley) death.

Hi Montec,

If I remember my collage laser course correctly:
Linear polarized light's axis of polarization remains the same as the polarized light travels through space.
Circular polarized light's axis of polarization rotates as the polarized light travels through space. The direction of rotation defines CCW or CW Circular/Elliptical polarization.

You have quoted correctly from the standard physics text.
However, have you consider the physical reality that every molecule, whether in the solid or liquid state, will wiggle and jiggle about in 3D space. This fact is clearly demonstrated by our observation of the Brownian Motion. If so, is it reasonable for us to assume a static condition where we make no provision with regards to how these photons from the laser would be transmitted after interacting with the molecules forming the linear polariser?
On your question pertaining to the circular polarized state, I beg you to defer the discussion until after we hear from our Mr Homm.

Hi Confused2,

It seems you are quite undecided on how light ought to be perceived.
You are right. Let us wait to hear the response from our Mr Homm.

Cheers.
hexa
Hi Everybody,

Some clarification on the Michelson & Morley Experiment.
We all know that the Michelson & Morley Experiment prove beyond reasonable doubt that aether does not exist. Ironically, the experiment was conducted by two protagonists that believe in the existence of aether.
Notwithstanding that both Michelson and Morley are awarded the Nobel prize for proving the non existence of the aether, Morley continues to believe in the existence of aether until his death.

I hope Mr Homm could comment on the posting ( http://forum.physorg.com/index.php?showtop...ndpost&p=136946 )
QUOTE

Continuing with my hypothesis, please allow me to describe the molecular arrangement of a linear polarizer, a QWP and a Circular Polarizer.

Linear Polarizer:
A linear polarizer with its polarizing axis aligned along the x-axis (0 or 180 deg) will have the molecules principally aligned along this axis. However, the molecules continue to fluctuate about this principal axis. Similarly, a linear polarizer with its axis aligned along the y-axis (+90 or –90 deg) will have the molecules aligned primarily along the y-axis with fluctuation about this other principal axis.

Quarter Wave Plate:
In the case of a QWP (which can be made from a calcite crystal), the molecules are aligned along two principal axes (not necessarily orthogonal to one another). There are two types of QWP. The Right QWP will rotate the orientation of an incoming photons (described by its physical axis) by giving it a clockwise rotation. For example, an incoming photon may have an angle of 80 degree but it will leave the Right QWP with an angle of 70 degree or more.
The Left QWP will rotate the photon in the counter-clockwise direction. This would mean that if the incoming photon has an angle of 20 degree, it will leave the Left QWP with an angle of say 30 degree or more and not an angle that is less than 20 degree.
Notwithstanding the rotational effect of one set of molecules, we must not ignore the action of another set of molecules that makes up the QWP.
In essence, this can be used to explain the presence of the Ordinary and Extraordinary ray passing through a Calcite Crystal.

Circular Polarizer:
If a Circular Polarizer uses a Right QWP after a Linear polarizer, then the composite filters will behave as a Right Circular Polarizer. If we use a Left QWP, the Circular polarizer will behave as a Left Circular Polarizer.

Using the hypotheses above, let us attempt to analyse the behavior of A PHOTON passing through say a x-linear polarizer:
1) The incoming photon may have an orientation of say 20 deg.
On interaction with the x-linear polarizer, it may be transmitted with an angle of 10 deg or 30 deg or any angle θ between 0 deg < θ < 45 deg and perhaps 315 deg < θ < 360 deg;
2) The incoming photon may have an orientation of say 330 deg.
On interaction with the linear polarizer, it may be transmitted with an angle of 340 deg or 350 deg or any angle θ between 315 deg < θ < 360 deg and perhaps 0 deg < θ < 45 deg
3) However, a photon that has an orientation of say 50 deg. or 300 deg. will be prevented from transmitting through the x-linear polarizer.

In short, the photons with angle θ between 0 deg < θ < 45 deg; 135 deg < θ < 225 deg; and 315 < θ < 360 deg. will be manifested as photons in the x-linearly polarized state.
Whereas the photons with angle θ between 45 deg < θ < 135 deg and 225 deg < θ < 315 deg. will be manifested as photons in the y-linearly polarized state.

From this description, you can see that a photon found with a specific orientation or angle θ at one linear polarized state can also be the same photon found in another linear polarized state.

With this hypothesis, you can see that in so far as the photons falls within the permissible range of the linear polarizer, the photons will continue to be transmitted through any numbers of x-linear polarizers.

In conclusion, does this hypothesis not explain the QM predictions:

1) l <x l Mx l x>l^2 = 1
2) l <y l My l x>l^2 = 0

Please comment on this propositions before I proceed to discuss the Circular Polarized state of A SINGLE photon and whether such a state in fact exist.

Cheers.
MrMysteryScience
I would like to offer a small sidetrack to this discussion. I admit as many must that I can not freely talk on everything that is now under consideration, but wish very simply to add a different dimension to the discussion, which can be casually considered and perhaps remembered at another time when this may be better understood.There has been discussion of classical and quantum renditions of photon behaviors. A spin one way, by way of definition "seems" to not allow a definition of another spin at the same "instant".(Quantum) Math does not perhaps equate, or at least seems that way as it relates to the observer. Imagine rather then a dimension where you can observe from beyond this and note with absolute knowledge that these spins must equate, and therefore are real ! Yes more than 1 axis, indeed defines the particle and it's "frequency" even in decay.Let that float.
Back a few years ago there were some somewhat "early" studies in the Optical Magnus Effect. Observations of photon behaviors in optical fiber, um, paraphrased definitions, simple and slightly more so it was as;"A rotation of the modal noise pattern generated in an optical fiber when the illuminating light polarization is switched from right-handed circular to left-handed circular. It demonstrates the spin-orbit interaction of a photon."Here is a second definition which is slightly more
advanced ; "It is predicted theoretically and registered experimentally that the speckle pattern of a laser beam transmitted through a multimode fiber undergoes an angular shift from the switching of the chirality of the polarization. The effect may be considered as the result of the spin-orbit interaction for the photon in the inhomogeneous medium." Here is a link related to these and a tribute therefore as a research paper; O.M.E.
I am not even suggesting that this is exactly right, that's part of the problem, there is nothing quite complete to point at, but it would perhaps be wise to open up to more potentials than are described by current interpretations of symbols and correct math that can be defined sometimes so many ways. But the spins are real ! Look at it as a given, and then begin experimental equations from there. Enough, I have not intended to muddle your direction, rather open you to fuller potentials. I wish you the best, good fortune.
hexa
Hi MrMysteryScience,

QUOTE

A spin one way, by way of definition "seems" to not allow a definition of another spin at the same "instant".(Quantum) Math does not perhaps equate, or at least seems that way as it relates to the observer. Imagine rather then a dimension where you can observe from beyond this and note with absolute knowledge that these spins must equate, and therefore are real ! Yes more than 1 axis, indeed defines the particle and it's "frequency" even in decay.

Your interjection is crucial and timely to our discussion.
I agree with your suggestion that spin is integral to the discussion of the polarized state of light. I must also thank you for introducing this interesting paper by K.Yu. Bliokh and Yu. P. Bliokh. Entitled “ Topological spin transport of photons: The Optical Magnus Effect and Berry Phase”.
I hesitated to bring spin into the discussion with Mr Homm until I am sure that there is a PHYSICAL axis (and not just a mathematical construct defined in Quantum Mechanics) that we can use to describe the physical state of a SINGLE PHOTON.

The question that I am raising is whether A PHOTON in one polarized state is distinguishable from another photon in another polarized state. If they are, then how do we distinguish them?

We know that an electron essentially has two and only two spin states. Spin up or spin down that can be demonstrated experimentally on a Stern Gerlach Apparatus by splitting one electron beam into two electron beams by a magnetic field. I suppose we could further assume (although not entirely correct) that the spin up has a physical reality represented by an electron physically spinning in the clockwise direction and the spin down state by the electron spinning in the counter-clockwise direction (like our earth rotating on its axis). I must qualify here that this perception of the spin state of an electron is rejected in Quantum Theory for the primary reason that it violates the speed of light, c dictated by the Theories of Relativity. The axes of these spins can then be used as the PHYSICAL axis in our 3D-world. Notwithstanding what is generally accepted, would it be more reasonable to assume that the Physical Axis of Each electron in the unpolarized state has a distribution that can be described by an angle in the plane orthogonal to the direction of translation? That any electron that is spin up may have the PHYSICAL axis pointed say at an angle θ, where θ is an angle between 0 deg <θ<180 deg; and that the spin down state will have their Physical Axis pointed at any angle 180 deg <θ<360 deg?

Can we then describe the spin state of A PHOTON by a similar description? If so, how do we reconcile this with the four polarized states (2 linear and 2 circular polarized states) with the spin mechanism described here?

You have mentioned:
QUOTE (->
 QUOTE A spin one way, by way of definition "seems" to not allow a definition of another spin at the same "instant".(Quantum) Math does not perhaps equate, or at least seems that way as it relates to the observer. Imagine rather then a dimension where you can observe from beyond this and note with absolute knowledge that these spins must equate, and therefore are real ! Yes more than 1 axis, indeed defines the particle and it's "frequency" even in decay.

Your interjection is crucial and timely to our discussion.
I agree with your suggestion that spin is integral to the discussion of the polarized state of light. I must also thank you for introducing this interesting paper by K.Yu. Bliokh and Yu. P. Bliokh. Entitled “ Topological spin transport of photons: The Optical Magnus Effect and Berry Phase”.
I hesitated to bring spin into the discussion with Mr Homm until I am sure that there is a PHYSICAL axis (and not just a mathematical construct defined in Quantum Mechanics) that we can use to describe the physical state of a SINGLE PHOTON.

The question that I am raising is whether A PHOTON in one polarized state is distinguishable from another photon in another polarized state. If they are, then how do we distinguish them?

We know that an electron essentially has two and only two spin states. Spin up or spin down that can be demonstrated experimentally on a Stern Gerlach Apparatus by splitting one electron beam into two electron beams by a magnetic field. I suppose we could further assume (although not entirely correct) that the spin up has a physical reality represented by an electron physically spinning in the clockwise direction and the spin down state by the electron spinning in the counter-clockwise direction (like our earth rotating on its axis). I must qualify here that this perception of the spin state of an electron is rejected in Quantum Theory for the primary reason that it violates the speed of light, c dictated by the Theories of Relativity. The axes of these spins can then be used as the PHYSICAL axis in our 3D-world. Notwithstanding what is generally accepted, would it be more reasonable to assume that the Physical Axis of Each electron in the unpolarized state has a distribution that can be described by an angle in the plane orthogonal to the direction of translation? That any electron that is spin up may have the PHYSICAL axis pointed say at an angle θ, where θ is an angle between 0 deg <θ<180 deg; and that the spin down state will have their Physical Axis pointed at any angle 180 deg <θ<360 deg?

Can we then describe the spin state of A PHOTON by a similar description? If so, how do we reconcile this with the four polarized states (2 linear and 2 circular polarized states) with the spin mechanism described here?

You have mentioned:

Back a few years ago there were some somewhat "early" studies in the Optical Magnus Effect. Observations of photon behaviors in optical fiber, um, paraphrased definitions, simple and slightly more so it was as; "A rotation of the modal noise pattern generated in an optical fiber when the illuminating light polarization is switched from right-handed circular to left-handed circular. It demonstrates the spin-orbit interaction of a photon."

and also:
QUOTE

"It is predicted theoretically and registered experimentally that the speckle pattern of a laser beam transmitted through a multimode fiber undergoes an angular shift from the switching of the chirality of the polarization. The effect may be considered as the result of the spin-orbit interaction for the photon in the inhomogeneous medium."

Finally, you have concluded:
QUOTE (->
 QUOTE "It is predicted theoretically and registered experimentally that the speckle pattern of a laser beam transmitted through a multimode fiber undergoes an angular shift from the switching of the chirality of the polarization. The effect may be considered as the result of the spin-orbit interaction for the photon in the inhomogeneous medium."

Finally, you have concluded:

I am not even suggesting that this is exactly right, that's part of the problem, there is nothing quite complete to point at, but it would perhaps be wise to open up to more potentials than are described by current interpretations of symbols and correct math that can be defined sometimes so many ways. But the spins are real !

I hope you could expand a little more on each of the points that you have stated as well as comment on the hypothesis that I am proposing to help resolve the anomaly that exist between the prediction by QM (Rotation Invariance of Circular Polarizer) and observation based on experiment.

Meanwhile, I hope Mr. Holmm could comment on this as it is important to the analysis of the circular polarized state based on his proposed construction of the True Right or Left Circular Polarizer.

Cheers.
hexa
Hi Mr Homm, MrMysteryScience, Confused2, Montec, They, Gtrax, Maltida, Dr Brettmann, Schneibster, etc,

It does not appear that Mr Homm or Mr MysteryScience has anything to add at the moment.

Continuing with my hypothesis and hopefully with the concurrence that we can use angle θ to describe the physical state of A PHOTON, I will next discuss the effect of photons passing through a QWP.

2.0 )The effect of passing a stream of unpolarized photons through a QWP:
2.1) The unpolarized photons source will have a mixture of photons with the angle θ of each photon spread in all directions—0 deg. < θ < 360 deg.
2.2) The function of the QWP is to reorganize the arrays of photons into two linearly polarized states: the x and the y linear polarized states with no loss to its original intensity (if we assume ideal conditions).
2.3) Under ideal conditions, a Right QWP is no different from a Left QWP. Since we continue to find photons with all angles from 0 to 360 deg.
2.4) If the polarizing axes of the QWP is not exactly orthogonal, then this would give rise to an uneven distribution of photons at the various orientations. In this case, there will be one stream of x-linear polarized state and another of y’-linear polarized state and not the y-linear polarized state that is orthogonal to the x-linear polarized state.
This would then imply that the photons passing through a Right QWP is not exactly the same as a Left QWP. One would have the extraordinary ray rotated to the right of the ordinary ray, while the other will be to the left.
2.5) The smaller the difference in angle, σ between the two polarizing axes that make up the QWP, the greater will be the ellipticity of the photons passing through the QWP.

From the hypothesis that I have just stated, you can see that it is not possible to distinctly distinguish ONE PHOTON after passing through a Right QWP from another photon through a Left QWP.

I know this is diagonally opposed to the proposition of QM and it appears to be a lot of “hand waving” on my part. As such, I will pause to hear your views before I proceed to describe the Circularly polarized state based on the construction of a TRUE Right and a TRUE Left circular polarizer proposed by Mr. Homm that enable us to make progress on our investigation of the question that I have raised in this thread.

Cheers.
Confused2
Hi hexa,

2.2) The function of the QWP is to reorganize the arrrays of photons into two linearly polarized states: the x and the y linear polarized states with no loss to its original intensity (if we assume ideal conditions).

Doesn't a QWP just do a (lossless) linear operation on θ ? With random in don't you just get (different) random out?

2.3) .. contradicts 2.2 and looks good to me.

2.4) goes back to the assumption of 2.2) which I wasn't sure about. Could it be that a non-orthogonal QWP can be resolved into an orthogonal non-QWP ( a bit less or a bit more than 1/4 wave action on incoming photons) .. so the operation would still be linear and random input would produce random output.

I don't know if this has any bearing on your conclusion.

Best wishes,

-C2.
hexa
Hi Confused2,

QUOTE

Doesn't a QWP just do a (lossless) linear operation on θ ? With random in don't you just get (different) random out?

Prima facie it appears that way. But No.
A QWP do have a distinct molecular arrangement that distinguish it from another material that do not have such regimental arrangement.
However, you are correct to state that A PHOTON with one Random angle will be dispersed to another random angle through a QWP or a linear polarizer. But in the Linear polarizer or a QWP, the final state of A PHOTON (the permissible range of angles θ) is governed by the molecular axes that make up these filters.

You have asked a very important question.
By 2.2, I am stating that the molecules making up the QWP has two distinct physical alignments: at 0 (and 180) deg. and the other at 90 (and 270) deg. This is unlike a linear polarizer where there is only one alignment.

If a x-linear polarizer would allow the passage of those photons falling in the range 0 deg. < θ < 45 deg, 135 deg. < θ < 225 deg and 315 deg. < θ < 360 deg; while a y-linear polarizer for those photons 45 deg. < θ < 135 deg and 225 deg. < θ < 315 deg, then the QWP would allow photons of all angles to pass through it and distribute them among all the angles, but characterised by the two principal axes. The reason I said that they are identical is because the y(Right) axis and the y(Left) axis will coincide with one another if the two molecular axes are orthogonal (based on the assumption that we fix the x-axis as common to both the QWP).

To reiterate, if the two molecular axes making up the QWP are truly orthogonal, it does not matter if the photons have been rotated clockwise or anticlockwise in the process of passing through the QWP. All the photons will be distributed principally along the two molecular axes.

However, if the two molecular axes of the QWP are not orthogonal, then the photons rotated to the right and the photons rotated to the left will be different. In both cases, all the photons that fall on the QWP will pass through it with no loss in intensity (again assuming ideal condition). But the distribution of photons in the random state passing through a Left QWP is different from one that is passing through a Right QWP.

Let me illustrate this by an example. If one of the molecular axis of a QWP is at 0 deg. a Right QWP will have the other molecular axis pointing at 80 deg or less. In the case of a Left QWP, the other molecular axis may be pointing at 100 deg. or more. The net effect is that the photons (in the random state) passing through a Right QWP will be quite different from that passing through a Left QWP.

With the above explanation, I hope you can see how this hypothesis will help us to explain the ellipticity of eccentric Circular polarizers (which I will discuss in greater details a little while later)?

I hope with the above explanation, you can see the subtle difference that I was trying to highlight with regards to the properties of a QWP. This may have led you to think that there is a discrepancy between 2.2 and 2.3.
QUOTE (->
 QUOTE Doesn't a QWP just do a (lossless) linear operation on θ ? With random in don't you just get (different) random out?

Prima facie it appears that way. But No.
A QWP do have a distinct molecular arrangement that distinguish it from another material that do not have such regimental arrangement.
However, you are correct to state that A PHOTON with one Random angle will be dispersed to another random angle through a QWP or a linear polarizer. But in the Linear polarizer or a QWP, the final state of A PHOTON (the permissible range of angles θ) is governed by the molecular axes that make up these filters.

You have asked a very important question.
By 2.2, I am stating that the molecules making up the QWP has two distinct physical alignments: at 0 (and 180) deg. and the other at 90 (and 270) deg. This is unlike a linear polarizer where there is only one alignment.

If a x-linear polarizer would allow the passage of those photons falling in the range 0 deg. < θ < 45 deg, 135 deg. < θ < 225 deg and 315 deg. < θ < 360 deg; while a y-linear polarizer for those photons 45 deg. < θ < 135 deg and 225 deg. < θ < 315 deg, then the QWP would allow photons of all angles to pass through it and distribute them among all the angles, but characterised by the two principal axes. The reason I said that they are identical is because the y(Right) axis and the y(Left) axis will coincide with one another if the two molecular axes are orthogonal (based on the assumption that we fix the x-axis as common to both the QWP).

To reiterate, if the two molecular axes making up the QWP are truly orthogonal, it does not matter if the photons have been rotated clockwise or anticlockwise in the process of passing through the QWP. All the photons will be distributed principally along the two molecular axes.

However, if the two molecular axes of the QWP are not orthogonal, then the photons rotated to the right and the photons rotated to the left will be different. In both cases, all the photons that fall on the QWP will pass through it with no loss in intensity (again assuming ideal condition). But the distribution of photons in the random state passing through a Left QWP is different from one that is passing through a Right QWP.

Let me illustrate this by an example. If one of the molecular axis of a QWP is at 0 deg. a Right QWP will have the other molecular axis pointing at 80 deg or less. In the case of a Left QWP, the other molecular axis may be pointing at 100 deg. or more. The net effect is that the photons (in the random state) passing through a Right QWP will be quite different from that passing through a Left QWP.

With the above explanation, I hope you can see how this hypothesis will help us to explain the ellipticity of eccentric Circular polarizers (which I will discuss in greater details a little while later)?

I hope with the above explanation, you can see the subtle difference that I was trying to highlight with regards to the properties of a QWP. This may have led you to think that there is a discrepancy between 2.2 and 2.3.

2.3) .. contradicts 2.2 and looks good to me.

I hope I have also addressed your queries pertaining to my statement on 2.4.
QUOTE

2.4) goes back to the assumption of 2.2) which I wasn't sure about. Could it be that a non-orthogonal QWP can be resolved into an orthogonal non-QWP ( a bit less or a bit more than 1/4 wave action on incoming photons) .. so the operation would still be linear and random input would produce random output.

Cheers.
Confused2
Hi hexa, Mr Homm et al,
hexa .. thanks for the clarification. All, thanks for following up this topic.
Best wishes, C2
hexa
Hi Confused2,

Since, Mr Homm may be too busy with his personal engagement while MrMysteryScience does not appears to have anything further to add at the moment, I will proceed to address the question on circular polarization that Montec had raised earlier.

Before we can understand Circular Polarization, we need to be familiar with this other property about the QWP. While a QWP can split a beam of light into two beams (Ordinary and extraordinary rays) it can also be used to recombine the two rays back into a single beam. This can be demonstrated by placing one calcite crystal sequentially to the first calcite crystal. Do it to see if what I say is true. A word of caution is that the geometry of the calcite crystals must be exactly right to yield this observation.

The standard construction (described in most books) of a Circular polarizer essentially comprise of a Linear Polarizer followed by a QWP. Since there are two types of QWP (Left and Right based on the description of my previous post), it is then possible for a beam of Linearly Polarized Photons to be split into two beams (Ordinary and Extraordinary) by the QWP with a Left or a Right Rotation. In other words, the photons after passing through the Linear Polarizer (and become , say, the X-Linear Polarized state) will be split into two beams (comprising the x-linear polarized state and the y’(Left) or the y’(Right) polarized state).

It is this process that enable us to obtain half the intensity of the photons if we should place another Linear Polarizer after the Circular Polarizer. Similarly, if we place another Circular Polarizer ( that has only One Linear Polarizer followed by a QWP), the intensity of Light that we are going to get from passing through two Circular Polarizers is ¼ and not ½ or 0 the intensity of the original source which QM predicts. This is because the passage of light through the first Circular Polarizer will half the intensity; and the passage through the second Circular polarizer will further reduce it by half. It is not possible to obtain the result predicted by QM based on this Simplified Definition of a Circular Polarizer. Do the experiment yourself to verify if what I say is correct.

The proposal by Mr Homm in describing what constitute a TRUE Right or a TRUE Left Circular Polarizer is indeed very innovative and interesting. His suggestion does solve the dispute I had with Schneibster with regards to how a Circular Polarizer ought to be constructed before it will yield SOME of the predictions in QM.
In most literature, the illustration of how light can be cut off by the passage of light through a Right followed by a Left Circular Polarizer is illustrated by reflecting the Right Circular Polarized Light with a mirror back into the Right Circular Polarizer in the opposite direction, that is, QWP then the Linear Polarizer.
This had led me to think that the Construction of a Left Circular Polarizer differs from a Right Circular Polarizer by simply reversing the position of the Linear Polarizer with the QWP. This perception was corrected by Mr Homm.

By this reverse translation, we can see that a substantial portion of the original beam (before passing through the Circular Polarizer) will be filtered off by the composite filter with the help of a mirror.

Let us try to analyse this experiment based on the hypothesis that I have proposed.
3.1 Passage of a beam of Light Through a Right Circular Polarizer followed by reflection of the Circularly Polarized Light through the same Circular Polarizer in the reverse direction.
3.1.1. The unpolarized light on passing through the Linear Polarizer will be polarized into photons in the say X-linearly polarized state:
l ψ > -----> [Mx] ----->l X >
3.1.2 The X-linearly polarized beam is then split into two beams by the Right QWP comprising:
l X > -----> [QWP(Right)] -----> l x1 (0 deg) > + l y2 (90 deg.)>
3.1.3 The reflection of the two beams by the mirror essentially changes nothing.
3.14 However with respect to the Right Circular Polarizer, the frame of reference is rotated by 180 deg.
3.1.5 The photons as described in 3.1.2 is now subject to a correction, similar to what I have describe on the recombination of the two beams back into a single beam by the QWP.
3.1.6 The molecules or the QWP essentially rotate the photons in the l x1 (0 deg) > state to the l y1 (90 deg) > state and then combine with the l y2(90 deg) > state to form one beam of l Y > state.
3.1.7 The Mx-Linear polarizer is now confronted with a l Y > state photons for photons traveling in the opposite direction. The net result is that the l Y > state photons are prevented from passing through the Mx-Linear Polarizer that constitute the Circular Polarizer.

This I believe is what took place to yield the Quantum Mechanical Prediction of :
a] l ψ > -----> [MR] -----> l R >
b] l <R lMR l R > l ^ 2 = 1
b] l <L lML l R > l ^ 2 = 0

I will pause again to hear from all of you as to whether it is reasonable and useful to engage in this hand waving exercise so as to find out if there is a simpler truth behind QM that we have overlooked in our contemporary physics?
While QM may have been used successfully in many areas, could QM be wrong to predict the Circular Polarized State of Light the way it does that has found its way into many physics text including the Lectures on Physics by Richard Feynman???

I hope the erudite participants following this thread could voice their opinion before I tackle the QM assertion that Circularly Polarized Light is Rotation Invariant based on the True Right and True Left Circular Polarizer proposd by Mr Homm.

Cheers.
Confused2
Hi hexa,

I must admit that my last post should have include the fact that I had my fingers crossed .. hoping Mr Homm would make a contribution.

I am well beyond my conmfort zone here .. but..

If we accept that a QWP is lossless then I suspect there are restrictions on what it can do. I suspect one restriction is that it can neither increase nor decrease the amount of order (entropy) of the beam of light.. I can't apply this beyond hand-waving .. it just seems to me that it cannot order the beam as you suggest.

I think the point can be partiallly resolved by rotating a QWP between two vertical polarizers .. I would predict a no loss point at 45 degrees to the axes of the crystal (four per full rotation) where the QWP is doing nothing rather than forcing the light into the axes of the crystal. Would you be kind enough to try it and report the result?

Best wishes,

-C2.
mr_homm
Hi everyone,

Once again, I am trying to catch up with a lot of posts in a row. I just don't seem to have enough time lately!

@Confused_2, Oct.19:
QUOTE
Hexa, For what it's worth I think the full 'link' between QM and EM is here .. http://www.physics.ucsb.edu/~mark/MS-QFT-11Feb06.pdf CAUTION .. it's a whole book of 600 pages on Quantum Field Theory .. Maxwell's equations start on page 336 .. my maths doesn't even get me to page 1. Mr Homm is very kindly giving us page 336 without us going through the first 300 pages .. in fairness I think we might have to take Mr Homms's word as gospel .. OR .. do it the hard way. I think it would be possible (though not probable) that one or other of us could learn the maths to sufficient level to understand the logic (though perhaps not apply it). A challenge?

You give me far too much credit! QFT is far beyond the level of discussion needed to analyze circular polarization. The point of QFT is to explain how particles can be created and destroyed by showing that they are really just epiphenomena (gotta love that word!) of a deeper underlying field. We don't need to go there for this discussion. My own knowledge of QFT is very shallow as I will be the first to admit.

However, I will say that upon looking at the text, it seems to be a pretty good one. Perhaps I'll read it in my spare time (joke -- like saying I'll read it when pigs fly, which is about as likely as my having spare time). Anyway, the math isn't a problem from my point of view, so that's not a hurdle for me, but I really don't know all that much about QFT.

By the way, those links you provided are great. Thanks a lot!

@hexa, Oct. 20
QUOTE (->
 QUOTE Hexa, For what it's worth I think the full 'link' between QM and EM is here .. http://www.physics.ucsb.edu/~mark/MS-QFT-11Feb06.pdf CAUTION .. it's a whole book of 600 pages on Quantum Field Theory .. Maxwell's equations start on page 336 .. my maths doesn't even get me to page 1. Mr Homm is very kindly giving us page 336 without us going through the first 300 pages .. in fairness I think we might have to take Mr Homms's word as gospel .. OR .. do it the hard way. I think it would be possible (though not probable) that one or other of us could learn the maths to sufficient level to understand the logic (though perhaps not apply it). A challenge?

You give me far too much credit! QFT is far beyond the level of discussion needed to analyze circular polarization. The point of QFT is to explain how particles can be created and destroyed by showing that they are really just epiphenomena (gotta love that word!) of a deeper underlying field. We don't need to go there for this discussion. My own knowledge of QFT is very shallow as I will be the first to admit.

However, I will say that upon looking at the text, it seems to be a pretty good one. Perhaps I'll read it in my spare time (joke -- like saying I'll read it when pigs fly, which is about as likely as my having spare time). Anyway, the math isn't a problem from my point of view, so that's not a hurdle for me, but I really don't know all that much about QFT.

By the way, those links you provided are great. Thanks a lot!

@hexa, Oct. 20
I am not too sure whether Mr Homm wanted us to take what he said as Gospel Truth. Perhaps Mr Homm would like to clarify this perception.

As to taking my word as gospel -- well, yes and no. I am trying to give a clear account of what standard QM says about circular polarization, and it would please me if you thought my reporting was trustworthy. I really am accurately reporting what the theory says, so in that sense, yes, it would be gratifying if everyone took my word for it. On the other hand, I'm just reporting what the standard theory SAYS, not what REALITY IS. These may be two different things, after all, since no theory is utterly immune to possible falsification by new data.

It is my OPINION that current QM gives a pretty good account of circular polarization, which agrees with experimental data. It is important to note also that part of what I find convincing about QM is its ability to use the same few concepts to explain and mathematically predict a wide variety of phenomena. To me, this is the hallmark of a good theory. There is a nice minimalism about QM, a good Occam's Razor quality of getting much explanation with few assumptions. I will agree that those few assumptions are pretty weird.

As always, I will try to clearly separate my own opinions from the tenets of standard QM.

QUOTE
While I may agree with much of what Mr Homm had shared with us, including his approach in defining what he called a TRUE Circular Polarizer, I continue to have my doubt as to whether a photon can be described as having a Distinct Circular Polarized State, since the photon has to pass through a series of filters.
Is it not a quantum rule that the interaction of a particle with the last filter decide the state vector of the photon emerging from the series of filters?
In the case of a photon passing through a SINGLE linear polarizer, the photon can be described as having an orientation (represented either by its electric axis or magnetic axis) that is aligned Vertically or Horizontally with the axis of the polarizer.

Here is a central point that we must clarify. QM states that a filter performs a measurement, which technically means just that it treats photons in different states differently, absorbing some states but not others. Linear polarizing filters absorb different orientations of linear photon states differently, so they preform a measurement; hence they are filters by the technical definition. On the other hand, a QWP delays the phase of one state relative to another state, but does not absorb either state. Every photon that goes into a QWP comes out the other side (except for a small amount of absorption because the crystal is not absolutely transparent -- but it absorbs all polarization states equally, so it still doesn't distinguish between them); therefore the QWP is NOT a filter by the technical definition.

This means that the RCP is not actually a series of filters. There is only one filter in the series, and the other two layers (the QWPs) alter the state without filtering it. One way to see that this is true is to ask what would happen if you omitted the LP layer and kept just the two QWPs. They are turned 90 degrees to each other, so one will delay the |H> state and the other will delay the |V> state. Since these states form a basis for all photon states, and since they are both delayed equally, the net result is that the photon state as a whole is delayed, but neither component is delayed relative to the other. This is exactly what you would expect from plain old glass, since its refractive index slows, and hence slightly delays, photons. In other words, if you omit the LP layer, the combination of the two QWPs does EXACTLY NOTHING to the light. Light would be delayed simply by traveling through space anyway, to the two QWPs are equivalent to simply letting the light travel a tiny extra distance forward. This obviously does not affect the state of the light in any way.

So you see that the only filtering action is provided by the LP layer. The two QWPs process the incoming state (WITHOUT measuring it, so no uncertainty relations are involved) so that light that was initially circularly polarized becomes linear, so that the LP can act on it, and then processes the resulting light back into its original circular state (because, as I said in the above paragraph, the effect of the two QWPs cancels out i.e. one is the inverse of the other). The action of this filter is mathematically identical to a single layer of circularly polarizing material. Now we don't happen to have single layer circularly polarizing materials to use in the experiment, but this is a technical limitation only, not part of the basic physics. It should be possible to create a circularly polarizing material, but the fact is that no one is likely to bother, since the QWP LP QWP sandwich already works well.

QUOTE (->
 QUOTE While I may agree with much of what Mr Homm had shared with us, including his approach in defining what he called a TRUE Circular Polarizer, I continue to have my doubt as to whether a photon can be described as having a Distinct Circular Polarized State, since the photon has to pass through a series of filters.Is it not a quantum rule that the interaction of a particle with the last filter decide the state vector of the photon emerging from the series of filters?In the case of a photon passing through a SINGLE linear polarizer, the photon can be described as having an orientation (represented either by its electric axis or magnetic axis) that is aligned Vertically or Horizontally with the axis of the polarizer.

Here is a central point that we must clarify. QM states that a filter performs a measurement, which technically means just that it treats photons in different states differently, absorbing some states but not others. Linear polarizing filters absorb different orientations of linear photon states differently, so they preform a measurement; hence they are filters by the technical definition. On the other hand, a QWP delays the phase of one state relative to another state, but does not absorb either state. Every photon that goes into a QWP comes out the other side (except for a small amount of absorption because the crystal is not absolutely transparent -- but it absorbs all polarization states equally, so it still doesn't distinguish between them); therefore the QWP is NOT a filter by the technical definition.

This means that the RCP is not actually a series of filters. There is only one filter in the series, and the other two layers (the QWPs) alter the state without filtering it. One way to see that this is true is to ask what would happen if you omitted the LP layer and kept just the two QWPs. They are turned 90 degrees to each other, so one will delay the |H> state and the other will delay the |V> state. Since these states form a basis for all photon states, and since they are both delayed equally, the net result is that the photon state as a whole is delayed, but neither component is delayed relative to the other. This is exactly what you would expect from plain old glass, since its refractive index slows, and hence slightly delays, photons. In other words, if you omit the LP layer, the combination of the two QWPs does EXACTLY NOTHING to the light. Light would be delayed simply by traveling through space anyway, to the two QWPs are equivalent to simply letting the light travel a tiny extra distance forward. This obviously does not affect the state of the light in any way.

So you see that the only filtering action is provided by the LP layer. The two QWPs process the incoming state (WITHOUT measuring it, so no uncertainty relations are involved) so that light that was initially circularly polarized becomes linear, so that the LP can act on it, and then processes the resulting light back into its original circular state (because, as I said in the above paragraph, the effect of the two QWPs cancels out i.e. one is the inverse of the other). The action of this filter is mathematically identical to a single layer of circularly polarizing material. Now we don't happen to have single layer circularly polarizing materials to use in the experiment, but this is a technical limitation only, not part of the basic physics. It should be possible to create a circularly polarizing material, but the fact is that no one is likely to bother, since the QWP LP QWP sandwich already works well.

I have drawn the parallel between the polarized states (linear and circular) of a photon with Boltzmann Kinetic Theory of Gas. In the Kinetic Theory of Gas, the macro phenomena of Temperature and Pressure can be understood more fundamentally as the motion of the gas molecules at a given energy state within a confine space.

I think we talked about this before in this thread, but I would like to add that although your idea is attractive, the behavior of photons doesn't seem to me to make it very workable. In the case of gases, the macro parameters such as P and T are the result of the motion of very many particles, but the laws the particles obey seem to be simpler or more fundamental than the laws gases obey; therefore, it is useful to try to reduce gas behavior to the study of particle behavior.

On the other hand, in the case of light, the behavior of individual photons does not seem to be simpler than that of strong light beams. In fact, the mathematics of the description of individual photon states in QM is pretty much the same as the mathematics of the description of polarization states for strong light beams. The only difference is that for the individual photons, the interpretation of the math is as a probability, while for the strong light beam, the interpretation is as a change of intensity. This means that light beams do not have any "emergent" properties that are not directly apparent in the individual photons. This is unlike the case of gases and particles.

@hexa, Oct. 24:

QUOTE
The answer is No. The Linear polarized state of an array of photons is not the most fundamental state of a photon. What I am asserting is that every photon translating along the z-axis has a physical axis defined by the angle θ on the Real x-y Cartesian plane. A linear polarizer can be described by another physical axis defined by another angle σ.
If the linear polarizer is placed at an angle σ = 0 (or 180) degree, the photons passing through it will have an array of angles given by [ 0 deg < θ < 45 deg; 135 deg < θ < 225 deg; and 315 < θ < 360 deg.]

I fully agree with the first paragraph here, but I also fully DISagree with the second paragraph. Let's start with your statement that every photon has a definite physical axis with a definite angle. OK, no problem with that. Now, how do you know what that angle is, i.e. how do you measure it? I don't see any way to do this except to put it through a polarizing filter. If it gets through the filter, then when it emerges its angle is the same as the filter's angle, correct? Let me know if you disagree with this, because it's a crucial point, and affects the reasoning from here on. Also, on that topic, if you do disagree with this, we need to define an alternative experimental technique for measuring the exact axis angle of a photon; without such a defined procedure there is a danger of losing contact with the physical world and producing a theory that has mathematical consistency and elegance but is not physically meaningful.

Now according to what you have said, a photon will get through a LP filter if the line of its axis is within +/-45 degrees of the line of the filter's axis. This gives the correct statistics for an unpolarized beam passing through a LP, because half the intensity will get through regardless of the angle of the filter axis. However, when you consider the light that emerges from one LP and then strikes a second LP, you get strange results from your rule. If the angle of the first filter is 0 degrees, then photons passing through it come out with an axis angle of 0 degrees also. Now suppose the second filter is at an angle 30 degrees. Then every photon that strikes the second filter has an axis angle of 0, which is less than 45 degrees from the axis of the second LP. Therefore, every photon will get through. As you rotate the second filter so that the angle becomes more than 45 degrees, now suddenly NO photons have an axis angle within 45 degrees of the second filter axis, so NO light gets through. This means that you get full intensity if the two filter axes are within 45 degrees of each other and zero intensity if they are more than 45 degrees apart. This clearly contradicts Malus's law, which is experimentally known to be true.

There is no way around this with your definition, unless you deny that each photon emerging from an LP has the same axis as the LP. However, that opens up the question 2 paragraphs above about how to define the axis angle experimentally.
QUOTE (->
 QUOTE The answer is No. The Linear polarized state of an array of photons is not the most fundamental state of a photon. What I am asserting is that every photon translating along the z-axis has a physical axis defined by the angle θ on the Real x-y Cartesian plane. A linear polarizer can be described by another physical axis defined by another angle σ.If the linear polarizer is placed at an angle σ = 0 (or 180) degree, the photons passing through it will have an array of angles given by [ 0 deg < θ < 45 deg; 135 deg < θ < 225 deg; and 315 < θ < 360 deg.]

I fully agree with the first paragraph here, but I also fully DISagree with the second paragraph. Let's start with your statement that every photon has a definite physical axis with a definite angle. OK, no problem with that. Now, how do you know what that angle is, i.e. how do you measure it? I don't see any way to do this except to put it through a polarizing filter. If it gets through the filter, then when it emerges its angle is the same as the filter's angle, correct? Let me know if you disagree with this, because it's a crucial point, and affects the reasoning from here on. Also, on that topic, if you do disagree with this, we need to define an alternative experimental technique for measuring the exact axis angle of a photon; without such a defined procedure there is a danger of losing contact with the physical world and producing a theory that has mathematical consistency and elegance but is not physically meaningful.

Now according to what you have said, a photon will get through a LP filter if the line of its axis is within +/-45 degrees of the line of the filter's axis. This gives the correct statistics for an unpolarized beam passing through a LP, because half the intensity will get through regardless of the angle of the filter axis. However, when you consider the light that emerges from one LP and then strikes a second LP, you get strange results from your rule. If the angle of the first filter is 0 degrees, then photons passing through it come out with an axis angle of 0 degrees also. Now suppose the second filter is at an angle 30 degrees. Then every photon that strikes the second filter has an axis angle of 0, which is less than 45 degrees from the axis of the second LP. Therefore, every photon will get through. As you rotate the second filter so that the angle becomes more than 45 degrees, now suddenly NO photons have an axis angle within 45 degrees of the second filter axis, so NO light gets through. This means that you get full intensity if the two filter axes are within 45 degrees of each other and zero intensity if they are more than 45 degrees apart. This clearly contradicts Malus's law, which is experimentally known to be true.

There is no way around this with your definition, unless you deny that each photon emerging from an LP has the same axis as the LP. However, that opens up the question 2 paragraphs above about how to define the axis angle experimentally.
The x-linearly polarized state, l x> IS NOT represented by photon with one unique angle as suggested by your statement:

That is how it is defined in QM, that's all I'm saying. Your definition is different, but (see above) I don't see how it can agree with experiment.
QUOTE
Hence, a photon with an angle θ=10 deg. may be found in the x-linear polarized state (defined by the angle σ = 0 deg.) as well as in another linear polarized state where σ = 20 deg. But that same photon will not be found in the y-linear polarized state where σ = 90 deg. or σ = 100 deg.

Here again, this is in direct contradiction to experiment, unless your definition of photon axis is different from what I am understanding. I think this is an important point that we need to clarify.
QUOTE (->
 QUOTE Hence, a photon with an angle θ=10 deg. may be found in the x-linear polarized state (defined by the angle σ = 0 deg.) as well as in another linear polarized state where σ = 20 deg. But that same photon will not be found in the y-linear polarized state where σ = 90 deg. or σ = 100 deg.

Here again, this is in direct contradiction to experiment, unless your definition of photon axis is different from what I am understanding. I think this is an important point that we need to clarify.
You are correct to add the caveat before we can mathematically account for the probability intensity of light passing through two linear polarizers inclined at an angle δ to one another. This is the classical Experimental Malus Law based on the cosine square of the angle δ between the two linear polarizers.
Currently, there is no rational basis in physics to explain why the probability intensity obeys the cosine square and not any other trigonomical function.

Yes there is! Probability cannot exceed 1.0, therefore the trigonometric function cannot be sec, csc, tan, or cot, only sin or cos. That is a mathematical reason, but there is also a physical one: if the function exceeds 1.0 then the energy coming out of the filter is more than what came in, so conservation of energy eliminates sec, tan, csc, and cot. Now consider two LP filters with their axes aligned. Since filters act by absorption, and the first LP filter has already absorbed all of the light component perpendicular to its axis, there is nothing for the second LP filter to absorb. Hence it must pass 100% of the light through. This means that the trig function must have a value of 1.0 when the angle is zero. Hence the only possibility is cosine. The reasons leading to this conclusion are all physical.
QUOTE
In short, it remains incomprehensible as to why the Quantum Law of physics cannot be expressed using some rational macro analogue or Real Numbers; and that it must be represented as an IMAGINARY COMPLEX Number within the mathematical framework of Quantum Mechanics.

Well, to describe the polarization of a beam of light, you need to give its axis and degree of polarization. These are two real numbers, but when you examine the way that light behaves experimentally, you find that these real numbers are not entirely independent, but work together. Something is tying them together, and an examination of their mathematical relationships shows that they behave exactly like the magnitude and phase of a complex number. In other words, if you choose not to use complex numbers, that's fine, but the two real numbers will ACT like they are part of a complex number whether you wish to write them that way or not. It seems to me that since the simplest mathematical model of the experimentally observed behavior uses complex numbers, and the complex behavior is THERE in the experimental data, to avoid complex numbers is simply artificial.

By the way, speaking as a mathematician now, complex numbers are no more or less real than real numbers. Both are artificial constructions based on systems of axioms. Both may or may not be useful in physical theory. One system is newer than the other, and is taught later in school, and has the unfortunate name "imaginary" attached to it, that's all. I see no reason to prefer the real numbers. Why stop there and not use newer structures if they are available and can simplify calculations? Or why not go the other direction and decline to use real numbers and insist that physics be formulated using only rational numbers, or even integers. That could be done, you know, if you wanted to. Complex numbers can be expressed as 2X2 matrices of real numbers, which can be expressed as limits of sequences of rationals, which can be expressed as pairs of integers. What level of mathematical "dressing up" the theory gets is just a matter of taste; the only thing that matters is the predictions of the theory. I see no reason not to use more modern number systems, since they can simplify calculations and make the theory easier to use, since I know that they can ALWAYS be reduced to expressions based on earlier number systems.
QUOTE (->
 QUOTE In short, it remains incomprehensible as to why the Quantum Law of physics cannot be expressed using some rational macro analogue or Real Numbers; and that it must be represented as an IMAGINARY COMPLEX Number within the mathematical framework of Quantum Mechanics.

Well, to describe the polarization of a beam of light, you need to give its axis and degree of polarization. These are two real numbers, but when you examine the way that light behaves experimentally, you find that these real numbers are not entirely independent, but work together. Something is tying them together, and an examination of their mathematical relationships shows that they behave exactly like the magnitude and phase of a complex number. In other words, if you choose not to use complex numbers, that's fine, but the two real numbers will ACT like they are part of a complex number whether you wish to write them that way or not. It seems to me that since the simplest mathematical model of the experimentally observed behavior uses complex numbers, and the complex behavior is THERE in the experimental data, to avoid complex numbers is simply artificial.

By the way, speaking as a mathematician now, complex numbers are no more or less real than real numbers. Both are artificial constructions based on systems of axioms. Both may or may not be useful in physical theory. One system is newer than the other, and is taught later in school, and has the unfortunate name "imaginary" attached to it, that's all. I see no reason to prefer the real numbers. Why stop there and not use newer structures if they are available and can simplify calculations? Or why not go the other direction and decline to use real numbers and insist that physics be formulated using only rational numbers, or even integers. That could be done, you know, if you wanted to. Complex numbers can be expressed as 2X2 matrices of real numbers, which can be expressed as limits of sequences of rationals, which can be expressed as pairs of integers. What level of mathematical "dressing up" the theory gets is just a matter of taste; the only thing that matters is the predictions of the theory. I see no reason not to use more modern number systems, since they can simplify calculations and make the theory easier to use, since I know that they can ALWAYS be reduced to expressions based on earlier number systems.
The Superposition Principle of Quantum Mechanics (based on the Copenhagen Interpretation) has a more serious problem than just the use of complex numbers. It violates one of the Cardinal Principle of Science—DETERMINISM. This has led to the speculation that Causality or Locality may be violated in Nature.
This has two very serious implications. Either we are living in a very very strange physical world where our physical existence can just vanish suddenly into thin air without leaving any traces whatsoever; or that the fundamental postulates of Quantum Mechanics is Wrong.
I am more incline to believe that that the fundamental postulate of Quantum Mechanics is wrong, notwithstanding its success, since nothing in the Macroworld suggest that any of the Cardinal Principle can be violated.

I'll agree that the Copenhagen interpretation is not satisfactory. However, that is just an interpretation of the theory, not the theory itself, which is merely the mathematical structure and its predictions. Of course the predictions are very successful as you note, and also of course that doesn't prove that the theory is TRUE. I believe you cited earlier the example of Ptolemaic astronomy as a theory that got the right answers but is manifestly absurd to modern people. I agree with this criticism you have made.

On the other hand, I personally don't thing that QM violates determinism. I think that that's just a misinterpretation of the theory. I do not hold with the probabilistic formulation, nor the uncertainty principle, as I think that really understanding the state vector as the fundamental reality makes all these troubles simply go away. By the way, the "collapse of the wave function" is designed to PRESERVE determinism, not to destroy it. It is based on the idea that if you measure a particle and find it in a particular state, then measure it again immediately, you must find it in the same state. This is basically saying that if no outside cause has time to affect the particle, it can not spontaneously change its state, which is EXACTLY the principle of determinism.

I've got lots more to say on these topics, and I still have several posts to catch up on, but I must stop here to go to work. This weekend, the University is flying me to Wisconsin to attend a training session for teachers who prepare students to take the Graduate Record Exam, and i won't be back until Monday night, so it may be several days before I can pick up the discussion again.

More later...

--Stuart Anderson
hexa
Hi Confused2,

Looks like both our prayer has been answered.
Thanks to Mr. Homm for setting aside some time from his busy schedule to share his opinion with us.

The reason I resort to alternative explanation is because, unlike Linear Polarization, QM does not appear to provide the correct prediction for Circular Polarization. Initially, even the most simple experiment on Circular Polarization fails to yield any result predicted by QM. Fortunately, Mr Homm proposal on the construction of a True Right or a True Left Circular Polarizer with the introduction of another QWP before the Linear Polarizer of the second Circular polarizer appears to have alleviated some of the problem that I faced earlier.
The discrepancy with regards to Rotation invariance between observation and prediction by QM, remains.

Hence, I must apologise if I have brought distress to you based on the proposition that I have made here.
QUOTE
Quote Confused2:
I am well beyond my comfort zone here .. but..

I believe you and perhaps the other members following our discussion are enlighten enough to see the possibility that some parts of Quantum Mechanics may be incorrect in spite of its astounding success in providing elegant answer (according to Mr. Homm) to account for many phenomena in Nature. He also cited Occam’s Razor.
Similarly, Newtonian Physics also stood for 300 years until the beginning of the 20th century.
Indeed, Ptolemy Law of the cosmos stood much longer even though it was totally wrong based on careful measurement of the motion of the planets by Kepler..
Please pardon me if I were to use this analogy to describe QM. It appears that we are using the shadow of an object to describe the object itself. In the process, we sometime may miss the important details that are needed to fully describe the object. If one may recall, it is none other than the allegory of the Plato’s Cave.

But before we accept QM whole heartedly based on the Copenhagen Interpretation, perhaps it is better for us to refer to what Richard Feynman had said when he lamented in his Lecture on physics as he described the Double slits Experiment:
QUOTE (->
 QUOTE Quote Confused2:I am well beyond my comfort zone here .. but..

I believe you and perhaps the other members following our discussion are enlighten enough to see the possibility that some parts of Quantum Mechanics may be incorrect in spite of its astounding success in providing elegant answer (according to Mr. Homm) to account for many phenomena in Nature. He also cited Occam’s Razor.
Similarly, Newtonian Physics also stood for 300 years until the beginning of the 20th century.
Indeed, Ptolemy Law of the cosmos stood much longer even though it was totally wrong based on careful measurement of the motion of the planets by Kepler..
Please pardon me if I were to use this analogy to describe QM. It appears that we are using the shadow of an object to describe the object itself. In the process, we sometime may miss the important details that are needed to fully describe the object. If one may recall, it is none other than the allegory of the Plato’s Cave.

But before we accept QM whole heartedly based on the Copenhagen Interpretation, perhaps it is better for us to refer to what Richard Feynman had said when he lamented in his Lecture on physics as he described the Double slits Experiment:

We have implied that in our experimental arrangement (or even in the best possible one) it would be impossible to predict exactly what would happen. We can only predict the odds!  This would mean, if it were true,  that physics has given up on the problem of trying to predict exactly what will happen in a definite circumstance. Yes! Physics has given up. We do not know how to predict what would happen in a given circumstance, and we believe now that it is impossible---that the only thing that can be predicted is the probability of different events. It must be recognized that this is a retrenchment in our earlier ideal of understanding nature. It may be a backward step, but no one has seen a way to avoid it.

Generally, I do not disagree that there will be uncertainty if we attempt to measure both position and momentum (or time and energy) simultaneously, as elicited by the Uncertainty Principle. What I find unacceptable, according to the Copenhagen Interpretation, is that we cannot even talk about it prior to making an observation. A particle has no physical reality until it is observed. According to the Superposition principle, a particle (an electron or any other elementary particle) passing through one of the Double Slits has no physical presence anywhere prior to making an observation. In fact some even make this ludicrous proposition that the particle could be EVERYWHERE prior to making an observation. That is to say that we cannot attached a cartesian coordinate in the Euclidean space to describe the position of the particle before observation. For those familiar wth relativity, there is no space-time coordinate where we can attach to the particle prior to observation. Hence, it is not possible to describe the electron as having a physical state until it interacts with the apparatus to provide an observation.
Personally, I abhor such a postulate and would prefer to use classical statistics to interpret the behavior of particles including that of the photons. This would allow us to describe every single particle (photons included) as having a Real Physical State that will enable us to predict how it would interact with the apparatus, at least, statistically. I have shown that this approach seem to give us the correct prediction where QM fails.

Sorry for the digression.

QUOTE

If we accept that a QWP is lossless then I suspect there are restrictions on what it can do. I suspect one restriction is that it can neither increase nor decrease the amount of order (entropy) of the beam of light. I can't apply this beyond hand-waving .. it just seems to me that it cannot order the beam as you suggest.

I don’t think entropy is violated. The photons continue to be deflected through the molecules making the polarizer randomly, except, that a linear polarizer has one molecular alignment while a QWP has two. In other materials such as ordinary glass, there is no specific molecular alignment that will restrict the photons deflecting through them.

QUOTE (->
 QUOTE If we accept that a QWP is lossless then I suspect there are restrictions on what it can do. I suspect one restriction is that it can neither increase nor decrease the amount of order (entropy) of the beam of light. I can't apply this beyond hand-waving .. it just seems to me that it cannot order the beam as you suggest.

I don’t think entropy is violated. The photons continue to be deflected through the molecules making the polarizer randomly, except, that a linear polarizer has one molecular alignment while a QWP has two. In other materials such as ordinary glass, there is no specific molecular alignment that will restrict the photons deflecting through them.

I think the point can be partiallly resolved by rotating a QWP between two vertical polarizers .. I would predict a no loss point at 45 degrees to the axes of the crystal (four per full rotation) where the QWP is doing nothing rather than forcing the light into the axes of the crystal. Would you be kind enough to try it and report the result?

Before I attempt to provide you the result, let me clarify your proposition to ensure that I do not misinterpret your request.

Are you saying that we pass MONOCHROMATIC or WHITE light through the following set of filters in this sequence and then give a full rotation to QWP(2):
Experiment (1)
l ψ> -----> My(1) -----> QWP(2) ------> My(3).

Where l ψ> is the unpolarized state of photons (Monochromatic or White Light)
My = Linear polarizer
QWP= Quarter wave plate

1.1 Using Monochromatic Light
You would have ¼ the original intensity of l ψ>.
The rotation of the QWP(2) has minimal effect (not perceptible to the naked eyes) on the intensity of light passing the three filters.

1.2 Using White Light
No perceptible variation in the color of the light passing through the composite filters as we rotate the QWP(2).

[Note: For want of a better name, I will continue to refer QWP as a filter in spite of Mr. Homm objection]

If you conduct this other experiments:
Experiment (2)
l ψ> -----> My(1) -----> QWP(R2) ------> QWP(R3)(inverted 180 deg.)------> My(4).

2.1 Using Monochromatic Light
You should obtain the same result as the experiment --had you used a mirror. The only difference, is that you may get a higher intensity passing through this set of filters compared with when you uses the mirror. It is not quite as dark compared to the experiment using the mirror.
The rotation of QWP(2) relative to QWP(3) causes a variation in the intensity of light passing through the filters that is perceptible to the naked eyes.

2.2 Using White Light
The chromaticity of the white light passing through the set of filters vary as we rotate one QWR(R3) relative to QWP(R2) as well as when we rotate both QWP relative to both the Linear Polarizer.

Finally, if we were to conduct this last experiment:
Experiment (3)
l ψ> -----> My(1) -----> QWP(R2) ------> QWP(L3)------> My(4).

3.1 Using Monochromatic Light
We will see that there will be a greater intensity of photons passing through all the filters than in the case for Experiment (2).
The rotation of QWP(L3) relative to QWP(R2) causes some perceptible changes to the intensity of the monochromatic light passing through it. Similar changes is also recorded as we rotate both the QWP relative to the Linear Polarizers (where we fix it).

3.2 Using White Light
The chromaticity of the white light passing through the set of filters vary as we rotate one QWP(L3) relative to the other QWP(R2) as well as when we rotate both QWP relative to both the Linear Polarizer (where they are fixed).

I hope you, Mr Homm or some other members who happen to have these apparatus could also independently verify the observation that I have described above.

I will address Mr Homm remarks in my next post.

Cheers.
Confused2
Hi hexa, Mr Homm et al,

Hexa, many thanks for trying out my suggestion. My lack of comfort is due to the fact that even I have no faith in my understanding of what is going on .

The result .. no change as the QWP is rotated between two vertical filters. Could this be that the QWP has only changed the z angle of the spin vector .. to which neither the filters nor the human eye are sensitive. A more sensitive test would be to start with the filters at right angles.

Best wishes,

-C2.
hexa
Hi Mr Homm,

Please do not mistake my replies to Confused2 as saying that you have been less than accurate in stating Quantum Theory. On the contrary, your command of Quantum Theory has been impeccable. You were able to distinguish the different shades of grey. This can only be the hallmark of a true master who knows Quantum Theory inside out.
But that does not mean that Quantum Theory represents the Gospel Truth of Nature. As what Richard Feynman had said, Quantum Theory is build on---to paraphrase him--- the ruins of Logic and Common sense. In the absence of Determinism (which you disputed my assertion), and an over reliance on mathemathics (Quantum Mechanics), do you see the danger that in the absence of a Logical Phenomenological account of Nature, we run the risk of predicting an outcome that may be contrary to experiment that is far remote from Reality? Can we learn anything from the allegory of Plato’s Cave?

I think you are mistaken, when you said:
QUOTE

It is my OPINION that current QM gives a pretty good account of circular polarization, which agrees with experimental data.

Prior to hearing your suggestion on what constitute a TRUE Right and a TRUE Left Circular Polarizer, all the experiments that I have conducted with Circular Polarizers does not agree with what was predicted by QM as stated in the Physics textbook. Even with the introduction of another QWP before the Circular Polarizer, ROTATION INVARIANCE continues to evade from my experimental observation. The other observation involves a heavy dose of discount before we can begin to infer the prediction made in QM with regards to Circular Polarization.

I sincerely hope you will be able to conduct the same experiments on Circular Polarization to satisfy yourself with regard to whether they are mere artefact or that there is something fundamentally wrong with the QM prediction.

To state that QM may be wrong on Circular Polarization, does not automatically make my proposition to use CLASSICAL STATISTICAL Method as correct.
One of the cardinal tests for this alternative approach is that it must be able to account LOGICALLY MALUS Experimental Law for the passage of light through two linear polarizers inclined at an angle δ. I will do this in my next post to show that Malus Law is only an approximation to what we will observe experimentally. There is a more fundamental Reality.

In this posting, I will only address your remarks that you request further clarification.

QUOTE (->
 QUOTE It is my OPINION that current QM gives a pretty good account of circular polarization, which agrees with experimental data.

Prior to hearing your suggestion on what constitute a TRUE Right and a TRUE Left Circular Polarizer, all the experiments that I have conducted with Circular Polarizers does not agree with what was predicted by QM as stated in the Physics textbook. Even with the introduction of another QWP before the Circular Polarizer, ROTATION INVARIANCE continues to evade from my experimental observation. The other observation involves a heavy dose of discount before we can begin to infer the prediction made in QM with regards to Circular Polarization.

I sincerely hope you will be able to conduct the same experiments on Circular Polarization to satisfy yourself with regard to whether they are mere artefact or that there is something fundamentally wrong with the QM prediction.

To state that QM may be wrong on Circular Polarization, does not automatically make my proposition to use CLASSICAL STATISTICAL Method as correct.
One of the cardinal tests for this alternative approach is that it must be able to account LOGICALLY MALUS Experimental Law for the passage of light through two linear polarizers inclined at an angle δ. I will do this in my next post to show that Malus Law is only an approximation to what we will observe experimentally. There is a more fundamental Reality.

In this posting, I will only address your remarks that you request further clarification.

Paragraph 1:
Here is a central point that we must clarify. [1.1]QM states that a filter performs a measurement, which technically means just that it treats photons in different states differently, absorbing some states but not others. [1.2]Linear polarizing filters absorb different orientations of linear photon states differently, so they perform a measurement; hence they are filters by the technical definition.[1.3] On the other hand, a QWP delays the phase of one state relative to another state, [1.4]but does not absorb either state. [1.5]Every photon that goes into a QWP comes out the other side (except for a small amount of absorption because the crystal is not absolutely transparent -- but it absorbs all polarization states equally, [1.6]so it still doesn't distinguish between them); therefore the QWP is NOT a filter by the technical definition.

[1.1] is accepted with qualification in [1.2].
[1.2] may not be technically correct. The molecules making up the polarizer does not significantly ABSORB the photons. Most of these photons that does not pass through a Linear Polarizer is reflected away from it. You can verify this assertion using a laser beam.
[1.3] can be accepted since the extraordinary ray takes a longer path. However there is nothing in the molecules of the QWP to suggest that the “PHASES” can be precisely control to depart from one another by exactly 90 deg. It is just not reasonable to make this assumption, with the knowledge that the molecules making up the QWP is constantly vibrating and oscillating.
[1.4] and [1.5] may be accepted.
[1.6] How do you account for the fact that a calcite crystal (which can be used as a QWP), split ONE Beam of photons into two DISTINCT beams (Ordinary and Extraordinary Beams) if it is unable to distinguish one photon from another?

QUOTE

Paragraph 2:
[2.1]This means that the RCP is not actually a series of filters. [2.2]There is only one filter in the series, and the other two layers (the QWPs) alter the state without filtering it. [2.3]One way to see that this is true is to ask what would happen if you omitted the LP layer and kept just the two QWPs. They are turned 90 degrees to each other, so one will delay the |H> state and the other will delay the |V> state. Since these states form a basis for all photon states, and since they are both delayed equally, the net result is that the photon state as a whole is delayed, but neither component is delayed relative to the other. This is exactly what you would expect from plain old glass, since its refractive index slows, and hence slightly delays, photons. In other words,[2.4]if you omit the LP layer, the combination of the two QWPs does EXACTLY NOTHING to the light. Light would be delayed simply by traveling through space anyway, to the two QWPs are equivalent to simply letting the light travel a tiny extra distance forward. [2.5]This obviously does not affect the state of the light in any way.

[2.1] is incorrect. This is where I will have to disagree with you on your proposition that QWP is not a filter based on the reason that I have stated in [1.6].
[2.2] and [2.3] appears to differ from your earlier proposition that there are two types of QWP. One that rotates light in the clockwise direction, and the other in the counterclockwise direction. In each of these cases, what is it that are being rotated?
[2.4] has a problem. According to you---in the set up involving two TRUE Right Circular Polarizers, the x-linearly polarized photon will have to pass through Two QWP (one rotates in one direction with the other in another direction), before passing through the next x-linear polarizer.
On another experiment involving ONE TRUE Right Circular Polarizer followed by a TRUE Left Circular Polarizer, the x-linearly polarized photon will have to pass through Two QWP (one rotate in one direction with the other reinforcing the rotation), before passing through another x-linear polarizer.
If both the QWP does nothing, how do we account for the fact that:
A] one allows more Light to pass through both the Linear Polarizers with TWO QWP than when only ONE QWP is being used? And
B] the other cut-off a substantial parts of the light as if the two linear polarizers are aligned orthogonally to one another?
Hence, I don’t think [2.5] is tenable.

QUOTE (->
 QUOTE Paragraph 2:[2.1]This means that the RCP is not actually a series of filters. [2.2]There is only one filter in the series, and the other two layers (the QWPs) alter the state without filtering it. [2.3]One way to see that this is true is to ask what would happen if you omitted the LP layer and kept just the two QWPs. They are turned 90 degrees to each other, so one will delay the |H> state and the other will delay the |V> state. Since these states form a basis for all photon states, and since they are both delayed equally, the net result is that the photon state as a whole is delayed, but neither component is delayed relative to the other. This is exactly what you would expect from plain old glass, since its refractive index slows, and hence slightly delays, photons. In other words,[2.4]if you omit the LP layer, the combination of the two QWPs does EXACTLY NOTHING to the light. Light would be delayed simply by traveling through space anyway, to the two QWPs are equivalent to simply letting the light travel a tiny extra distance forward. [2.5]This obviously does not affect the state of the light in any way.

[2.1] is incorrect. This is where I will have to disagree with you on your proposition that QWP is not a filter based on the reason that I have stated in [1.6].
[2.2] and [2.3] appears to differ from your earlier proposition that there are two types of QWP. One that rotates light in the clockwise direction, and the other in the counterclockwise direction. In each of these cases, what is it that are being rotated?
[2.4] has a problem. According to you---in the set up involving two TRUE Right Circular Polarizers, the x-linearly polarized photon will have to pass through Two QWP (one rotates in one direction with the other in another direction), before passing through the next x-linear polarizer.
On another experiment involving ONE TRUE Right Circular Polarizer followed by a TRUE Left Circular Polarizer, the x-linearly polarized photon will have to pass through Two QWP (one rotate in one direction with the other reinforcing the rotation), before passing through another x-linear polarizer.
If both the QWP does nothing, how do we account for the fact that:
A] one allows more Light to pass through both the Linear Polarizers with TWO QWP than when only ONE QWP is being used? And
B] the other cut-off a substantial parts of the light as if the two linear polarizers are aligned orthogonally to one another?
Hence, I don’t think [2.5] is tenable.

Paragraph 3:
[3.1]So you see that the only filtering action is provided by the LP layer. [3.2]The two QWPs process the incoming state (WITHOUT measuring it, so no uncertainty relations are involved) so that light that was initially circularly polarized becomes linear, so that the LP can act on it, and then processes the resulting light back into its original circular state (because, as I said in the above paragraph, the effect of the two QWPs cancels out i.e. one is the inverse of the other). The action of this filter is mathematically identical to a single layer of circularly polarizing material. [3.3]Now we don't happen to have single layer circularly polarizing materials to use in the experiment, but this is a technical limitation only, not part of the basic physics. It should be possible to create a circularly polarizing material, but the fact is that no one is likely to bother, since the QWP LP QWP sandwich already works well.

[3.1] is accepted.
[3.2] need to answer the question that I have raised in [2.4].
[3.3] I remain skeptical as to whether we could construct a single layer of polarizing material based on how we define a Circular Polarizer.

Please pardon me for my impudence. I hope you could continue to set aside sometime from your busy schedule to clarify some of the issues that I have raised here. I will attempt to provide an explanation on Malus Law using simple Classical Statistical Method after your clarification to the issues that I have raised here.

Cheers.

Hi Confused2,

QUOTE

Hexa, many thanks for trying out my suggestion. My lack of comfort is due to the fact that even I have no faith in my understanding of what is going on

Do not feel exasperated because you have lost faith in what we have been taught in school on how this wonderful Quantum Theory has brought us the benefits that we are enjoying in the 21stCentury.
Look at it as another phase where Mankind take another quantum leap in trying to understand Nature. Quantum Theory and Relativity had replaced the Deterministic World of Newtonian Physics. Maybe, it is time to see if Quantum Theory can be understood more rationally. This urge to understand physics MORE RATIONALLY can be traced to the founding fathers of Quantum Physics. Einstein headed the list including giants like, de Broglie, Schrodinger and many others. Bohr and Heisenberg while recognising the problem chose to ignore the issue. Some have proposed String, Membrane, etc, etc in hope that they could better describe Nature. Many are discussing the prospect of a theory beyond the Standard Model that had commanded the Loyalty of the mainstream community for the 20th Century.

QUOTE (->
 QUOTE Hexa, many thanks for trying out my suggestion. My lack of comfort is due to the fact that even I have no faith in my understanding of what is going on

Do not feel exasperated because you have lost faith in what we have been taught in school on how this wonderful Quantum Theory has brought us the benefits that we are enjoying in the 21stCentury.
Look at it as another phase where Mankind take another quantum leap in trying to understand Nature. Quantum Theory and Relativity had replaced the Deterministic World of Newtonian Physics. Maybe, it is time to see if Quantum Theory can be understood more rationally. This urge to understand physics MORE RATIONALLY can be traced to the founding fathers of Quantum Physics. Einstein headed the list including giants like, de Broglie, Schrodinger and many others. Bohr and Heisenberg while recognising the problem chose to ignore the issue. Some have proposed String, Membrane, etc, etc in hope that they could better describe Nature. Many are discussing the prospect of a theory beyond the Standard Model that had commanded the Loyalty of the mainstream community for the 20th Century.

The result .. no change as the QWP is rotated between two vertical filters. Could this be that the QWP has only changed the z angle of the spin vector .. to which neither the filters nor the human eye are sensitive. A more sensitive test would be to start with the filters at right angles.

I think that is an excellent suggestion.
The insertion of the QWP would allow light to pass through the two linear polarizers that are orthogonal to one another. At first sight, the subsequent rotation of the QWP appears not to change anything (for Monochromatic and White Light) that is significant to the naked eyes. I was Wrong. I have discounted the fluctuation when I rotated the QWP as artefacts of the QWP when I gave you the earlier result in my previous post. On hindsight, this fluctuation is due to the permutation of the two molecular axes found in the QWP against the Single axis of each of the Linear Polarizer. This confirms unequivocally that Circular Polarizer is not ROTATION INVARIANT as what QM has predicted. I don’t think Mr Homm assertion that the QWP is not a filter is defensible.

Alternatively, we could fix the QWP and rotate one of the linear polarizer; or fix one linear polarizer and rotate both the QWP and another linear polarizer simultaneously. You will observe that the intensity of the monochromatic light passing the entire set of filters will vary. If White Light is used, you will notice a variation in the chromaticity as the filters are being rotated.

You are correct to state that changes of the spin vector changes nothing with regard to the intensity. Hence, you are correct to state that the changes are not perceptible to the naked eyes. However, careful observation of the experiment suggested by you do reveal a fluctuation to the intensity that is perceptible to the naked eyes.

I hope the information will enable you to formulate your own physical reality with regards to Circular Polarization of Light. Personally, I do not find QM to have provided the Mathematics nor the Theory behind Circular Polarization.

Cheers.
mr_homm
Hi all,

I'm back from my trip, but still quite busy, so I'll try to squeeze in a few replies:

Continuing to discuss hexa's Oct 24 post:

QUOTE

Linear Polarizer:
A linear polarizer with its polarizing axis aligned along the x-axis (0 or 180 deg) will have the molecules principally aligned along this axis. However, the molecules continue to fluctuate about this principal axis. Similarly, a linear polarizer with its axis aligned along the y-axis (+90 or –90 deg) will have the molecules aligned primarily along the y-axis with fluctuation about this other principal axis.

This description has the angles backwards. The molecules are oriented along the direction in which polarized light would be absorbed, not transmitted. This doesn't change anything essential to your argument, but I thought I would point it out. Here is a reference from a British university astronomy department (see especially sections 6.5 and 6.6): Polarization notes You can ignore the stuff about "complex refractive index" as that's just a mathematical trick to make the calculations work smoothly, the same way that complex voltages are used in electrical engineering. It doesn't mean anything is "really" complex, only that complex numbers provide a calculation shortcut.
QUOTE (->
 QUOTE Linear Polarizer:A linear polarizer with its polarizing axis aligned along the x-axis (0 or 180 deg) will have the molecules principally aligned along this axis. However, the molecules continue to fluctuate about this principal axis. Similarly, a linear polarizer with its axis aligned along the y-axis (+90 or –90 deg) will have the molecules aligned primarily along the y-axis with fluctuation about this other principal axis.

This description has the angles backwards. The molecules are oriented along the direction in which polarized light would be absorbed, not transmitted. This doesn't change anything essential to your argument, but I thought I would point it out. Here is a reference from a British university astronomy department (see especially sections 6.5 and 6.6): Polarization notes You can ignore the stuff about "complex refractive index" as that's just a mathematical trick to make the calculations work smoothly, the same way that complex voltages are used in electrical engineering. It doesn't mean anything is "really" complex, only that complex numbers provide a calculation shortcut.

Quarter Wave Plate:
In the case of a QWP (which can be made from a calcite crystal), the molecules are aligned along two principal axes (not necessarily orthogonal to one another). There are two types of QWP. The Right QWP will rotate the orientation of an incoming photons (described by its physical axis) by giving it a clockwise rotation. For example, an incoming photon may have an angle of 80 degree but it will leave the Right QWP with an angle of 70 degree or more.
The Left QWP will rotate the photon in the counter-clockwise direction. This would mean that if the incoming photon has an angle of 20 degree, it will leave the Left QWP with an angle of say 30 degree or more and not an angle that is less than 20 degree.
Notwithstanding the rotational effect of one set of molecules, we must not ignore the action of another set of molecules that makes up the QWP.
In essence, this can be used to explain the presence of the Ordinary and Extraordinary ray passing through a Calcite Crystal.

Now this one is just plain wrong. There is no such thing as a right QWP or left QWP, there is only one type of QWP. Also, a QWP will NOT rotate the orientation of a linearly polarized photon. I think you are confusing QWPs with optically active biological molecules here: there certainly are molecules which will rotate the axis of polarization of linearly polarized light; these are called levorotary (left) and dextrorotary (right) molecules. For example a solution of glucose in water will rotate the plane of polarization of a light beam passing through it. The amount of rotation depends on the distance the light travels through the solution and the concentration of the solution. In fact, this effect is used in chemical labs to measure solution concentrations optically without having to take a sample of the solution -- a pretty clever idea!

Essentially, a QWP is made of a material which transmits light at different speeds depending on the orientation of the electric field of the light. In the case of calcite (a "triclinic" crystal, meaning that the repeating unit of the crystal is a "skewed" cube with no right angles), there is one direction within the crystal that is distinguished. Light passing through the crystal with its E field aligned with this special direction (the "optic axis" of the crystal) will pass through more slowly than light that has its E field oriented perpendicular to the optic axis.

Now notice a couple of things here: if you send a light beam through the crystal so that the propagation direction is along the optic axis, then the E field is necessarily perpendicular to the optic axis (since light is transverse), and so all polarization states will pass through the crystal in equal times IF the propagation is along the optic axis. In that case, the crystal doesn't do anything interesting, and acts just like an ordinary piece of glass.

If on the other hand, you send the light through the crystal so that the propagation direction is perpendicular to the optic axis, then the E field may be either perpendicular or parallel to the optic axis (or any angle in between, of course). In this case, a light ray with its E polarized to be parallel to the optic axis will pass through the crystal slower, and one with its E perpendicular to the optic axis will pass through faster. Both rays will travel along the same path, and there will NOT be separate ordinary and extraordinary rays. In that case, the crystal does phase delay one polarization direction relative to the other, but does NOT separate the light into tow paths, so it is NOT filtering in this orientation.

Finally, suppose you send the light through the crystal at an angle to the optic axis. This one is trickier, so let's set up some coordinates. Say the optic axis as along the line from the origin to (x,y,z) = (1,0,0) and the light ray is along the line from the origin to (1,1,0). Then consider two polarization states: First, E is along (0,0,1), and second along (1,-1,0). Both of these are perpendicular to the direction of propagation as they should be. The first E is also perpendicular to the optic axis, while the second E makes a 45 degree angle to the axis. The second E field could be brought more into alignment with the optic axis if the ray were to change direction slightly, say to (1.1,0.9,0). This would slow the travel of the ray, because E is more nearly aligned with the optic axis. Conversely, bending the ray slightly away from the optic axis would cause it to speed up. Since light must take the quickest path, this ray will bend slightly away from the optic axis to achieve the speed increase. This is the extraordinary ray. The other ray cannot achieve a speed increase, because its E is already perpendicular to the axis, so it is already going at the maximum speed. Therefore this ray does not bend away from the optic axis. This is the ordinary ray. As a matter of fact, when I was taking first year physics, our class calculated the exact angle of deviation of the extraordinary ray based on this analysis (looking for the angle that would produce the shortest travel time), and it agrees perfectly with measured values.

So you can see that the behavior of the calcite depends on how you CUT the crystal. If you cut it to a shape where the front and back faces are perpendicular to the optic axis and shine light straight into it, it will do nothing. If you cut it to a shape where the front and back faces are parallel to the optic axis and shine light straight into it, it will delay one E orientation relative to the other, but not split the ray into two rays. If you cut it into a shape where the optic axis makes a 45 degree angle with the surface normal vector, and then shine light straight into ti, it will split the beam into separate ordinary and extraordinary rays, each polarized perpendicular to the other.

These three behaviors are obtained by preparing the crystal in three different ways. The second preparation is what produces a QWP if the thickness of the crystal is adjusted so that the phase delay is exactly 1/4 wave. This preparation of the crystal does NOT exhibit the separation into two rays, so it is NOT acting as a filter. The third case is most definitely a filter, but that behavior is not present in the second case.

QUOTE
Circular Polarizer:
If a Circular Polarizer uses a Right QWP after a Linear polarizer, then the composite filters will behave as a Right Circular Polarizer. If we use a Left QWP, the Circular polarizer will behave as a Left Circular Polarizer.

This one is of course not correct either, because it is based on the previous one. The correct statement is: If a Circular Polarizer uses a QWP after a linear polarizer, and its optic axis is turned 45 degrees counterclockwise relative to the transmission axis of the linear polarizer, then the composite filter will behave as a Right Circular Polarizer. If we use a QWP with its axis turned 45 degrees clockwise relative to the transmission axis of the linear polarizer, then it will be a Left Circular Polarizer.

I must confess that I am rather distressed that this was not already clear. I spent a lot of effort over several posts to describe these filters exactly, but I must have failed to make it clear. This is my fault of course, so I am disappointed in myself as a teacher. Could you please do me a favor and look over this post and the ones just before it, and show me where I went wrong? I always want to improve the clarity of my explanations, so this would be a great help.

QUOTE (->
 QUOTE Circular Polarizer:If a Circular Polarizer uses a Right QWP after a Linear polarizer, then the composite filters will behave as a Right Circular Polarizer. If we use a Left QWP, the Circular polarizer will behave as a Left Circular Polarizer.

This one is of course not correct either, because it is based on the previous one. The correct statement is: If a Circular Polarizer uses a QWP after a linear polarizer, and its optic axis is turned 45 degrees counterclockwise relative to the transmission axis of the linear polarizer, then the composite filter will behave as a Right Circular Polarizer. If we use a QWP with its axis turned 45 degrees clockwise relative to the transmission axis of the linear polarizer, then it will be a Left Circular Polarizer.

I must confess that I am rather distressed that this was not already clear. I spent a lot of effort over several posts to describe these filters exactly, but I must have failed to make it clear. This is my fault of course, so I am disappointed in myself as a teacher. Could you please do me a favor and look over this post and the ones just before it, and show me where I went wrong? I always want to improve the clarity of my explanations, so this would be a great help.

Using the hypotheses above, let us attempt to analyse the behavior of A PHOTON passing through say a x-linear polarizer:
1) The incoming photon may have an orientation of say 20 deg.
On interaction with the x-linear polarizer, it may be transmitted with an angle of 10 deg or 30 deg or any angle θ between 0 deg < θ < 45 deg and perhaps 315 deg < θ < 360 deg;
2) The incoming photon may have an orientation of say 330 deg.
On interaction with the linear polarizer, it may be transmitted with an angle of 340 deg or 350 deg or any angle θ between 315 deg < θ < 360 deg and perhaps 0 deg < θ < 45 deg
3) However, a photon that has an orientation of say 50 deg. or 300 deg. will be prevented from transmitting through the x-linear polarizer.

In short, the photons with angle θ between 0 deg < θ < 45 deg; 135 deg < θ < 225 deg; and 315 < θ < 360 deg. will be manifested as photons in the x-linearly polarized state.
Whereas the photons with angle θ between 45 deg < θ < 135 deg and 225 deg < θ < 315 deg. will be manifested as photons in the y-linearly polarized state.

Let me restate this in my own words to see if I understand you correctly: Start with an LP filter with axis angle θ_0. When a photon hits this LP filter, it will either get through or not. If it does get through, we say that the photon is in polarization state |θ_0>. This means exactly that the photon got through an LP filter with axis angle θ_0, nothing more. This is how the measurement of photon polarization is defined: a photon is in polarization state |θ_0> if and only if it has just emerged from an LP filter with axis angle θ_0.

However, the photon itself has its own true polarization angle θ, which may not be identical to θ_0. This exact angle is not measured by the LP filter. The action of the filter is to reject all photons whose true polarization angle θ differs from the filter's axis angle θ_0 by more than 45 degrees. Photons with a polarization angle θ that differs by less than 45 degrees from the filter's axis angle θ_0 will pass through the filter, but they will not preserve their polarization angle in the process. Instead, they will have a new exiting polarization angle θ' which must differ from the filter's axis angle by less than 45 degrees.

Summary:
1: If |θ-θ_0|>45 degrees, photon does not get through the filter
2: If |θ-θ_0|<45 degrees, photon does get through filter.
3: In case 2, the exiting photon has an axis θ' satisfying |θ'=θ_0|<45 degrees.
4: In case 3, θ' is not necessarily equal to θ.

QUOTE
From this description, you can see that a photon found with a specific orientation or angle θ at one linear polarized state can also be the same photon found in another linear polarized state.

To me, this seems like the central point. Your hypothesis allows you to associate the same real photon with various different measured polarization states, which means that you do not have to assume that the state is described by a state vector. The purpose of the state vector in standard QM is to account for the fact that a particle that has just been measured and found in a particular state, can then be measured again with a different filter, and found in a different state with nonzero probability. QM accounts for this by saying that the state vector of the particle is resolved into components by each filter, and the component aligned with the filter gets through. In order for this to work, EVERYTHING in QM has to be a state vector, which gives the whole complex-valued, uncertainty-limited standard quantum weirdness.

Your hypothesis avoids all this by postulating an unmeasured real photon angle θ , which is changed by the filter to a new angle θ' that is still within the acceptance range of the filter. I think a host of troubles will arise later from this unmeasured real angle θ, but I will wait until after I have discussed the rest of the details to lay out these general concerns.

QUOTE (->
 QUOTE From this description, you can see that a photon found with a specific orientation or angle θ at one linear polarized state can also be the same photon found in another linear polarized state.

To me, this seems like the central point. Your hypothesis allows you to associate the same real photon with various different measured polarization states, which means that you do not have to assume that the state is described by a state vector. The purpose of the state vector in standard QM is to account for the fact that a particle that has just been measured and found in a particular state, can then be measured again with a different filter, and found in a different state with nonzero probability. QM accounts for this by saying that the state vector of the particle is resolved into components by each filter, and the component aligned with the filter gets through. In order for this to work, EVERYTHING in QM has to be a state vector, which gives the whole complex-valued, uncertainty-limited standard quantum weirdness.

Your hypothesis avoids all this by postulating an unmeasured real photon angle θ , which is changed by the filter to a new angle θ' that is still within the acceptance range of the filter. I think a host of troubles will arise later from this unmeasured real angle θ, but I will wait until after I have discussed the rest of the details to lay out these general concerns.

With this hypothesis, you can see that in so far as the photons falls within the permissible range of the linear polarizer, the photons will continue to be transmitted through any numbers of x-linear polarizers.

In conclusion, does this hypothesis not explain the QM predictions:

1) l <x l Mx l x>l^2 = 1
2) l <y l My l x>l^2 = 0

Yes, your hypothesis does indeed predict 1) and 2), which are experimentally correct. In fact, you can go to any angle and predict
|<θ|Mθ|θ>| = 1 and |<θ +/- 90|Mθ|θ>| = 0, which also agree with experiment.

So far, your hypothesis is looking good, but I would like to know further details:

How is θ' determined from θ? Is this actually deterministic, controlled by the unknown details of the molecular structure of the LP filter? Or is it truly random? I am assuming that you intend the first interpretation, based on your comments earlier about determinism.

In either case, how are the possible angles θ' distributed? Is the probability of getting a specific angle θ' evenly spread across the range θ_0 - 45 to θ_0 + 45? Is it influenced in any way by the incoming angle θ? In other words does θ' tend to stay close to θ?

Is θ' impossible in principle to measure, or is it just a technical limitation of our current filter technology? That makes a big difference for the interpretation of the theory. In the first case, you have a "local hidden variable" theory, which Bell's theorem should apply to. How do you plan to escape from Bell's theorem? In the second case, new filters could produce radically different experimental results from current filters, invalidating Malus's Law.

@hexa Oct.25

Yes, that is a very amusing post of Gtrax. My attitude is similar. If a theory can be made more and more elaborate to account for everything, then that theory is useful for making predictions, but it still might not be TRUE. On the other hand, if the theory is actually true, then you should be able to use it to make predictions of phenomena you hadn't even thought of when you constructed the theory. In other words, the theory should predict outcomes for experiments OTHER than the ones that it was founded upon, and it should get these predictions RIGHT. Then you have a very strong suspicion that at least something about your theory is really on the right track. However, even then it might be possible to reorganize the theory into a different format that would be much cleaner and clearer, and still make the same predictions. QM is in this position now: it has successfully predicted the outcomes of many experiments beyond the ones that were used to define it; therefore, there is something right about it; on the other hand, all common interpretations of QM have logical or philosophical problems of one kind or another, and the math may seem unnecessarily complicated (though that's a matter of taste), so there is something wrong about it as well (or at least something wrong about how we are interpreting it).

@montec, Oct. 25
QUOTE
Linear polarized light's axis of polarization remains the same as the polarized light travels through space.
Circular polarized light's axis of polarization rotates as the polarized light travels through space. The direction of rotation defines CCW or CW Circular/Elliptical polarization.

The first part is correct. The second part is kind of right, but the circularly polarized light does not have an axis of polarization. I think what you mean is that the E field vector rotates as the light travels through space. That is standard textbook physics. When the E field vector does not rotate, then you have linearly polarized light, and the polarization axis is then the same as the direction of the E field vector.

Now there are two ways to picture this, and only one of them is right. First, some people picture the circularly polarized wave as like a ribbon with a twist in it, so that the light is plane polarized at any point, but the angle of polarization changes as you go along the wave. In that case, if you placed an antenna in the path of the wave and moved it back and forth along the path of propagation, you would sometimes see the antenna pick up a lot of energy (when it is in a position where the E field lines up with it) and sometimes pick up no energy (when E is perpendicular to it). This is NOT what happens, so this is not the correct picture.

The other picture is to think of the threads on a screw and imagine spinning the screw WITHOUT moving it forward. You will see the threads appear to move forward. Now imagine that the E field vector at each point on the wave points radially out from the axis of the screw to the thread, so that the arrow heads of all the E vectors form the ridge of the screw thread. Then at each point in space, the E vector is rotating around as the screw turns. In this case, you would expect an antenna to pick up exactly half of the energy of the wave (because it misses the part that comes when the E field is rotated perpendicular to the antenna) regardless of position. This IS what happens, so this is the correct picture. In other words, the circularly polarized wave does not consist of a twisted plane polarized wave; instead the E field vector rotates around and around at EACH point along the wave path.

Hope that clears it up!

@Confused2, Oct. 26
QUOTE (->
 QUOTE Linear polarized light's axis of polarization remains the same as the polarized light travels through space.Circular polarized light's axis of polarization rotates as the polarized light travels through space. The direction of rotation defines CCW or CW Circular/Elliptical polarization.

The first part is correct. The second part is kind of right, but the circularly polarized light does not have an axis of polarization. I think what you mean is that the E field vector rotates as the light travels through space. That is standard textbook physics. When the E field vector does not rotate, then you have linearly polarized light, and the polarization axis is then the same as the direction of the E field vector.

Now there are two ways to picture this, and only one of them is right. First, some people picture the circularly polarized wave as like a ribbon with a twist in it, so that the light is plane polarized at any point, but the angle of polarization changes as you go along the wave. In that case, if you placed an antenna in the path of the wave and moved it back and forth along the path of propagation, you would sometimes see the antenna pick up a lot of energy (when it is in a position where the E field lines up with it) and sometimes pick up no energy (when E is perpendicular to it). This is NOT what happens, so this is not the correct picture.

The other picture is to think of the threads on a screw and imagine spinning the screw WITHOUT moving it forward. You will see the threads appear to move forward. Now imagine that the E field vector at each point on the wave points radially out from the axis of the screw to the thread, so that the arrow heads of all the E vectors form the ridge of the screw thread. Then at each point in space, the E vector is rotating around as the screw turns. In this case, you would expect an antenna to pick up exactly half of the energy of the wave (because it misses the part that comes when the E field is rotated perpendicular to the antenna) regardless of position. This IS what happens, so this is the correct picture. In other words, the circularly polarized wave does not consist of a twisted plane polarized wave; instead the E field vector rotates around and around at EACH point along the wave path.

Hope that clears it up!

@Confused2, Oct. 26
Of EM radiation .. it is either infinitely divisible or some sort of 'granule' will become apparent.. the 'granule' (photon) seems to be apparent whether we like it or not. We readily observe that one beam of light appears able to pass through another without modification and we are drawn to the conclusion that an individual photon can only interfere constructively or destructively with itself. It is in the nature of 'interference' that the path taken by the photon becomes hard to describe (and understand). I am under the impression that it is not easy to define the precise properties of a photon such that Maxwell's equations and QED can be seen to be manifestations of one and the same thing. I am content with the words "It can be shown..".

You're right, defining those properties correctly is hard. You have to derive QED by applying quantum field theory to the photon (as it has been defined) and then show that classical EM follows as the limit of QED when Planck's constant approaches zero. This is (as they say in mathematics) "highly nontrivial."

@hexa, Oct. 28
QUOTE
We all know that the Michelson & Morley Experiment prove beyond reasonable doubt that aether does not exist. Ironically, the experiment was conducted by two protagonists that believe in the existence of aether.
Notwithstanding that both Michelson and Morley are awarded the Nobel prize for proving the non existence of the aether, Morley continues to believe in the existence of aether until his death.

This experiment has been called "the most important NEGATIVE result in the history of physics." You are right, it is ironic that Morely refused to believe his own result. It was observed once (by Arthur C. Clarke, if I remember correctly, but perhaps he was quoting someone else) that the way to advance physics was to (1) prove your result was correct and (2) wait for all the old physicists to die.

As to the large quoted material from your earlier post, I have responded to it in this post (see above).

@MrMysteryScience, Oct. 28

I am having some trouble understanding your post in detail. Without intending any disrespect, I will confine my remarks to trying for clarification rather than responding to the content of what you have said. When clarity is reached, then will be the time to respond without fear of misunderstanding.

Your main points seem to be these:
1: It is hard to picture a particle having more than 1 spin axis at the same time. It seems intuitively that if the particle is spinning one particular way, then it is NOT spinning some other way.
2: You have mentioned a possible "higher dimensional" viewpoint where you can see that the particle has only one true spin, but that in this higher dimension, there may be more than 1 spin axis.
3: You cite two papers on the Optical Magnus Effect, showing that the chirality (right or left handedness of the circular polarization) affects the physical distribution of light at the exit of the fiber. This looks like it is intended to show that circular polarization is a real state for photons, because it has observable effects.

Am I understanding you correctly?

One comment about point 3. There are other experiments as well that show circular polarization has physical effects. For instance, set up the apparatus for a Cavendish experiment, blacken the bottom side of the torsion pendulum with carbon dust, and shine a right circular polarized laser beam up onto it from below. This beam contains angular momentum, so when it is absorbed by the torsion pendulum, it will exert a (very small) torque on it. Knowing the period of the pendulum, you can reverse the polarization at the same period to give the pendulum a series of torsional boosts, much like pushing a child on a swing. The pendulum will build up a rotational oscillation, and by measuring the amplitude of the oscillation and its damping, you can calculate the amount of torque the laser exerted on the pendulum.

Now this is important in view of linearity. Since plane polarized light carries NO angular momentum, it CANNOT be the most fundamental state for light. This is because by linearity, any combination of plane polarized photons must then have a total angular momentum of exactly zero (just the sum of the individual contributions, which are all zero). If linear polarization were truly fundamental, all other polarizations could be built by summing linear polarizations, and no light beam would ever carry angular momentum, directly contradicting the experiment. On the other hand, if the fundamental states of light are RCP and LCP, and if these DO carry angular momentum, it is easy to see that if linear polarizations are constructed from equal mixtures of RCP and LCP, they will have zero angular momentum, agreeing with experiment. In short, you can build zero angular momentum states from nonzero ones, but you cannot build nonzero angular momentum states from zero ones. Therefore, the photon must intrinsically have angular momentum.

It is true that ALGEBRAICALLY all states are equally fundamental in standard QM, but physically the photons must have an intrinsic angular momentum. Now, how can it be that you can algebraically combine states like |H> and |V> to get |R> and |L>? After all, the first two do not have angular momentum but the last two do have it. It turns out that the complex numbers are what make this work. The fact that |R> and |L> are complex linear combinations of |H> and |V>, not real linear combinations, is what allows them to have angular momentum. It is the complex numbers that allow all states to be thought of as equally fundamental. Without them, you would be forced to say that the circular states are fundamental and the linear states are not.

I must stop here for the night, but will try to catch up with more recent posts tomorrow.

Cheers!

--Stuart Anderson
hexa
Hi Mr Homm,

Thanks for setting aside time to provide clarification to all our queries.
Thanks for the link ( http://www.star.le.ac.uk/~rw/courses/lect4313.html#tth_sEc6 ) and the explanation of the two terms levorotary (left) and dextrorotary (right) molecules.

I am afraid I am getting a bit confused with your latest clarification:

QUOTE

QUOTE (->
 QUOTE QUOTE Hexa:Quarter Wave Plate:In the case of a QWP (which can be made from a calcite crystal), the molecules are aligned along two principal axes (not necessarily orthogonal to one another). There are two types of QWP. The Right QWP will rotate the orientation of an incoming photons (described by its physical axis) by giving it a clockwise rotation. For example, an incoming photon may have an angle of 80 degree but it will leave the Right QWP with an angle of 70 degree or more.The Left QWP will rotate the photon in the counter-clockwise direction. This would mean that if the incoming photon has an angle of 20 degree, it will leave the Left QWP with an angle of say 30 degree or more and not an angle that is less than 20 degree.Notwithstanding the rotational effect of one set of molecules, we must not ignore the action of another set of molecules that makes up the QWP.In essence, this can be used to explain the presence of the Ordinary and Extraordinary ray passing through a Calcite Crystal. Now this one is just plain wrong. There is no such thing as a right QWP or left QWP, there is only one type of QWP. Also, a QWP will NOT rotate the orientation of a linearly polarized photon.

This does not appear to agree with your statement that you had made with regards to QWP in your earlier post: (http://forum.physorg.com/index.php?showtopic=3310&view=findpost&p=113085 ):
QUOTE

This means that relative to the direction of the LP axis, the first QWP axis is 45 degrees counterclockwise and the second QWP axis is 45 degrees clockwise. Let's say counterclockwise is the positive rotation direction, as is usual, so QWP(+45) means a QWP with its axis 45 degrees counterclockwise relative to the LP axis, and QWP(-45) means the same thing but clockwise. Then:

True left circular filter = TLCF = QWP(+45) + LP + QWP(-45)

True right circular filter = TRCF QWP(-45) + LP + QWP(+45)

Photographic left circular polarizer = PLCP = LP + QWP(-45)

Photographic right circular polarizer = PRCP = LP + QWP(+45)

Photographic left circular analyzer = PLCA = QWP(+45) + LP

Photographic right circular analyzer = PRCA = QWP(-45) + LP.

With your latest clarification, I now know that I have totally misinterpreted the meaning of the statement that you intend to convey. What you in fact said is that a Linear Polarizer somehow become a Right or Left Circular Polarizer if the optical axis of the QWP is rotated clockwise or anti-clockwise relative to the polarizing axis of the Linear Polarizer.
By the way:
1)What does this OPTICAL Axis of the QWP represent?
2)How is this related to the Molecular arrangement of the QWP?
3)Does the molecules of the QWP not determine how any PHOTON is going to interact with it?

QUOTE (->
 QUOTE This means that relative to the direction of the LP axis, the first QWP axis is 45 degrees counterclockwise and the second QWP axis is 45 degrees clockwise. Let's say counterclockwise is the positive rotation direction, as is usual, so QWP(+45) means a QWP with its axis 45 degrees counterclockwise relative to the LP axis, and QWP(-45) means the same thing but clockwise. Then:True left circular filter = TLCF = QWP(+45) + LP + QWP(-45)True right circular filter = TRCF QWP(-45) + LP + QWP(+45)Photographic left circular polarizer = PLCP = LP + QWP(-45)Photographic right circular polarizer = PRCP = LP + QWP(+45)Photographic left circular analyzer = PLCA = QWP(+45) + LPPhotographic right circular analyzer = PRCA = QWP(-45) + LP.

With your latest clarification, I now know that I have totally misinterpreted the meaning of the statement that you intend to convey. What you in fact said is that a Linear Polarizer somehow become a Right or Left Circular Polarizer if the optical axis of the QWP is rotated clockwise or anti-clockwise relative to the polarizing axis of the Linear Polarizer.
By the way:
1)What does this OPTICAL Axis of the QWP represent?
2)How is this related to the Molecular arrangement of the QWP?
3)Does the molecules of the QWP not determine how any PHOTON is going to interact with it?

Mr Homm:
QUOTE

QUOTE Hexa:
Circular Polarizer:If a Circular Polarizer uses a Right QWP after a Linear polarizer, then the composite filters will behave as a Right Circular Polarizer. If we use a Left QWP, the Circular polarizer will behave as a Left Circular Polarizer.

This one is of course not correct either, because it is based on the previous one. The correct statement is: If a Circular Polarizer uses a QWP after a linear polarizer, and its optic axis is turned 45 degrees counterclockwise relative to the transmission axis of the linear polarizer, then the composite filter will behave as a Right Circular Polarizer. If we use a QWP with its axis turned 45 degrees clockwise relative to the transmission axis of the linear polarizer, then it will be a Left Circular Polarizer.

I must confess that I am rather distressed that this was not already clear. I spent a lot of effort over several posts to describe these filters exactly, but I must have failed to make it clear. This is my fault of course, so I am disappointed in myself as a teacher. Could you please do me a favor and look over this post and the ones just before it, and show me where I went wrong? I always want to improve the clarity of my explanations, so this would be a great help.

Sorry to have misunderstood you. The fault is not entirely yours.
However, there is a BIGGER PROBLEM if the photons are not rotated clockwise or anti-clockwise relative to the linear polarizer as you now intended to mean. This is because you have also stated that it is the Linear Polarizer in the TRUE Circular Polarizer (QWP + LP + QWP) that will either allow more light to pass through or none at all. If it does not rotate the orientation of the photons, then How is the Linear polarizer going to do what it does, if it is the ONLY FILTER by your definition?

I am sure you are aware of this experiment.
Experiment-1
Place x-linear polarizer at position 1 and y-linear polarizer at position 3 along the z-axis.
Pass a beam of photons along the z-axis passing through the two linear polarizers.
What do you see?

Experiment-2
Place a linear polarizer (inclined at 45 deg. to the x-linear polarizer) at position 2 in between the x-linear polarizer at position-1 and y-linear polarizer at position 3.
What do you see?

How do you account for the fact that the photons can now pass through the polarizers in Experiment-2 but not in Experiment-1 if none of the photons are being rotated by the linear polarizer inclined at 45 degree to the x and y linear polarizers?

QUOTE (->
 QUOTE QUOTE Hexa:Circular Polarizer:If a Circular Polarizer uses a Right QWP after a Linear polarizer, then the composite filters will behave as a Right Circular Polarizer. If we use a Left QWP, the Circular polarizer will behave as a Left Circular Polarizer.

This one is of course not correct either, because it is based on the previous one. The correct statement is: If a Circular Polarizer uses a QWP after a linear polarizer, and its optic axis is turned 45 degrees counterclockwise relative to the transmission axis of the linear polarizer, then the composite filter will behave as a Right Circular Polarizer. If we use a QWP with its axis turned 45 degrees clockwise relative to the transmission axis of the linear polarizer, then it will be a Left Circular Polarizer.

I must confess that I am rather distressed that this was not already clear. I spent a lot of effort over several posts to describe these filters exactly, but I must have failed to make it clear. This is my fault of course, so I am disappointed in myself as a teacher. Could you please do me a favor and look over this post and the ones just before it, and show me where I went wrong? I always want to improve the clarity of my explanations, so this would be a great help.

Sorry to have misunderstood you. The fault is not entirely yours.
However, there is a BIGGER PROBLEM if the photons are not rotated clockwise or anti-clockwise relative to the linear polarizer as you now intended to mean. This is because you have also stated that it is the Linear Polarizer in the TRUE Circular Polarizer (QWP + LP + QWP) that will either allow more light to pass through or none at all. If it does not rotate the orientation of the photons, then How is the Linear polarizer going to do what it does, if it is the ONLY FILTER by your definition?

I am sure you are aware of this experiment.
Experiment-1
Place x-linear polarizer at position 1 and y-linear polarizer at position 3 along the z-axis.
Pass a beam of photons along the z-axis passing through the two linear polarizers.
What do you see?

Experiment-2
Place a linear polarizer (inclined at 45 deg. to the x-linear polarizer) at position 2 in between the x-linear polarizer at position-1 and y-linear polarizer at position 3.
What do you see?

How do you account for the fact that the photons can now pass through the polarizers in Experiment-2 but not in Experiment-1 if none of the photons are being rotated by the linear polarizer inclined at 45 degree to the x and y linear polarizers?

How is θ' determined from θ? Is this actually deterministic, controlled by the unknown details of the molecular structure of the LP filter? Or is it truly random? I am assuming that you intend the first interpretation, based on your comments earlier about determinism.

The answer is Yes and No. The angle that you refer to for the molecules of the LP is angle σ. I hope we can keep to the convention that I have adopted here. At the individual level, the passage of a SINGLE PHOTON through the molecules is still random. The range of angle θ' upon which a SINGLE PHOTON passes through a given Molecular arrangement of the Linear Polarizer is fixed by angle σ. Whether that PHOTON passes through the linear polarizer is governed by the angle θ. Beyond the permissible range, the PHOTON DOES NOT pass through the linear polarizer.

The molecular structure of the Linear Polarizing filter can be known quite accurately using a Transmission Electron Microscope or X-ray spectroscopy. The molecular axis can also be determined quite accurately when the linear polarizers are being constructed. Notwithstanding all that I have said about a unique molecular axis, this must be understood in the context that the molecules are constantly vibrating and oscillating about this axis which is the mean.

QUOTE

In either case, how are the possible angles θ' distributed? Is the probability of getting a specific angle θ' evenly spread across the range θ_0 - 45 to θ_0 + 45?

The angle θ is NOT evenly spread across the range between θ= +45 deg and –45 deg. It has a bell curve that takes its reference from the molecular axis of the linear polarizer. Angle σ is important.

QUOTE (->
 QUOTE In either case, how are the possible angles θ' distributed? Is the probability of getting a specific angle θ' evenly spread across the range θ_0 - 45 to θ_0 + 45?

The angle θ is NOT evenly spread across the range between θ= +45 deg and –45 deg. It has a bell curve that takes its reference from the molecular axis of the linear polarizer. Angle σ is important.

Is it influenced in any way by the incoming angle θ? In other words does θ' tend to stay close to θ?

Not necessary. But it does has a higher probability. It is influenced by angle σ. This is the angle measured with reference to the molecular axis of the polarizer. In a linear polarizer, there is only one alignment. In a QWP there are two such axes.

QUOTE

Is θ' impossible in principle to measure, or is it just a technical limitation of our current filter technology? That makes a big difference for the interpretation of the theory.

The angle θ of a SINGLE PHOTON cannot be measured physically and is unlikely that we can measure it definitively in the near future. This is because a PHOTON is a boson. Unlike fermion, a boson is not affected by magnetic field or electric field. Hence, it is impossible to measure the angle θ with the precision that we can measure for the spin of an electron or any other fermion. I could be wrong, but I don't see how one could measure this angle θ definitively, given the limitation that I have mentioned above.
But that does not mean that we cannot infer the range of angle θ from its group behavior.

QUOTE (->
 QUOTE Is θ' impossible in principle to measure, or is it just a technical limitation of our current filter technology? That makes a big difference for the interpretation of the theory.

The angle θ of a SINGLE PHOTON cannot be measured physically and is unlikely that we can measure it definitively in the near future. This is because a PHOTON is a boson. Unlike fermion, a boson is not affected by magnetic field or electric field. Hence, it is impossible to measure the angle θ with the precision that we can measure for the spin of an electron or any other fermion. I could be wrong, but I don't see how one could measure this angle θ definitively, given the limitation that I have mentioned above.
But that does not mean that we cannot infer the range of angle θ from its group behavior.

In the first case, you have a "local hidden variable" theory, which Bell's theorem should apply to. How do you plan to escape from Bell's theorem?

In my case, since I look at everything as having a REAL Physical State, I also look at a SINGLE PHOTON as having a PHYSICAL STATE where we can use an axis in Cartesian Coordinate to describe this physical state.
The Local Hidden Variable Theory made the assumption that the angle θ of the photons are evenly distributed. This is an incorrect assumption which I will explain when I provide you the proof for Malus Law.
Bell’s theorem is made on this erroneous premises. This has led to the ludicrous presumption that Locality is violated and that it is possible to communicate information faster than the speed of light. No. The claim is even more preposterous. It is instant communication irrespective of whether the two communicating parties may be half a Univese away from one another. This is the current claim of Quantum entanglement.

QUOTE

In the second case, new filters could produce radically different experimental results from current filters, invalidating Malus's Law.

Before I provide the proof for Malus Law (which is only an approximation), I would need you to help me by stating the probability intensity provided by QM. It is OK if you want to use Malus Law to state the value of the Intensity of light passing through this set of linear polarizers:
1)The polarizing axis of first Linear polarizer is aligned at 0 degree.
2)The second linear polarizer is aligned at 45 degree.
3)The third linear polarizer is aligned at 90 degree.
Question:
Determine the probability intensity of light passing through all the three linear polarizers.

It is important that you state the value so that we can make a comparison between what QM predict and what I will be predicting. After which, we can both do the experiment to satisfy ourselves whether QM prediction is correct or the one that I am proposing that rest squarely on Determinism.

Cheer
MrMysteryScience
Hello mr_homm,

Thank you for your very polite response. Now is not a great time for me to respond. And I do respect the direction this thread is taking and do not wish to post anything that would take away from that. Perhaps you are willing to take a message using this forum's messaging system. In the meantime, a primitive research on Magnus effects, that were even hinted at by Newton, might give you a very simplified concept as to why that effect was used as a descriptive in the "Optical Magnus Effect". Of course there is more...

Thanks again.
mott.carl
there is yes two distict polarizations to the light,left-handed and vright-handed,due
the the light appear of quantic vaccum as anisotropic,then could have the non-locality and orientaby,where the polarization of the light rays are circular,then occur a mirror symmetry breaking that turn the light with two opposed polarization
,it is, permit that that speed of light has it speed altered when can to pass from medium to other with negative refraction index,that does see the light ray with pathway forward in time,and therefore there are negative spaces conjugated to
imaginary space-time when observer the light go out before to enter in the medium,it is the break of symmetry of mirror that permit that pathwat of speed of lught be non-linear,then occur a reversion of parity and reversal-time that does the
show it opposed direction,as if the light was oriented by a determined direction
and returned by the non-oriented direction.then could see the "future" as ptential vector that contain all the information sent to future and reflected through of hidden variables that occult the symmetries broken when occur the reversion of image as real through of the virtual potential vectors;as the speed goes to past,with velocity faster than the light,that goes backward in space-time(not only in the time) with nrgative energy,then the relations univocity between the events
in the place of negative space-time and positive space-time.then occur a circularity
of the phenomenons of space-time through of two polarizations driven to the space-time(left-handed- that goes forward in given orientation and goes backward
with contrary orientation)
mott.carl
the opposed rotations of background of the universe,generate in the vaccum,two disctint polarizations to the light that is left-handed and right-handed,it is,non-symmetry of pt,that does the polarizations be non-local,then creating several parallel pathway to the light rays.then the oriented and non-oriented rotations
generate a circular polarization of light.the subquantic vaccum symmetry breaking generate the circular polarization of light through of the left-handed and right-handed polarizations,that does curve the light .
Peter Robert
Hi Mott.Carl,

What are you saying???????:
QUOTE

1) quantic vaccum as anisotropic,
2) non-locality and orientaby,where the polarization of the light rays are circular,then occur a mirror symmetry breaking that turn the light with two opposed polarization
3) speed of light has it speed altered when can to pass from medium to other with negative refraction index
4)that does see the light ray with pathway forward in time,
5)therefore there are negative spaces conjugated to
imaginary space-time
6) the light go out before to enter in the medium,
7) it is the break of symmetry of mirror that permit that pathwat of speed of lught be non-linear
8) then occur a reversion of parity and reversal-time that does the
show it opposed direction,
9) the light was oriented by a determined direction
10)returned by the non-oriented direction
11).then could see the "future" as ptential vector
12) that contain all the information sent to future and reflected through of hidden variables that occult the symmetries broken when occur the reversion of image as real through of the virtual potential vectors;
13) as the speed goes to past,with velocity faster than the light,that goes backward in space-time(not only in the time)
14) with nrgative energy,then the relations univocity between the events
in the place of negative space-time and positive space-time.then occur a circularity
of the phenomenons of space-time through of two polarizations driven to the space-time(left-handed- that goes forward in given orientation and goes backward
with contrary orientation)

I can now understand why these other members are so critical about you:
QUOTE (->
 QUOTE 1) quantic vaccum as anisotropic, 2) non-locality and orientaby,where the polarization of the light rays are circular,then occur a mirror symmetry breaking that turn the light with two opposed polarization 3) speed of light has it speed altered when can to pass from medium to other with negative refraction index 4)that does see the light ray with pathway forward in time, 5)therefore there are negative spaces conjugated to imaginary space-time 6) the light go out before to enter in the medium, 7) it is the break of symmetry of mirror that permit that pathwat of speed of lught be non-linear 8) then occur a reversion of parity and reversal-time that does the show it opposed direction, 9) the light was oriented by a determined direction 10)returned by the non-oriented direction 11).then could see the "future" as ptential vector 12) that contain all the information sent to future and reflected through of hidden variables that occult the symmetries broken when occur the reversion of image as real through of the virtual potential vectors; 13) as the speed goes to past,with velocity faster than the light,that goes backward in space-time(not only in the time) 14) with nrgative energy,then the relations univocity between the events in the place of negative space-time and positive space-time.then occur a circularity of the phenomenons of space-time through of two polarizations driven to the space-time(left-handed- that goes forward in given orientation and goes backward with contrary orientation)

I can now understand why these other members are so critical about you:

1)Euler Posted: Nov 4 2006, 08:31 PM
Negative This guy doesn't know what he's talking about. The same goes for anyone stupid enough to leave him positive feedback.
2)Pupamancur Posted: Nov 3 2006, 04:00 PM
Negative BS-er of first class.
3)AlphaNumeric Posted: Nov 3 2006, 11:51 AM
Negative Has absolutely no idea about the things he mentions. Obsessed with using buzzwords he doesn't understand.
4) na'kuru'sil Posted: Nov 2 2006, 11:00 PM
Negative Complete idiot.
5)Alpha Posted: Oct 26 2006, 10:48 AM
Negative Arm-waving champion.
6)Pupamancur Posted: Oct 17 2006, 04:01 PM
Negative Total BS posts.

You could not express yourself but chose to use Big Stupid Bombastic Terms.
Worst, you don't seem to be able to spell.
In fact, if what these other members is saying about you is true, you should not even be allowed in this forum. It just make you look extremely STUPID and OBNOXIOUS.

I am a fan of Mr Homm. He will always have my respect as an astute teacher that is extremely careful with his choice of words. He is among the best who could express himself in such vivid terms and provide the mathematics when needed.
While I have been taught Quantum Mechanics and believe that that is the best we can describe nature, I find it difficult to dismiss the Deterministic approach proposed by hexa. I hope Mr Homm could provide a satisfactory answer to the questions posed by hexa. I also hope that hexa would continue to challenge the prevailing doctrine in Science. If what he said is true, then learning Science would certainly be a breeze and not a chore with tons and tons of abstract mathematics that nobody seem to be able to fully comprehend that they can relate to reality.

From the views put forward by Mr Homm, hexa, Confused2, Dr Brettmann, Schneibster, MrMysteryScience, Montec, etc, in this thread, I find it quite humbling to put any view across.
As such I am only listening quietly and learning as much of what is being discussed.
I cannot say about the other members following this thread. As for you Mott.Carl, I am Very, Very Sure you have nothing worthwhile to contribute. So, why don't you just SHUT UP like me.

Please accept my APOLOGY. But I am Extremely frustrated with your stupid remarks and interuption like a kindergarden kid, that makes me break my silence.

Peter Robert.
hexa
Hi Peter Robert,

While I tend to agree with much of all you have said, I hope you could be a little more forgiving on Mott. Carl.
In all honesty, much of what we understand as contemporary physics are heavily coated with abstract mathematical postulates that are essentially non accessible to the common folks. Some are just as absurd as what Mott.Carl had attempted to say, although he may not have the command of the language to express himself in those terms used by the experts. Look at the plea by Good Elf in this other thread: (http://forum.physorg.com/index.php?showtopic=6587&view=findpost&p=141392 )
QUOTE

Hi Confused2, Yquantum, StevenA, Laserlight, Why Not?, TRoc et al,

I am not really trying to be evasive here and in the best spirit of the exploration of knowledge.. but just what is the point of StevenA's experiment? What will it show that is relevant to photons? Non-locality is a very established principle and it will need to be addressed... sometime.

.........
Does anyone suggest that you do not need polarization information to connect photon qubits or that the information with entangled pairs travels at any speed other than Light or travels some other way other than with the system being measured. We are speaking of properties here and actual properties can be measured, and that is what we do. What is noted is that Quantum Mechanicsa local theory,  will not explain this non-local nature of Photons because it would need to travel faster than light to do so. It is not just Bell's Inequality but a number of other non-local phenomena that disagree with Quantum Mechanics such as Aharonov-Bohm Effect, Aharonov-Anandan Effect and the Aharonov-Casher Effect. These show global spacetime dislocations that connect phase and spin of particles through "infinite" barriers at any range. These "forces" extend beyond all locality theories of Electromagnetism. I refer the the experimental works of Tonomura and others...
Verification of the Aharonov-Bohm Effect: Akira Tonomura
Wikipedia: Nonlocality
Wolfram Research: Aharonov-Bohm Effect
Direct observation of the Aharonov-Casher phase: M. Koenig, A. Tschetschetkin, E.M. Hankiewicz, Jairo Sinova, V. Hock, V. Daumer, M. Schaefer, C.R. Becker, H. Buhmann, L.W. Molenkamp
The Aharonov-Casher and Aharonov-Anandan Effect: Kendal Clark

A careful read of these results (and others) show there is indeed a question to be addressed as soon as some Theoretical Physicists get down from unapproachable "Ivory Towers" and deal with existing testable and tangible problems in their theories, bringing them into line with real experiments.

This is an area that has been probed quite deeply and any experiment you propose must also explain all the accumulated information already at hand about entanglement, phase and spin. It is very clear that entanglement in general correlates quantum properties and affects qubit information independent of time and even through barriers that should be opaque to any effects such as these. You can't just "trick it up". The property itself is not important, it is the correlation that is superluminal. Recent experiments indicate you do not have to be an atomic particle to be entangled and the speed of that entanglement is "instantaneous". , you can entangle several properties This phenomenon occurs across many different disciplines such as Condensed Matter, Relativity, Optics, Photonics, Quantum Computing etc.

Photons are particularly well researched and I assume you understand the results of the Delayed Choice Quantum Eraser Experiment and have you really got any results anywhere that shows any separate or anomalous possibility.
........
I do not care if it is written in your Holy Texts as an additional Commandment, every theory must pass all tests despite all human "opinion".

With all respect... Is it that some people have a problem with the Universe and are petitioning to have some Laws Repealed?

From the discussion in this other thread, you can see that Contemporary Physics is very very weird. QM is also being attacked. Unfortunately, the alternatives are not much better as it also require us to depart from what we consider as Rational and the Cardinal Principle of Science. DETERMINISM that do not violate Locality and Causality.

The reason I posed this question here is because the experiment that I have conducted using Circular Polarizers does not yield the result predicted by QM. Thanks to Mr. Homm, he has helped to solve a major construction problem by introducing the definition of a TRUE Right and TRUE Left Circular Polarizer that I could not find anywhere in any Physics Text.

As you can see, our discussion has now reach a crucial stage that we need to be very precise on what we meant. It will have quite significant repercussion between what we predict and what we will in fact observe.

In this respect, I will need Mr. Homm help in stating the prediction by QM (where he can use Malus Law if that is his preference) to state the prediction before I proceed to state the proof of Malus Law. Although the result is meant for Linear Polarizers, it is important that we understand it phenomenonlogically and how the mathematics is being derived that will be crucial for us to understand the crux of Circular Polarization.

QUOTE (->
 QUOTE Hi Confused2, Yquantum, StevenA, Laserlight, Why Not?, TRoc et al,I am not really trying to be evasive here and in the best spirit of the exploration of knowledge.. but just what is the point of StevenA's experiment? What will it show that is relevant to photons? Non-locality is a very established principle and it will need to be addressed... sometime..........Does anyone suggest that you do not need polarization information to connect photon qubits or that the information with entangled pairs travels at any speed other than Light or travels some other way other than with the system being measured. We are speaking of properties here and actual properties can be measured, and that is what we do. What is noted is that Quantum Mechanicsa local theory,  will not explain this non-local nature of Photons because it would need to travel faster than light to do so. It is not just Bell's Inequality but a number of other non-local phenomena that disagree with Quantum Mechanics such as Aharonov-Bohm Effect, Aharonov-Anandan Effect and the Aharonov-Casher Effect. These show global spacetime dislocations that connect phase and spin of particles through "infinite" barriers at any range. These "forces" extend beyond all locality theories of Electromagnetism. I refer the the experimental works of Tonomura and others... Verification of the Aharonov-Bohm Effect: Akira TonomuraWikipedia: NonlocalityWolfram Research: Aharonov-Bohm EffectDirect observation of the Aharonov-Casher phase: M. Koenig, A. Tschetschetkin, E.M. Hankiewicz, Jairo Sinova, V. Hock, V. Daumer, M. Schaefer, C.R. Becker, H. Buhmann, L.W. MolenkampThe Aharonov-Casher and Aharonov-Anandan Effect: Kendal ClarkA careful read of these results (and others) show there is indeed a question to be addressed as soon as some Theoretical Physicists get down from unapproachable "Ivory Towers" and deal with existing testable and tangible problems in their theories, bringing them into line with real experiments.This is an area that has been probed quite deeply and any experiment you propose must also explain all the accumulated information already at hand about entanglement, phase and spin. It is very clear that entanglement in general correlates quantum properties and affects qubit information independent of time and even through barriers that should be opaque to any effects such as these. You can't just "trick it up". The property itself is not important, it is the correlation that is superluminal. Recent experiments indicate you do not have to be an atomic particle to be entangled and the speed of that entanglement is "instantaneous". , you can entangle several properties This phenomenon occurs across many different disciplines such as Condensed Matter, Relativity, Optics, Photonics, Quantum Computing etc.Photons are particularly well researched and I assume you understand the results of the Delayed Choice Quantum Eraser Experiment and have you really got any results anywhere that shows any separate or anomalous possibility. ........I do not care if it is written in your Holy Texts as an additional Commandment, every theory must pass all tests despite all human "opinion".With all respect... Is it that some people have a problem with the Universe and are petitioning to have some Laws Repealed?

From the discussion in this other thread, you can see that Contemporary Physics is very very weird. QM is also being attacked. Unfortunately, the alternatives are not much better as it also require us to depart from what we consider as Rational and the Cardinal Principle of Science. DETERMINISM that do not violate Locality and Causality.

The reason I posed this question here is because the experiment that I have conducted using Circular Polarizers does not yield the result predicted by QM. Thanks to Mr. Homm, he has helped to solve a major construction problem by introducing the definition of a TRUE Right and TRUE Left Circular Polarizer that I could not find anywhere in any Physics Text.

As you can see, our discussion has now reach a crucial stage that we need to be very precise on what we meant. It will have quite significant repercussion between what we predict and what we will in fact observe.

In this respect, I will need Mr. Homm help in stating the prediction by QM (where he can use Malus Law if that is his preference) to state the prediction before I proceed to state the proof of Malus Law. Although the result is meant for Linear Polarizers, it is important that we understand it phenomenonlogically and how the mathematics is being derived that will be crucial for us to understand the crux of Circular Polarization.

Before I provide the proof for Malus Law (which is only an approximation), I would need you to help me by stating the probability intensity provided by QM. It is OK if you want to use Malus Law to state the value of the Intensity of light passing through this set of linear polarizers:
1)The polarizing axis of first Linear polarizer is aligned at 0 degree.
2)The second linear polarizer is aligned at 45 degree.
3)The third linear polarizer is aligned at 90 degree.
Question:
Determine the probability intensity of light passing through all the three linear polarizers.

It is important that you state the value so that we can make a comparison between what QM predict and what I will be predicting. After which, we can both do the experiment to satisfy ourselves whether QM prediction is correct or the one that I am proposing that rest squarely on Determinism.

I think we will need to address the issue of the Double Slits Experiement after we have thoroughly explored the subject on Circular Polarization. I hope you will be with us on this Journey of Exploration. Hopefully, we can all understand Nature a little better than continue to be chained to the myth of yesteryear. Personally, I am confident that Determinism is preserved. But this require us to understand the apparatus at the nanoscale and in the same way that we are trying to understand the topic on Polarization of Light.

Cheers.
Confused2
Hi hexa, Mr Homm et al,

Mostly to show I've been paying attention

LP (V)
(0,0)
(0,1)

My notation may be rubbish but hopefully self-consistent and produce the right numbers

we get an output of (0,1) < no loss which we expected.
Can we rotate this instead of the LP ?
( cos(45), sin (45) )
applying LP again
LP (V)
(0,0)
(0,1)

I think we get
( 0 , sin (45) ) <<<< 0.7 ?? not the same as Malus..

A simple mistake somewhere?

C2.
hexa
Hi Confused2,

I was hoping that Mr Homm could help by stating the prediction based on the straight forward application of Malus Law. Anyway there are many sites in the cyberworld that give a very good account of Malus Law. This site looks pretty good to me: ( http://scholar.hw.ac.uk/site/physics/topic6.asp?outline= ).

If we start with an intensity (Io), the passage of UNPOLARIZED light through the polarizer will half that intensity when it passes through the first x-linear polarizer:

(1) I[1] = (1/2)Io

Malus Law only applies when light passes through TWO SUCCESSIVE linear polarizers.
Hence, the light passing through the second linear polarizer inclined at 45 degree to the x-linear polarizer will have an intensity given by Malus Law as:

I[2] = I(1).cos(45 deg)^2

Expressed as the original intensity Io, we have:

(2) I[2] = (1/2)(Io). (cos(45 deg)^2)

Finally, the passage through the third y-linear polarizer inclined at 45 degree to the previous polarizer will mean that Malus Law will continue to apply. Hence the intensity through the y-linear polarizer will have this value:

I[3] = I[2].cos(45 deg)^2.

Expressed as the original intensity Io, we will have,

(3) I[3] = (1/2)(Io).(cos(45 deg)^4)

Hence, we can essentially derive a general equation to predict the intensity of light passing through a series of linear polarizers using Malus Law:

(4) I[n] = (1/2)(Io).{cos(θ)^[2(n-1)]}
where n = the number of linear polarizers
θ= the difference in angle between successive polarizers that we will fix for comparison.

The point that I wanted to highlight by this illustration is that QM essentially took Malus Law as another confirmation of its validity even though QM provide no generic explanation. By the way, Malus Law also do not have a generic explanation.
QM simply states that the state vector of photons passing through a polarizer inclined at an angle θ from an earlier linear polarizer as:

(5) lx'> = cosθlx> + sinθly>

Eliminating sinθ and retaining cosθ based on the quantum rule that l<xlx>l = 1
and l<ylx>l=0, we end up with the wave function of cosθ.
The square of the imaginery wave function l<θlx>l= cosθ will then give us the probability of the intensity predicted by Malus Law. Looks to me like QM is engaging in tautology.

With Eq(4) which I have derived from Malus Law, we are now in a position to extend the test on Malus Law against empirical observation. This is because any error will be grossly amplified by the power factor in Eq(4).

I hope you and the other members following this thread could now comment on Eq(4). Is this a valid test before I make an attempt to state the prediction using a deterministic approach that maintain photon as a real physical entity. One that has the following physical attributes, such as:
1) having a physical axis in our 3D-Space;
2) where we could use θ (on the x-y plane) to describe its orietation while translating through space along the z-axis;
3) where it will interact with molecules making up the polarizers as if they are real particles even though we are unable to measure its mass and charge (a key attributes that is associated with particle) but not forgetting that we can physically measure the momentum and energy associated with EACH photon;
4) and how the photons passing through a polarizer is guided statistically by the alignment of the molecular axis given by the angle σ relative to each photon;
5) and how angle σ determine the range of angles θ' that will in turn determine how they will pass through a subsequent polarizer inclined at another angle σ'.

In the meantime, I hope those with the apparatus can conduct the experiment to check the validity of Malus Law when we heighten the sensitivity using Eq(4). You don't need to have very sophisticated instruments. Just a lux. meter with sensitivity of 1 lux., a few linear polarizers and a stable light source.

Cheers.
mr_homm
Continuing to catch up:

@hexa, Oct. 29
QUOTE
I hesitated to bring spin into the discussion with Mr Homm until I am sure that there is a PHYSICAL axis (and not just a mathematical construct defined in Quantum Mechanics) that we can use to describe the physical state of a SINGLE PHOTON.

The question that I am raising is whether A PHOTON in one polarized state is distinguishable from another photon in another polarized state. If they are, then how do we distinguish them?

This is a tougher question than it first appears to be. Here are my thoughts on it:

First, "distinguishable" must mean that there is some experiment you can perform which will have observable different outcomes for these two individual photons. I think this much is very clear; I'm just stating it to make sure.

Next, is it required to perform just a single experiment, or could it possibly require multiple experiments to tell the photons apart? The trouble is, in standard QM you only get ONE TRY. This is because experiments cannot ask questions like "what state is the photon in?" They can only ask questions like "which one of THESE STATES is the photon in (for some specific list of states)?" That seems to be a basic limitation. No one has ever been able to devise an experiment that will just tell you exactly what a particle is doing, only experiments that select its behavior from a defined list of options.

In the case of photon polarization, what does this mean? Well, suppose you have two linearly polarized photons with axis angles θ1 and θ2. The only way to tell them apart is to see if one gets through a filter and the other doesn't. If you don't already know what these two angles are, you will not know how to orient your filter. Suppose you place the filter with an angle θ3. Then depending on the angles, one or the other photon might get through, or both, or neither. The experiment is inconclusive of course if both or neither get through. If one gets through but not the other, the experiment is still inconclusive, because photons that are not perfectly aligned with the filter still have some probability of getting through. (This is the standard QM interpretation. Because there is some probability that one photon gets through and the other doesn't EVEN IF their angles are equal, you therefore cannot infer that their angles are different in this case. In your hypothesis, it looks like two photons with identical angles MUST both get through the filter or neither get through.)

In the special case that θ1 = θ2 +/- 90 deg, then you can definitely tell the photons apart, because with the filter aligned so θ3 = θ1, the photon at angle θ1 will get through with 100% certainty, and the photon at angle θ2 will be stopped by the filter with 100% certainty. Thus they are clearly distinguishable.

If you are allowed to repeat the experiment with a series of photons (let's say you have prepared a source of photons at angle θ1 and another source at θ2), then you can certainly tell the sources apart by adjusting the filter angle until all the photons from one source get through and then observing that not all the photons from the other source get through. Since these are sources are repeatedly emitting identical photons, if the sources are different, the individual photons must be different. Note that you do not have to use bright lights here; you can have the sources emit photons one at a time.

Summary: If you can't repeat the test, then you can only tell photons apart with certainty if their polarization states are perpendicular. If you can repeat the test on a series of identical photons, then you can tell them apart easily.

It might seem strange that repetition is necessary, but this is not really anything new. Only if an experiment is repeatable is it considered valid anyway, so this does not change anything in the basic scientific method.

QUOTE (->
 QUOTE I hesitated to bring spin into the discussion with Mr Homm until I am sure that there is a PHYSICAL axis (and not just a mathematical construct defined in Quantum Mechanics) that we can use to describe the physical state of a SINGLE PHOTON.The question that I am raising is whether A PHOTON in one polarized state is distinguishable from another photon in another polarized state. If they are, then how do we distinguish them?

This is a tougher question than it first appears to be. Here are my thoughts on it:

First, "distinguishable" must mean that there is some experiment you can perform which will have observable different outcomes for these two individual photons. I think this much is very clear; I'm just stating it to make sure.

Next, is it required to perform just a single experiment, or could it possibly require multiple experiments to tell the photons apart? The trouble is, in standard QM you only get ONE TRY. This is because experiments cannot ask questions like "what state is the photon in?" They can only ask questions like "which one of THESE STATES is the photon in (for some specific list of states)?" That seems to be a basic limitation. No one has ever been able to devise an experiment that will just tell you exactly what a particle is doing, only experiments that select its behavior from a defined list of options.

In the case of photon polarization, what does this mean? Well, suppose you have two linearly polarized photons with axis angles θ1 and θ2. The only way to tell them apart is to see if one gets through a filter and the other doesn't. If you don't already know what these two angles are, you will not know how to orient your filter. Suppose you place the filter with an angle θ3. Then depending on the angles, one or the other photon might get through, or both, or neither. The experiment is inconclusive of course if both or neither get through. If one gets through but not the other, the experiment is still inconclusive, because photons that are not perfectly aligned with the filter still have some probability of getting through. (This is the standard QM interpretation. Because there is some probability that one photon gets through and the other doesn't EVEN IF their angles are equal, you therefore cannot infer that their angles are different in this case. In your hypothesis, it looks like two photons with identical angles MUST both get through the filter or neither get through.)

In the special case that θ1 = θ2 +/- 90 deg, then you can definitely tell the photons apart, because with the filter aligned so θ3 = θ1, the photon at angle θ1 will get through with 100% certainty, and the photon at angle θ2 will be stopped by the filter with 100% certainty. Thus they are clearly distinguishable.

If you are allowed to repeat the experiment with a series of photons (let's say you have prepared a source of photons at angle θ1 and another source at θ2), then you can certainly tell the sources apart by adjusting the filter angle until all the photons from one source get through and then observing that not all the photons from the other source get through. Since these are sources are repeatedly emitting identical photons, if the sources are different, the individual photons must be different. Note that you do not have to use bright lights here; you can have the sources emit photons one at a time.

Summary: If you can't repeat the test, then you can only tell photons apart with certainty if their polarization states are perpendicular. If you can repeat the test on a series of identical photons, then you can tell them apart easily.

It might seem strange that repetition is necessary, but this is not really anything new. Only if an experiment is repeatable is it considered valid anyway, so this does not change anything in the basic scientific method.

We know that an electron essentially has two and only two spin states. Spin up or spin down that can be demonstrated experimentally on a Stern Gerlach Apparatus by splitting one electron beam into two electron beams by a magnetic field. I suppose we could further assume (although not entirely correct) that the spin up has a physical reality represented by an electron physically spinning in the clockwise direction and the spin down state by the electron spinning in the counter-clockwise direction (like our earth rotating on its axis). I must qualify here that this perception of the spin state of an electron is rejected in Quantum Theory for the primary reason that it violates the speed of light, c dictated by the Theories of Relativity. The axes of these spins can then be used as the PHYSICAL axis in our 3D-world. Notwithstanding what is generally accepted, would it be more reasonable to assume that the Physical Axis of Each electron in the unpolarized state has a distribution that can be described by an angle in the plane orthogonal to the direction of translation? That any electron that is spin up may have the PHYSICAL axis pointed say at an angle θ, where θ is an angle between 0 deg <θ<180 deg; and that the spin down state will have their Physical Axis pointed at any angle 180 deg <θ<360 deg?

Yes, the picture of the rotating electron cannot work. Given its mass and the upper limit on its size from scattering experiments, it would need to spin so fast that its surface moved faster than c in order to generate the observed amount of angular momentum.

As to the physical axis, QM requires the uncertainty principle to be universally valid, so it cannot be true that spin UP means that the electron's axis is aligned upwards. The total angular momentum of a particle is sqrt(l(l+1)) in units of h/2pi. An electron is a spin 1/2 particle, which means that its spin quantum number l = 1/2. Therefore, the total angular momentum L = sqrt(1/2(3/2)) = sqrt(3)/2.

The reason for this is that the angular momentum measurement operators in the x y and z directions do not commute. Non-commuting operators are always related by an uncertainty principle, so if you measure the angular momentum in the z direction, you must have a minimum uncertainty of 1 (again in units of h/2pi) in the x and y directions. With a total angular momentum magnitude of sqrt(3)/2, and a component of +/- 1/2 in the z direction, the component in the xy plane has a magnitude 1/sqrt(2). Since the direction of the xy component of the angular momentum is completely undefined (because it is completely uncertain), you can split this xy component into x and y components with values of 1/2. Therefore, the x and y components could be as much as 1/2 or as little as -1/2, so the uncertainty is 1 as required. Summary: spin up means that the z component of the angular momentum vector is +1/2 and there is a vector component of magnitude sqrt(3)/2 and undefined direction in the xy plane.

A similar calculation shows that a photon should have 3 spin states, with z components of spin being +1, 0, or -1, and a total angular momentum vector magnitude sqrt(1(1+1)) = sqrt(2). However, the 0 state turns out to be impossible for other reasons (which I'll discuss later, perhaps, if there is any interest). Unlike an electron, a photon always has a natural axis. Because the electron is massive and travels at speeds < c, there is always a reference frame in which it is at rest, and in this frame, an observer is free to define any three perpendicular directions in space as the x y and z axes. So for an electron, "up" is whatever direction you CHOOSE to measure its spin along.

Photons, on the other hand, always travel at speed = c, so there is no reference frame where they appear stationary. There is always a direction they are traveling, and this direction is therefore physically different from directions in which the photon is not traveling. The mere existence of this physical difference is equivalent to a measurement, since a photon's behavior differs in this direction from its behavior in all other directions. Therefore, the photon's spin is AUTOMATICALLY always measured along its direction of travel. The observer has no choice in the matter. Photons may have their spins aligned FORWARD or BACKWARD along their path, analogous to the electron's spin being UP or DOWN.

QUOTE
Can we then describe the spin state of A PHOTON by a similar description? If so, how do we reconcile this with the four polarized states (2 linear and 2 circular polarized states) with the spin mechanism described here?

FORWARD photons are |R> photons, and BACKWARD photons are |L> photons. The state space of photon polarization is only 2 dimensional, so the other polarizations (linear, elliptical) are just linear combinations of these. In other words, from the QM of photons as particles of spin 1, the eigenvectors of the angular momentum measurement are |R> and |L>, and this set of states forms a basis for the space of polarization states. Remember though, that ANY two independent states could be used as a basis; just because these two arise as eigenvectors of a well-known operator, that does not make them more fundamental than any other polarization states. I could find another operator whose eigenvectors were |V> and |H> if I wanted, and then I could claim (with equal validity or lack thereof) that these two were fundamental.

@hexa, Oct. 31
QUOTE (->
 QUOTE Can we then describe the spin state of A PHOTON by a similar description? If so, how do we reconcile this with the four polarized states (2 linear and 2 circular polarized states) with the spin mechanism described here?

FORWARD photons are |R> photons, and BACKWARD photons are |L> photons. The state space of photon polarization is only 2 dimensional, so the other polarizations (linear, elliptical) are just linear combinations of these. In other words, from the QM of photons as particles of spin 1, the eigenvectors of the angular momentum measurement are |R> and |L>, and this set of states forms a basis for the space of polarization states. Remember though, that ANY two independent states could be used as a basis; just because these two arise as eigenvectors of a well-known operator, that does not make them more fundamental than any other polarization states. I could find another operator whose eigenvectors were |V> and |H> if I wanted, and then I could claim (with equal validity or lack thereof) that these two were fundamental.

@hexa, Oct. 31
2.0 )The effect of passing a stream of unpolarized photons through a QWP:
2.1) The unpolarized photons source will have a mixture of photons with the angle θ of each photon spread in all directions—0 deg. < θ < 360 deg.

This sounds acceptable to me, provided each photon also has a phase number. Angle plus phase should provide a full description of the photon state.
QUOTE

2.2) The function of the QWP is to reorganize the arrays of photons into two linearly polarized states: the x and the y linear polarized states with no loss to its original intensity (if we assume ideal conditions).

This is also acceptable. "Reorganize" sounds like it is sorting them out separately from each other, which is more or less what is happening. A more accurate statement might be that it "treats x and y linear polarized states differently," which implies the separation.
QUOTE (->
 QUOTE 2.2) The function of the QWP is to reorganize the arrays of photons into two linearly polarized states: the x and the y linear polarized states with no loss to its original intensity (if we assume ideal conditions).

This is also acceptable. "Reorganize" sounds like it is sorting them out separately from each other, which is more or less what is happening. A more accurate statement might be that it "treats x and y linear polarized states differently," which implies the separation.

2.3) Under ideal conditions, a Right QWP is no different from a Left QWP. Since we continue to find photons with all angles from 0 to 360 deg.

Yes. We also continue to find random phase numbers. While individual photons are affected by the QWP, the statistics of the overall beam of light are not changed, so full intensity unpolarized light appears at the output.
QUOTE

2.4) If the polarizing axes of the QWP is not exactly orthogonal, then this would give rise to an uneven distribution of photons at the various orientations. In this case, there will be one stream of x-linear polarized state and another of y’-linear polarized state and not the y-linear polarized state that is orthogonal to the x-linear polarized state.
This would then imply that the photons passing through a Right QWP is not exactly the same as a Left QWP. One would have the extraordinary ray rotated to the right of the ordinary ray, while the other will be to the left.

Here I do not know what you mean. A QWP has only one axis, the optic axis. The effect of the QWP is to slow down light that is polarized along the axis relative to light that is polarized perpendicular to the axis.

Note the similarity to linear polarizing filters:
LP filters treat polarizations differently. Light polarized along the LP axis passes through; light polarized perpendicular to the LP axis does not.
QWPs treat polarizations differently. Light polarized along the QWP axis is slowed; light polarized perpendicular to the QWP axis is not.
QUOTE (->
 QUOTE 2.4) If the polarizing axes of the QWP is not exactly orthogonal, then this would give rise to an uneven distribution of photons at the various orientations. In this case, there will be one stream of x-linear polarized state and another of y’-linear polarized state and not the y-linear polarized state that is orthogonal to the x-linear polarized state.This would then imply that the photons passing through a Right QWP is not exactly the same as a Left QWP. One would have the extraordinary ray rotated to the right of the ordinary ray, while the other will be to the left.

Here I do not know what you mean. A QWP has only one axis, the optic axis. The effect of the QWP is to slow down light that is polarized along the axis relative to light that is polarized perpendicular to the axis.

Note the similarity to linear polarizing filters:
LP filters treat polarizations differently. Light polarized along the LP axis passes through; light polarized perpendicular to the LP axis does not.
QWPs treat polarizations differently. Light polarized along the QWP axis is slowed; light polarized perpendicular to the QWP axis is not.

2.5) The smaller the difference in angle, σ between the two polarizing axes that make up the QWP, the greater will be the ellipticity of the photons passing through the QWP.

I also cannot understand what you mean here, since I am not aware of there being TWO polarizing axes in a QPW. Can you please clarify this?

Out of time once again -- at least I have finally caught up to the current month!

--Stuart Anderson
Montec
Hello all

What would happen if you cascaded two or more Stern Gerlach Apparatuses behind each other and rotated their orientation to 45deg, 90deg, etc.? Would each apparatus split the electron beam or not?

hexa
Hi Mr Homm,

QUOTE

QUOTE (->
 QUOTE Quote hexa:The question that I am raising is whether A PHOTON in one polarized state is distinguishable from another photon in another polarized state. If they are, then how do we distinguish them? This is a tougher question than it first appears to be.

The problem arises from my attempt to see whether we could visually distinguish one photon in one polarized state from another even though we may never know the details of the bolts and nuts that goes into the making of a Single Photon. This stem from my personal belief that if a Photon is Real, then it must also have a PHYSICAL existence that is capable of being described like a marble, a plate, a ball or a planet. It must also have a shape, a size and a mass even though the means available to measure any of these attributes are not available to us. Thanks for highlighting this difficulties in your latest post.

Before we attempt to visualize a photon, perhaps you may want to ask the following questions:
1) Is Light a particle or a wave?
Answer: I think the answer has been pretty much decided by the Michelson and Morley Experiment; Max Planck account of the Black body radiation and Einstein account of the photoelectric effect. Light is a PARTICLE.
2) If it is a particle, how do you account for the observation in the Double Slits Experiment?
Answer:This is a Topic by itself. You may want to refer to the discussion in another thread. But if you want to know what I think about this topic Now, you can backtrack to my earlier discussion with Schneibster on the experiment conducted by the scientists in Hitachi Research Lab. I will return to this topic after we have thoroughly explored Polarization of Light.
3) If it is a particle, why is it that we are unable to measure its mass or charge?
Answer: It is simply because the APPARATUS that we can devise relies on electric field and magnetic field to measure mass or charge. Photon does not feel the effect of either of these fields BECAUSE of the Relativistic Effect. I will discuss this topic a little later.
4) Would it be reasonable to assume that one photon that has exactly the same amount of energy or momentum would look exactly the same as the next photon that has exactly the same energy or momentum?
5) Can we visually distinguish one photon that has more energy or momentum than another photon like a deck of cards or a box of marbles?
Answer: I think it is more probable that it has the appearance of a deck of cards based on the information on polarization of light.
6) If we assume that a photon is more like a deck of cards than a box of marbles, can we then attach a PHYSICAL AXIS that is NORMAL to the face of the cards to describe the orientation of the cards in Euclidean space?
Answer: Why not? Mathematically, that is how we define a plane.
7) If that can be done, are we able to describe the orientation of a photon in Cartesian coordinates that translate along the z-axis?
8) Since it is a deck of cards, is it reasonable to assume that the photon looks exactly the same if we flip the cards by 180 degree?
9) If this is possible, how are we going to distinguish a packet of photon that passes through a x-linear polarizer from another that passes through a y-linear polarizer.
Answer: If we define each photon as having an angle θ that this PHYSICAL AXIS makes on the x-y plane, then we can describe a ray of unpolarized photons as having angles that are distributed evenly from 0 deg < θ <360 deg.
The presence of a x-linear polarizer with its molecular axis aligned along the x-axis will allow photons with angles 0 deg < θ <45 deg. 135 deg < θ <225 deg. 315 deg < θ <360 deg. to pass through the x-linear polarizer. The distribution of the photon through the x-linear polarizer is not uniform. It has a bell curve distribution with a higher concentration for those closer to the x-axis. I will discuss this in greater details in my next post. In the meantime, please take it as correct. This is also important for us to understand why Malus Law works even though it is only an approximation.
With this proposition, you can see that a random population can be neatly divided into the Xs or the Ys. But makes no mistake that one photon in this X vector state may be different from another photon in the same X vector state.
With this, you can see that prediction using this visual proposition will also obtain the QM predictions of l<Xl X>l = 1 and l<YlX>l=0.
10) How are we going to distinguish one Right Circularly polarized photon from a Left circularly polarized photon?
Answer: We Can’t! We can’t distinguish it for a SINGLE PHOTON. Collectively, a circularly polarized group of photons is more organized than a beam of unpolarized photon. It has both the populations of the Xs and the Ys. The only difference, is that the Xs is concentrated along the x-molecular axis and the Ys is concentrated along the y-molecular axis. The two molecular axes found in the QWP need not be orthogonal.
11) How do you explain that a Left Circular polarizer will cut off the photons coming out from a Right Circular Polarizer?
Answer: The short answer is that there is no generic Circular Polarizer. It need the Linear Polarizer to do the job. The QWP can’t play that role. It merely direct the X and Y populations along the two molecular axes. Since you have played around with calcite crystal before, I am sure that you must be aware that it is quite difficult to recombine the ordinary and extraordinary ray after it has been split by a previous calcite crystal.
To answer this question, I will use the standard apparatus that involves the use of a mirror. The forward path of a ray of light (unpolarized) passing through the x-linear polarizer(M1) followed by the QWP(M2) is then reflected back to the QWP (M3) before passing through the original x-linear polarizer (M4).
This is what happen:
A] lψ> -----> M1 -----> lx>
B] lx> -----> M2 ----> lX> + lY>
C] lX> + lY> -----> M3 ----> ly>
D] ly> -----> M4 ----> 0
Notes: The X and Y in [C] is laterally inverted. The M3 will further rotate the photons into the ly> vector state.

From the above explanation, you can see that if we were to rotate M4, then it is unlikely that we will be able to stop the ly> state photons from passing through the linear polarizer. The experiment that I have carried out using two different sets of circular polarizers (based on your suggestion of a TRUE Right and a TRUE Left Circular Polarizer) confirmed this proposition. It is NOT ROTATION INVARIANT as what is suggested in QM. Please verify my result.

Please excuse me for the digression. But I think it was necessary for you to understand the reason behind my postulates. With the above explanation, I will now attempt to clarify the queries that you have raised in this post:
QUOTE

QUOTE (->
 QUOTE Quote Hexa:2.4) If the polarizing axes of the QWP is not exactly orthogonal, then this would give rise to an uneven distribution of photons at the various orientations. In this case, there will be one stream of x-linear polarized state and another of y’-linear polarized state and not the y-linear polarized state that is orthogonal to the x-linear polarized state.This would then imply that the photons passing through a Right QWP is not exactly the same as a Left QWP. One would have the extraordinary ray rotated to the right of the ordinary ray, while the other will be to the left. Here I do not know what you mean. [1]A QWP has only one axis, the optic axis. [2]The effect of the QWP is to slow down light that is polarized along the axis relative to light that is polarized perpendicular to the axis.Note the similarity to linear polarizing filters:[3]LP filters treat polarizations differently. Light polarized along the LP axis passes through; [4]light polarized perpendicular to the LP axis does not.[5]QWPs treat polarizations differently. Light polarized along the QWP axis is slowed;[6] light polarized perpendicular to the QWP axis is not.

Please excuse me for not making myself understood.
[1] I am afraid you may have confused the terms used in classical optics with our discussion here.
I think many physicists also over-simplifies the problem by not looking deep enough into the Construction of the APPARATUS. If you ask an expert in material science, he will tell you that there are many arrangements within a crystal. There could be the AX crystal structure as well as the ABX crystal structure. The packing arrangement could be the Simple cubic, FCC or BCC. Next, we need to consider the shape of each unit of crystal: cubic, hexagonal, tetragonal, rhombohedral, orthorhombic, monoclinic and triclinic. Each of these molecular arrangements will mean that the photon interacting with it will emerge from the array of atoms differently. I am SUGGESTING that there are TWO distinct axes that are present in the QWP that ROTATES the photons one way or the other.
[2] I don’t think it is technically correct to suggest that light “slow down”. It does not. This is the fallacy of the Fermat Principle. I think the classical explanation on refraction of light is also incorrect. Light being light will always travels at the speed c. It can be made to take a longer path that will give rise to the perception that light “slow down”. Like refraction of different frequency light through a prism. Hence, what decide that one photon take the vertical path while another take the horizontal path, must be decided by the ATOMS interacting with it. The only reasonable explanation is that their paths are determined by their molecular alignment together with the physical state of the photons prior to interacting with the APPARATUS. In the case of a QWP, there are two DISTINGUISHABLE molecular axes that will interact with an unpolarized light. Figuratively, there are TWO doors in QWP instead of one in the Linear polarizer.
[3]Agree.
[4] They are generally reflected than absorbed. You can test this using a laser beam.
[5] Disagree—please refer to the reason stated in [2]. But you are correct to state that the time it takes to emerge from the QWP is different from another photon that takes the other path. The phase factor is an irrelevant consideration.
[6] I don't think speed is a correct consideration.

QUOTE

QUOTE (->
 QUOTE Quote Hexa:2.5) The smaller the difference in angle, σ between the two polarizing axes that make up the QWP, the greater will be the ellipticity of the photons passing through the QWP. I also cannot understand what you mean here, since I am not aware of there being TWO polarizing axes in a QPW. Can you please clarify this?

Again, please accept my apology for not stating it clearly.
I have used angle θ to define the generic state of a photon. The angle σ is used to define the orientation of the photon relative to the molecular axis of the atoms making up the linear polarizer. A photon may have a generic angle of θ=80 deg. But if the molecular axis (polarizing axis) of a linear polarizer is positioned at 60 deg., then the angle σ of the photon relative to the molecular axis is 20 degree. It is this angle that determine whether or not this particular photon will emerge from this linear polarizer. Not the generic angle θ.

If instead of a linear polarizer, we now use a QWP with two molecular axes.
This single photon will have two angles σ that are approximately orthogonal to one and the other. Let us use σ1 and σ2 to distinguish the two angles of ONE photon relative to the TWO axes. If σ1= 30 deg and σ2=60 deg, then this PHOTON will emerge from the QWP by taking the path of least resistance, ie. the one that it makes an angle of σ1= 30.
If the above explanation can be accepted, then we can look at the ellipticity of the QWP. Basically, the alignment of the two molecular axes in a QWP need not be orthogonal. The more acute the angle that one axis makes with the other, the greater will be the ellipticity of the QWP.
I am sorry for the confusion that I have generated.
I hope with the above explanation you can now better critique what I will be proposing to examine the issue surrounding Circular Polarization.

Finally, please pardon me for seeking this clarification:
QUOTE

It is my OPINION that current QM gives a pretty good account of circular polarization, which agrees with experimental data.

Can I assume that your OPINION is not based on the experiments that you have conducted personally with regards to Circular Polarization of Light?

Cheers.

Hi Montec,

You raised a very important question to the discussion that we are having here. Perhaps Mr Homm, Confused2 and other proficient in QM may want to provide the explanation before I attempt to provide you an alternative explanation based on what we will physically observed in a Stern Gerlach Apparatus.

Cheers.
mr_homm
@Confused2, Nov.1
QUOTE
(hexa said:) 2.2) The function of the QWP is to reorganize the arrays of photons into two linearly polarized states: the x and the y linear polarized states with no loss to its original intensity (if we assume ideal conditions).

Doesn't a QWP just do a (lossless) linear operation on θ ? With random in don't you just get (different) random out?

Not really. In my previous post I described the action of a QWP, so here I'll just mention that it does not affect θ directly. Rather, it delays one polarization direction relative to the other (perpendicular) direction. This may or may not affect angle or degree of ellipticity; it depends on the value of θ. If θ happens to be perpendicular to the delaying axis of the QWP, then the plate does essentially nothing to the light. If θ happens to be parallel to the delaying axis, then it is delayed (of course!), but again this produces no change in its polarization angle.

If θ is some other angle, then the vector along the θ direction is resolved into components parallel and perpendicular to the delaying axis, and the parallel component is delayed by 1/4 wavelength. (These components are in QM the components of the photon's state vector, and in classical EM they are the components of the E field vector -- two interpretations, but the resulting predictions agree.) Since the components are now out of phase, the light is clearly not plane polarized anymore. If θ happens to be exactly 45 degrees away from the delaying axis, then the delayed and undelayed components will have equal magnitudes. This is the recipe for a circularly polarized light beam. Whether the polarization is right or left circular depends on whether θ is 45 degrees CCW or 45 degrees CW of the delaying axis.

@hexa, Nov. 1
QUOTE (->
 QUOTE (hexa said:) 2.2) The function of the QWP is to reorganize the arrays of photons into two linearly polarized states: the x and the y linear polarized states with no loss to its original intensity (if we assume ideal conditions).Doesn't a QWP just do a (lossless) linear operation on θ ? With random in don't you just get (different) random out?

Not really. In my previous post I described the action of a QWP, so here I'll just mention that it does not affect θ directly. Rather, it delays one polarization direction relative to the other (perpendicular) direction. This may or may not affect angle or degree of ellipticity; it depends on the value of θ. If θ happens to be perpendicular to the delaying axis of the QWP, then the plate does essentially nothing to the light. If θ happens to be parallel to the delaying axis, then it is delayed (of course!), but again this produces no change in its polarization angle.

If θ is some other angle, then the vector along the θ direction is resolved into components parallel and perpendicular to the delaying axis, and the parallel component is delayed by 1/4 wavelength. (These components are in QM the components of the photon's state vector, and in classical EM they are the components of the E field vector -- two interpretations, but the resulting predictions agree.) Since the components are now out of phase, the light is clearly not plane polarized anymore. If θ happens to be exactly 45 degrees away from the delaying axis, then the delayed and undelayed components will have equal magnitudes. This is the recipe for a circularly polarized light beam. Whether the polarization is right or left circular depends on whether θ is 45 degrees CCW or 45 degrees CW of the delaying axis.

@hexa, Nov. 1
A QWP do have a distinct molecular arrangement that distinguish it from another material that do not have such regimental arrangement.
However, you are correct to state that A PHOTON with one Random angle will be dispersed to another random angle through a QWP or a linear polarizer. But in the Linear polarizer or a QWP, the final state of A PHOTON (the permissible range of angles θ) is governed by the molecular axes that make up these filters.

You have asked a very important question.
By 2.2, I am stating that the molecules making up the QWP has two distinct physical alignments: at 0 (and 180) deg. and the other at 90 (and 270) deg. This is unlike a linear polarizer where there is only one alignment.

If a x-linear polarizer would allow the passage of those photons falling in the range 0 deg. < θ < 45 deg, 135 deg. < θ < 225 deg and 315 deg. < θ < 360 deg; while a y-linear polarizer for those photons 45 deg. < θ < 135 deg and 225 deg. < θ < 315 deg, then the QWP would allow photons of all angles to pass through it and distribute them among all the angles, but characterised by the two principal axes. The reason I said that they are identical is because the y(Right) axis and the y(Left) axis will coincide with one another if the two molecular axes are orthogonal (based on the assumption that we fix the x-axis as common to both the QWP).

To reiterate, if the two molecular axes making up the QWP are truly orthogonal, it does not matter if the photons have been rotated clockwise or anticlockwise in the process of passing through the QWP. All the photons will be distributed principally along the two molecular axes.

However, if the two molecular axes of the QWP are not orthogonal, then the photons rotated to the right and the photons rotated to the left will be different. In both cases, all the photons that fall on the QWP will pass through it with no loss in intensity (again assuming ideal condition). But the distribution of photons in the random state passing through a Left QWP is different from one that is passing through a Right QWP.

Let me illustrate this by an example. If one of the molecular axis of a QWP is at 0 deg. a Right QWP will have the other molecular axis pointing at 80 deg or less. In the case of a Left QWP, the other molecular axis may be pointing at 100 deg. or more. The net effect is that the photons (in the random state) passing through a Right QWP will be quite different from that passing through a Left QWP.

This description of what a QWP does and how it does it is so completely different from my understanding that I can't even recognize what most of it is. As I understand it:

a QWP is a crystal, therefore it DOES NOT HAVE MOLECULES,
it has only ONE AXIS,
it DOES NOT ROTATE polarization angle, and
there is only ONE TYPE of QWP.

Is your account of how a QWP works based on some reference you could point me to? Or is it part of your alternative hypothesis? In the latter case, I'll accept it as an assumption about how QWP might work, but we'll have to investigate the consequences of this assumption and see whether they agree with experiment. Is this agreeable?

I am once again out of time, so I will comment on later posts separately.

--Stuart Anderson
Montec
Hi hexa

I ran across this link posted by jal in this thread :http://forum.physorg.com/index.php?showtopic=6587

This may give us some incite to what is actually happening at the filters. If this paper is creditable then the crystal structures of the QWP and LP plates is summing the available EM energy at that point. The summing action varies with the optic axis of the crystal.

I am still trying to work out how the QWP can delay just one vector of the linear polarized light. Something to do with cavity resonance and EM density within the plate I think.

Confused2
Chasing up Emilio Panarella.. (cited by Roychoudhuri )

http://en.wikipedia.org/wiki/Physics_Essays
QUOTE (wiki+)

As a result, many of the theories published in Physics Essays are fringe science, rarely published in other scientific journals, and are often considered pseudoscience. Most publications in Physics Essays are rarely cited by other authors in other scientific journals.

-C2.
hexa
Hi Mr Homm,

QUOTE

Is your account of how a QWP works based on some reference you could point me to? Or is it part of your alternative hypothesis? In the latter case, I'll accept it as an assumption about how QWP might work, but we'll have to investigate the consequences of this assumption and see whether they agree with experiment. Is this agreeable?

Yes. There are some references available in the public domain where we can infer from it.
Take a look at this paper entitled Three-dimensional molecular orientation with combined electrostatic and elliptically polarized laser fields in Phys. Rev. A 72, 063401 (2005) by these authors: (Haruka Tanji, Shinichirou Minemoto, and Hirofumi Sakai ).
There is also this paper entitled Controlling Two-Center Interference in Molecular High Harmonic Generation in Phys. Rev. Lett. 95, 153902 (2005) by (C. Vozzi, F. Calegari, E. Benedetti, J.-P. Caumes, G. Sansone, S. Stagira, and M. Nisoli ).
But I think the idea of molecular axis is most significantly illustrated from this paper, entitled "Optical polarization grating induced liquid crystal micro-structure using azo-dye command layer" in Vol.14. No.22/OPTICS EXPRESS 10558. Take a look at the URL ( http://www.opticsexpress.org/DirectPDFAcce...CFTOKEN=1471927 ).

Having said that, I must concede that what I have proposed in our discussion here is an ALTERNATIVE HYPOTHESIS to the postulates used in Quantum Mechanics. You may call it hand waving if you like. It is an assumption on how QWP might work which I have investigated based on EXPERIMENT that I have conducted. As I have stated earlier, the experiment that I had conducted based on QM prediction does not seem to agree with my observation.

Let me share with you the experimental data that I have obtained using a circular polarizer followed by a linear polarizer that act as an analyzer.
QUOTE (->
 QUOTE Is your account of how a QWP works based on some reference you could point me to? Or is it part of your alternative hypothesis? In the latter case, I'll accept it as an assumption about how QWP might work, but we'll have to investigate the consequences of this assumption and see whether they agree with experiment. Is this agreeable?

Yes. There are some references available in the public domain where we can infer from it.
Take a look at this paper entitled Three-dimensional molecular orientation with combined electrostatic and elliptically polarized laser fields in Phys. Rev. A 72, 063401 (2005) by these authors: (Haruka Tanji, Shinichirou Minemoto, and Hirofumi Sakai ).
There is also this paper entitled Controlling Two-Center Interference in Molecular High Harmonic Generation in Phys. Rev. Lett. 95, 153902 (2005) by (C. Vozzi, F. Calegari, E. Benedetti, J.-P. Caumes, G. Sansone, S. Stagira, and M. Nisoli ).
But I think the idea of molecular axis is most significantly illustrated from this paper, entitled "Optical polarization grating induced liquid crystal micro-structure using azo-dye command layer" in Vol.14. No.22/OPTICS EXPRESS 10558. Take a look at the URL ( http://www.opticsexpress.org/DirectPDFAcce...CFTOKEN=1471927 ).

Having said that, I must concede that what I have proposed in our discussion here is an ALTERNATIVE HYPOTHESIS to the postulates used in Quantum Mechanics. You may call it hand waving if you like. It is an assumption on how QWP might work which I have investigated based on EXPERIMENT that I have conducted. As I have stated earlier, the experiment that I had conducted based on QM prediction does not seem to agree with my observation.

Let me share with you the experimental data that I have obtained using a circular polarizer followed by a linear polarizer that act as an analyzer.

Objective
To investigate the intensity of light passing through a circular polarizer followed by a linear polarizer when the linear polarizer is rotated relative to the circular polarizer.
The Apparatus:
M1 = linear polarizer ; M2 = QWP; M3=QWP and a Lux. meter with a resolution of 1 lux.
The Procedures
The polarizing axis of M1 is set along the x-axis.
Pass a steady source of Light (unpolarized) through M1, M2 and M3.
Rotate the polarizing axis of M3 starting from 0 degree by giving it an anti-clockwise rotation of 11.25 deg.
Measure the corresponding intensity using a lux. meter.

QUOTE

1) 0 deg. = 315 lux
2) 11.25 deg. = 298 lux.
3) 22.50 deg. = 283 lux.
4) 33.75 deg. = 273 lux.
5) 45.00 deg. = 266 lux.
6) 56.25 deg. = 264 lux. (Minimum)
7) 67.50 deg. = 267 lux.
8) 78.75 deg. = 276 lux.
9) 90.00 deg. = 287 lux.
10) 101.25 deg. = 299 lux.
11) 112.50 deg. = 313 lux.
12) 123.75 deg. = 320 lux.
13) 135.00 deg. = 326 lux.
14) 146.25 deg. = 329 lux. (Maximum)
15) 157.50 deg. = 326 lux.
16) 168.75 deg. = 318 lux.
17) 180.00 deg. = 309 lux.

Based on result obtained from this experiment, do you think it is reasonable for me to conclude as what I have done in my previous post:
QUOTE (->
 QUOTE Readings1) 0 deg. = 315 lux2) 11.25 deg. = 298 lux.3) 22.50 deg. = 283 lux. 4) 33.75 deg. = 273 lux. 5) 45.00 deg. = 266 lux. 6) 56.25 deg. = 264 lux. (Minimum)7) 67.50 deg. = 267 lux. 8) 78.75 deg. = 276 lux. 9) 90.00 deg. = 287 lux. 10) 101.25 deg. = 299 lux. 11) 112.50 deg. = 313 lux. 12) 123.75 deg. = 320 lux. 13) 135.00 deg. = 326 lux. 14) 146.25 deg. = 329 lux. (Maximum)15) 157.50 deg. = 326 lux. 16) 168.75 deg. = 318 lux. 17) 180.00 deg. = 309 lux.

Based on result obtained from this experiment, do you think it is reasonable for me to conclude as what I have done in my previous post:

11) How do you explain that a Left Circular polarizer will cut off the photons coming out from a Right Circular Polarizer?
Answer: The short answer is that there is no generic Circular Polarizer. It need the Linear Polarizer to do the job. The QWP can’t play that role. It merely direct the X and Y populations along the two molecular axes. Since you have played around with calcite crystal before, I am sure that you must be aware that it is quite difficult to recombine the ordinary and extraordinary ray after it has been split by a previous calcite crystal.
To answer this question, I will use the standard apparatus that involves the use of a mirror. The forward path of a ray of light (unpolarized) passing through the x-linear polarizer(M1) followed by the QWP(M2) is then reflected back to the QWP (M3) before passing through the original x-linear polarizer (M4).
This is what happen:
A] lψ> -----> M1 -----> lx>
B] lx> -----> M2 ----> lX> + lY>
C] lX> + lY> -----> M3 ----> ly>
D] ly> -----> M4 ----> 0
Notes: The X and Y in [C] is laterally inverted. The M3 will further rotate the photons into the ly> vector state.

Cheers.

Hi Montec,

Thanks for the reference.
In the paper, C, Roychoudhuri have highlighted two possibilities on how A PHOTON could be perceived. One by Planck and the other by Einstein. Looks like the deck of cards that I am proposing is closer to that proposed by Planck.

Cheers.

Hi Confused2,

Thanks for the reference.
Do you think the last paper that I have quoted above by Vladimir Presnyakov, and others from OPTICS EXPRESS falls into the same category as the site that you have posted here?

Cheers.
mr_homm
@hexa, Nov. 2

QUOTE
Before we can understand Circular Polarization, we need to be familiar with this other property about the QWP. While a QWP can split a beam of light into two beams (Ordinary and extraordinary rays) it can also be used to recombine the two rays back into a single beam. This can be demonstrated by placing one calcite crystal sequentially to the first calcite crystal. Do it to see if what I say is true. A word of caution is that the geometry of the calcite crystals must be exactly right to yield this observation.

I agree with this mostly, but I would note that the basic material here is a calcite crystal, and whether it is acting as a QWP or not depends on how it is cut. If it is cut at the proper angle, it will act to split light into two separated beams with perpendicular polarizations, as you say. However, it is not then acting as a QWP. On the other hand, when it is cut so that it acts as a QWP, it will not split light into two beams, so it is not then acting as a polarizer.

By way of analogy, you could take a piece of wood and carve it to form a fork or a spoon. When it is cut in the shape of a spoon, it is not a fork, and vice versa. It would be very confusing if you carved it into the shape of a spoon and then called it a fork, just because that is something it is commonly carved into. In the same way, when calcite is cut into a QWP it is not a polarizer, and when it is cut into a polarizer, it is not a QWP. It is confusing to cut calcite into a polarizer and then refer to it as a QWP. I'm just mentioning this to avoid possible confusion.

QUOTE (->
 QUOTE Before we can understand Circular Polarization, we need to be familiar with this other property about the QWP. While a QWP can split a beam of light into two beams (Ordinary and extraordinary rays) it can also be used to recombine the two rays back into a single beam. This can be demonstrated by placing one calcite crystal sequentially to the first calcite crystal. Do it to see if what I say is true. A word of caution is that the geometry of the calcite crystals must be exactly right to yield this observation.

I agree with this mostly, but I would note that the basic material here is a calcite crystal, and whether it is acting as a QWP or not depends on how it is cut. If it is cut at the proper angle, it will act to split light into two separated beams with perpendicular polarizations, as you say. However, it is not then acting as a QWP. On the other hand, when it is cut so that it acts as a QWP, it will not split light into two beams, so it is not then acting as a polarizer.

By way of analogy, you could take a piece of wood and carve it to form a fork or a spoon. When it is cut in the shape of a spoon, it is not a fork, and vice versa. It would be very confusing if you carved it into the shape of a spoon and then called it a fork, just because that is something it is commonly carved into. In the same way, when calcite is cut into a QWP it is not a polarizer, and when it is cut into a polarizer, it is not a QWP. It is confusing to cut calcite into a polarizer and then refer to it as a QWP. I'm just mentioning this to avoid possible confusion.

The standard construction (described in most books) of a Circular polarizer essentially comprise of a Linear Polarizer followed by a QWP. Since there are two types of QWP (Left and Right based on the description of my previous post), it is then possible for a beam of Linearly Polarized Photons to be split into two beams (Ordinary and Extraordinary) by the QWP with a Left or a Right Rotation. In other words, the photons after passing through the Linear Polarizer  (and become , say, the X-Linear Polarized state) will be split into two beams (comprising  the x-linear polarized state and the y’(Left) or the y’(Right) polarized state).

This is a continuation of your earlier description of how QWPs behave, which is still not clear to me, so I cannot comment on this until I understand the basics. As far as I understand it, a QWP does not produce an ordinary and extraordinary ray, but does produce different phase delays for different polarization components.

QUOTE
It is this process that enable us to obtain half the intensity of the photons if we should place another Linear Polarizer after the Circular Polarizer. Similarly, if we place another Circular Polarizer ( that has only One Linear Polarizer followed by a QWP), the intensity of Light that we are going to get from passing through two Circular Polarizers is ¼ and not ½ or 0 the intensity of the original source which QM predicts. This is because the passage of light through the first Circular Polarizer will half the intensity; and the passage through the second Circular polarizer will further reduce it by half. It is not possible to obtain the result predicted by QM based on this Simplified Definition of a Circular Polarizer. Do the experiment yourself to verify if what I say is correct.

Both QM and classical EM predict that if you use LP + QWP + LP you will get 1/4 of the light through, assuming that you start with unpolarized light. The classical prediction goes like this: The first LP lets one polarization component through, which cuts the intensity in half. The QWP then converts this linearly polarized light to circularly polarized light. Since the E field in circularly polarized light is rotating, it can be thought of as a superposition of two plane polarized E fields 1/4 wave out of phase. One of these gets through the second LP and the other does not. This cuts the intensity in half again, so you get 1/4 of the original intensity. If you try with LP + QWP + LP + QWP, the final QWP does not remove any light from the beam, so you still get 1/4 of the intensity. The QM prediction uses matrices and state vectors, but you can calculate for yourself that the result is the same prediction as classical EM makes. (Use the matrices and vectors in one of my earlier posts to try this out.)

So you see that QM and classical EM are both predicting exactly what you have observed, PROVIDED that you use the correct description of the experimental apparatus in working out the predictions. The bad prediction comes about from assuming that these are true circular polarizing filters, which (as we already know at this point) they are not. If you use true circular polarizing filters, you should find that your results are much closer to what QM and classical EM predict.

QUOTE (->
 QUOTE It is this process that enable us to obtain half the intensity of the photons if we should place another Linear Polarizer after the Circular Polarizer. Similarly, if we place another Circular Polarizer ( that has only One Linear Polarizer followed by a QWP), the intensity of Light that we are going to get from passing through two Circular Polarizers is ¼ and not ½ or 0 the intensity of the original source which QM predicts. This is because the passage of light through the first Circular Polarizer will half the intensity; and the passage through the second Circular polarizer will further reduce it by half. It is not possible to obtain the result predicted by QM based on this Simplified Definition of a Circular Polarizer. Do the experiment yourself to verify if what I say is correct.

Both QM and classical EM predict that if you use LP + QWP + LP you will get 1/4 of the light through, assuming that you start with unpolarized light. The classical prediction goes like this: The first LP lets one polarization component through, which cuts the intensity in half. The QWP then converts this linearly polarized light to circularly polarized light. Since the E field in circularly polarized light is rotating, it can be thought of as a superposition of two plane polarized E fields 1/4 wave out of phase. One of these gets through the second LP and the other does not. This cuts the intensity in half again, so you get 1/4 of the original intensity. If you try with LP + QWP + LP + QWP, the final QWP does not remove any light from the beam, so you still get 1/4 of the intensity. The QM prediction uses matrices and state vectors, but you can calculate for yourself that the result is the same prediction as classical EM makes. (Use the matrices and vectors in one of my earlier posts to try this out.)

So you see that QM and classical EM are both predicting exactly what you have observed, PROVIDED that you use the correct description of the experimental apparatus in working out the predictions. The bad prediction comes about from assuming that these are true circular polarizing filters, which (as we already know at this point) they are not. If you use true circular polarizing filters, you should find that your results are much closer to what QM and classical EM predict.

The proposal by Mr Homm in describing what constitute a TRUE Right or a TRUE Left Circular Polarizer is indeed very innovative and interesting. His suggestion does solve the dispute I had with Schneibster with regards to how a Circular Polarizer ought to be constructed before it will yield SOME of the predictions in QM.
In most literature, the illustration of how light can be cut off by the passage of light through a Right followed by a Left Circular Polarizer is illustrated by reflecting the Right Circular Polarized Light with a mirror back into the Right Circular Polarizer in the opposite direction, that is, QWP then the Linear Polarizer.
This had led me to think that the Construction of a Left Circular Polarizer differs from a Right Circular Polarizer by simply reversing the position of the Linear Polarizer with the QWP. This perception was corrected by Mr Homm.

Glad to be of help! I note you say "SOME of the predictions of QM," so I look forward to hearing more about where the predictions do not agree with your experiment. I know you have already mentioned some of them, of course, the lack of rotation invariance chief among them.

QUOTE
Let us try to analyse this experiment based on the hypothesis that I have proposed.
3.1 Passage of a beam of Light Through a Right Circular Polarizer followed by reflection of the Circularly Polarized Light through the same Circular Polarizer in the reverse direction.
3.1.1. The unpolarized light on passing through the Linear Polarizer will be polarized into photons in the say X-linearly polarized state:
l ψ > ----->  [Mx] ----->l X >

I agree 100% with this. All good so far.

QUOTE (->
 QUOTE Let us try to analyse this experiment based on the hypothesis that I have proposed.3.1 Passage of a beam of Light Through a Right Circular Polarizer followed by reflection of the Circularly Polarized Light through the same Circular Polarizer in the reverse direction.3.1.1. The unpolarized light on passing through the Linear Polarizer will be polarized into photons in the say X-linearly polarized state:l ψ > ----->  [Mx] ----->l X >

I agree 100% with this. All good so far.

3.1.2 The X-linearly polarized beam is then split into two beams by the Right QWP comprising:
l X > -----> [QWP(Right)] -----> l x1 (0 deg) > + l y2 (90 deg.)>

Instead of commenting on this and the rest of the steps individually, I'll give my understanding of the process so you can compare it to yours.

QUOTE
This I believe is what took place to yield the Quantum Mechanical Prediction of :
a] l ψ > -----> [MR] -----> l R >
b] l <R lMR l R > l ^ 2 = 1
b] l <L lML l R > l ^ 2 = 0

For comparison, here is my rendering of the classical EM account of the process, and the QM account:

Classical EM:

Unpolarized light of intensity I is traveling along the z axis. Because it is unpolarized, its E field is oriented along a randomly changing direction in the xy plane. The E field is equally likely at any given moment to be pointing in any direction in the xy plane.

This light hits the first LP filter, which is oriented along the x axis. At each instant in time, the E field vector is resolved into x and y component vectors, and the y component is absorbed by the filter. Because of the equally distributed probability of the E field direction, on average half of the energy gets through the filter, so the intensity is now I/2.

(This occurs because the orientation of the polymer molecules in the filter is along the y axis, and they are conductive; therefore, the y component of E drives AC currents along them, which uses up the energy in this E component. As the light moves through the thickness of the filter, the strength of the y component dies away exponentially, until in the exiting light, there is only a negligible amount left. Therefore, only the x component of the E vector exits from the LP filter.)

This light now hits the QWP which is oriented so that its optic axis x' is 45 degrees away from the x axis, along the line y=x. The E vector is resolved into EQUAL components the x' and y' directions, and the component along x' is delayed by 1/4 wavelength.

The light reflects from the mirror, which changes nothing essential, and then returns to the QWP.

It passes again through the QWP, which again delays the x' component by 1/4 wavelength. Since the x' component has now been delayed twice, it is 1/2 wavelength behind the y' component. But a 1/2 wavelength delay is the same thing as a sign change (since cos(x+180) = -cos(x)). Therefore the light has had its x' component reversed, but its y' component is not reversed.

(Note: reversing x' is the same as reflecting the E vector around the y' axis. But this axis is at a 45 degree angle to the x axis, so reflecting around y' SWITCHES the x and y components of the original wave. Therefore, the E vector is now 100% in the y direction, since before it was 100% in the x direction.)

This light then strikes the LP filter. Since the light is now y polarized, and the filter absorbs the y component of the E vector, the filter will absorb ALL of this light. Therefore, no light will escape through the LP filter.

(Caveat: this assumes ideal filters. If the LPs are less than perfect, QWPs not exactly at 45 degrees, or not the right thickness to produce exactly 1/4 wave delay, then these results are only approximate. See my last error analysis post for a full accounting of the errors.)

QM:

Light of intensity I consisting of a mixture of photons in various polarization states travels along the z axis. Each photon is in a definite state, but the states are spread with equal probability through all possible polarizations.

Each photon hits the LP filter. The filter absorbs any photon found in the |Y> state and passes through any photon found in the |X> state. For each photon, its state vector l ψ > is resolved into components which are |X> and |Y> states. In other words, l ψ > = a|X> + b|Y>, where |a|^2 + |b|^2 = 1. Therefore, each photon has a probability |a|^2 of being found in the |X> state by the filter and being passed through. Since all polarization states are equally probable, the average value of |a|^2 is 1/2, so on average half the photons get through the LP filter. Therefore the intensity is now I/2, and every photon exiting the filter is in the |X> state.

Thse photons now hit the QWP. The QWP resolves the state vector |X> into EQUAL components along the x' and y' directions, and delays the x' component by 1/4 wavelength. This means that |X> = 1/√2|X'> + 1/√2|Y'> ----> -i/√2|X'> + 1/√2|Y'>. The factors of 1/√2 are the solutions to |a|^2 + |b|^2 = 1 when a = b. The factor of -i is the 1/4 wave phase delay.

These photons now reflects off the mirror, which changes nothing essential, and returns to the QWP.

They pass again through the QWP, which again delays the x' component by 1/4 wave. Since -i*-i = -1, this gives the action of the QWP as -i/√2|X'> + 1/√2|Y'> ----> -1/√2|X'> + 1/√2|Y'>.

(Note: reversing the sign of |X'> is the same as reflecting the state vector around the y' axis. But this axis is at a 45 degree angle to the x axis, so reflecting around y' SWITCHES the |X> and |Y> components of the original state. Therefore, the state vector is now 100% |Y>, since before it was 100% |X>.)

The photons then strike the LP filter. Since every photon is now in the |Y> state, and the filter absorbs any photon found in the |Y> state, it absorbs every photon that strikes it. Therefore, no photons will escape through the LP filter.

(Same caveat: this result is for ideal filters, and will only be approximate for non-ideal ones.)

@Confused2, Nov.3
QUOTE (->
 QUOTE This I believe is what took place to yield the Quantum Mechanical Prediction of :a] l ψ > -----> [MR] -----> l R >b] l l ^ 2 = 1b] l l ^ 2 = 0

For comparison, here is my rendering of the classical EM account of the process, and the QM account:

Classical EM:

Unpolarized light of intensity I is traveling along the z axis. Because it is unpolarized, its E field is oriented along a randomly changing direction in the xy plane. The E field is equally likely at any given moment to be pointing in any direction in the xy plane.

This light hits the first LP filter, which is oriented along the x axis. At each instant in time, the E field vector is resolved into x and y component vectors, and the y component is absorbed by the filter. Because of the equally distributed probability of the E field direction, on average half of the energy gets through the filter, so the intensity is now I/2.

(This occurs because the orientation of the polymer molecules in the filter is along the y axis, and they are conductive; therefore, the y component of E drives AC currents along them, which uses up the energy in this E component. As the light moves through the thickness of the filter, the strength of the y component dies away exponentially, until in the exiting light, there is only a negligible amount left. Therefore, only the x component of the E vector exits from the LP filter.)

This light now hits the QWP which is oriented so that its optic axis x' is 45 degrees away from the x axis, along the line y=x. The E vector is resolved into EQUAL components the x' and y' directions, and the component along x' is delayed by 1/4 wavelength.

The light reflects from the mirror, which changes nothing essential, and then returns to the QWP.

It passes again through the QWP, which again delays the x' component by 1/4 wavelength. Since the x' component has now been delayed twice, it is 1/2 wavelength behind the y' component. But a 1/2 wavelength delay is the same thing as a sign change (since cos(x+180) = -cos(x)). Therefore the light has had its x' component reversed, but its y' component is not reversed.

(Note: reversing x' is the same as reflecting the E vector around the y' axis. But this axis is at a 45 degree angle to the x axis, so reflecting around y' SWITCHES the x and y components of the original wave. Therefore, the E vector is now 100% in the y direction, since before it was 100% in the x direction.)

This light then strikes the LP filter. Since the light is now y polarized, and the filter absorbs the y component of the E vector, the filter will absorb ALL of this light. Therefore, no light will escape through the LP filter.

(Caveat: this assumes ideal filters. If the LPs are less than perfect, QWPs not exactly at 45 degrees, or not the right thickness to produce exactly 1/4 wave delay, then these results are only approximate. See my last error analysis post for a full accounting of the errors.)

QM:

Light of intensity I consisting of a mixture of photons in various polarization states travels along the z axis. Each photon is in a definite state, but the states are spread with equal probability through all possible polarizations.

Each photon hits the LP filter. The filter absorbs any photon found in the |Y> state and passes through any photon found in the |X> state. For each photon, its state vector l ψ > is resolved into components which are |X> and |Y> states. In other words, l ψ > = a|X> + b|Y>, where |a|^2 + |b|^2 = 1. Therefore, each photon has a probability |a|^2 of being found in the |X> state by the filter and being passed through. Since all polarization states are equally probable, the average value of |a|^2 is 1/2, so on average half the photons get through the LP filter. Therefore the intensity is now I/2, and every photon exiting the filter is in the |X> state.

Thse photons now hit the QWP. The QWP resolves the state vector |X> into EQUAL components along the x' and y' directions, and delays the x' component by 1/4 wavelength. This means that |X> = 1/√2|X'> + 1/√2|Y'> ----> -i/√2|X'> + 1/√2|Y'>. The factors of 1/√2 are the solutions to |a|^2 + |b|^2 = 1 when a = b. The factor of -i is the 1/4 wave phase delay.

These photons now reflects off the mirror, which changes nothing essential, and returns to the QWP.

They pass again through the QWP, which again delays the x' component by 1/4 wave. Since -i*-i = -1, this gives the action of the QWP as -i/√2|X'> + 1/√2|Y'> ----> -1/√2|X'> + 1/√2|Y'>.

(Note: reversing the sign of |X'> is the same as reflecting the state vector around the y' axis. But this axis is at a 45 degree angle to the x axis, so reflecting around y' SWITCHES the |X> and |Y> components of the original state. Therefore, the state vector is now 100% |Y>, since before it was 100% |X>.)

The photons then strike the LP filter. Since every photon is now in the |Y> state, and the filter absorbs any photon found in the |Y> state, it absorbs every photon that strikes it. Therefore, no photons will escape through the LP filter.

(Same caveat: this result is for ideal filters, and will only be approximate for non-ideal ones.)

@Confused2, Nov.3
If we accept that a QWP is lossless then I suspect there are restrictions on what it can do. I suspect one restriction is that it can neither increase nor decrease the amount of order (entropy) of the beam of light.. I can't apply this beyond hand-waving .. it just seems to me that it cannot order the beam as you suggest.

I think the point can be partially resolved by rotating a QWP between two vertical polarizers .. I would predict a no loss point at 45 degrees to the axes of the crystal (four per full rotation) where the QWP is doing nothing rather than forcing the light into the axes of the crystal. Would you be kind enough to try it and report the result?

I suspect that you are right about the entropy, but it probably doesn't affect hexa's basic contention, because it can be framed in terms of single photons, where the concept of entropy doesn't apply.

Your idea for a test is a good one, but your prediction is off by 45 degrees. Here is what both QM and classical EM have to say on the matter:

Since the effect of a QWP is merely to delay light that is polarized along its optic axis, but not light that is polarized perpendicular to its optic axis, there are 4 positions where it will not affect the passage of light through the composite filter:

When its optic axis is at 0 or 180 degrees, it will be aligned with the filters. The only light striking the QWP is light that has passed through the first filter, so it will all be aligned with the QWP's axis, and it will all be delayed equally. This will produce no effect (since delaying light equally is just what you would expect from a vacuum, due to travel time, it is equivalent to just letting the light travel a short distance). Therefore, when the light strikes the second LP, it is still polarized along the original axis, which matches that of the second filter, so 100% of the light will get through.

Similarly, when the optic axis is at 90 or 270 degrees, all the light striking the QWP will be perpendicular to its optic axis, so none of the light will be delayed. Therefore there will be no effect of the QWP, and the light will still be polarized along the original axis, and once again 100% will get through.

The minimum amount would be when the QWP is turned at 45, 135, 225, or 315 degrees, because then it will convert the plane polarized light to circularly polarized light, half of which will get through the second LP filter. Therefore, as you rotate the QWP, the intensity exiting the composite filter will vary from 100% to 50%, the variation repeating 4 times.

A related test would be to do the same experiment but with the second LP rotated 90 degrees from the first. In that case, the intensity will still be 50% at 45, 135, 225, and 315 degrees, but 0% at 0, 90, 180, and 270 degrees. It is easy to see why this should be so: rotating the second LP by 90 degrees lets through exactly the light that DIDN'T get through in the first experiment. Therefore, the light getting through in the two experiments must sum to 100% at any angle, so the amount getting through in the second experiment is 100% - what got through in the first experiment.

@hexa, Nov. 4
QUOTE
I believe you and perhaps the other members following our discussion are enlighten enough to see the possibility that some parts of Quantum Mechanics may be incorrect in spite of its astounding success in providing elegant answer (according to Mr. Homm) to account for many phenomena in Nature. He also cited Occam’s Razor.
Similarly, Newtonian Physics also stood for 300 years until the beginning of the 20th century.
Indeed, Ptolemy Law of the cosmos stood much longer even though it was totally wrong based on careful measurement of the motion of the planets by Kepler..
Please pardon me if I were to use this analogy to describe QM. It appears that we are using the shadow of an object to describe the object itself. In the process, we sometime may miss the important details that are needed to fully describe the object. If one may recall, it is none other than the allegory of the Plato’s Cave.

While I'm perfectly willing to admit that QM may not be the final truth (in fact, I consider it highly likely that it is not), I would like to point out that the predictions of QM regarding circular polarization (in fact ALL its polarization predictions) agree EXACTLY with the predictions of classical EM. Therefore, there is NO SUCH THING as an experiment that disproves QM's account of polarization with out ALSO disproving classical EM's account. This is very important, because if rotation invariance of circularly polarized light is not true, not only QM is wrong, but most of classical physics. I'm not saying that this is impossible, but you should be clear that this experiment is NOT just something that calls into question the weird and counterintuitive parts of QM (such as duality, uncertainty, abstract state vectors, etc.). It also forces us to discard all those nice understandable intuitive explanations that classical EM gives us. In other words, nearly all of physics since the year 1840 is simply wrong. So the stakes here are very high indeed.

QUOTE (->
 QUOTE I believe you and perhaps the other members following our discussion are enlighten enough to see the possibility that some parts of Quantum Mechanics may be incorrect in spite of its astounding success in providing elegant answer (according to Mr. Homm) to account for many phenomena in Nature. He also cited Occam’s Razor.Similarly, Newtonian Physics also stood for 300 years until the beginning of the 20th century.Indeed, Ptolemy Law of the cosmos stood much longer even though it was totally wrong based on careful measurement of the motion of the planets by Kepler..Please pardon me if I were to use this analogy to describe QM. It appears that we are using the shadow of an object to describe the object itself. In the process, we sometime may miss the important details that are needed to fully describe the object. If one may recall, it is none other than the allegory of the Plato’s Cave.

While I'm perfectly willing to admit that QM may not be the final truth (in fact, I consider it highly likely that it is not), I would like to point out that the predictions of QM regarding circular polarization (in fact ALL its polarization predictions) agree EXACTLY with the predictions of classical EM. Therefore, there is NO SUCH THING as an experiment that disproves QM's account of polarization with out ALSO disproving classical EM's account. This is very important, because if rotation invariance of circularly polarized light is not true, not only QM is wrong, but most of classical physics. I'm not saying that this is impossible, but you should be clear that this experiment is NOT just something that calls into question the weird and counterintuitive parts of QM (such as duality, uncertainty, abstract state vectors, etc.). It also forces us to discard all those nice understandable intuitive explanations that classical EM gives us. In other words, nearly all of physics since the year 1840 is simply wrong. So the stakes here are very high indeed.

Generally, I do not disagree that there will be uncertainty if we attempt to measure both position and momentum (or time and energy) simultaneously, as elicited by the Uncertainty Principle. What I find unacceptable, according to the Copenhagen Interpretation, is that we cannot even talk about it prior to making an observation. A particle has no physical reality until it is observed. According to the Superposition principle, a particle (an electron or any other elementary particle) passing through one of the Double Slits has no physical presence anywhere prior to making an observation. In fact some even make this ludicrous proposition that the particle could be EVERYWHERE prior to making an observation. That is to say that we cannot attached a Cartesian coordinate in the Euclidean space to describe the position of the particle before observation. For those familiar with relativity, there is no space-time coordinate where we can attach to the particle prior to observation. Hence, it is not possible to describe the electron as having a physical state until it interacts with the apparatus to provide an observation.
Personally, I abhor such a postulate and would prefer to use classical statistics to interpret the behavior of particles including that of the photons. This would allow us to describe every single particle (photons included) as having a Real Physical State that will enable us to predict how it would interact with the apparatus, at least, statistically. I have shown that this approach seem to give us the correct prediction where QM fails.

This is a very interesting topic to me, and I have a lot to say about it, but for now, I'll try to be brief: I tend to agree that there are deep problems with the Copenhagen interpretation. It basically makes the problem of interpretation go away by saying you are not allowed to ask certain questions. This is deeply unsatisfactory. If there were a reason why these questions could not be asked (for example, if it could be proven that they were logically inconsistent), then I would be happier; but just to declare by fiat that they are not allowed seems like just sweeping the troubles under the rug.

Surprisingly perhaps, I am less accepting of uncertainty than you are. I feel that the whole uncertainty idea represents a primitive interpretation of the theory, and is just a leftover from its early days. My position is that there is fundamentally no uncertainty. Instead, there are perfectly definite states AT ALL TIMES (which I think agrees with your position), but further, I think that these states are abstract (here is where I disagree with your position), and that uncertainty is basically an illusion created by our expectations. We expect to get separate answers for momentum and position for example, but for the particle, these are actually only ONE property. We expect to get two different answers to one question -- of course it doesn't work. In classical physics, there are so many particles in an object that we can ask the question twice in two different ways without disturbing the object much, so we can get the two answers we want, and we have gotten used to that, so we think it is our RIGHT now.

So basically, my position is that every particle is always in a perfectly definite state, but it might not be a state that we are comfortable with from our classical physics experience. Statements like "the particle doesn't have a definite position" are misguided attempts to express a more fundamental idea: position and momentum are points of view on a single underlying reality, just as are space and time, or energy and momentum. (BTW, I am not accusing you, hexa, of being misguided. It's the statements in popular accounts of QM (and in textbooks, even some of Feynman's) that I find misguided.

As an aside, the idea that a particle doesn't have a property until that property is measured is in my opinion not such a philosophically bad idea. In fact, prior to Newton, natural philosophy was very much concerned with just this kind of question: how do you know what anything is doing when you aren't looking, how can we assume continuity of properties or even existence between observations. When Newton's work came out, the physical explanations and the calculus that went with it were so powerful and convincing that people FORGOT to worry about these questions any more. They did not solve them or answer them, they just put them aside. QM forces us to confront these questions again, which is a good thing. Just like physicists, philosophers should not be allowed to sweep questions under the rug either.

However, that doesn't mean that I think the answer to the question is to adopt the Copenhagen interpretation. In fact, as I said just above, I think there is continuity and a well defined state at every moment in time. The value of the Copenhagen interpretation, to me, is not that it answers these questions, but that it reminds us that we've never answered them properly in previous centuries.

QUOTE
Experiment (1)
l ψ> -----> My(1) -----> QWP(2) ------> My(3).

Where l ψ> is the unpolarized state of photons (Monochromatic or White Light)
My = Linear polarizer
QWP= Quarter wave plate

1.1 Using Monochromatic Light
You would have ¼ the original intensity of l ψ>.
The rotation of the QWP(2) has minimal effect (not perceptible to the naked eyes) on the intensity of light passing the three filters.

This is unexpected. My analysis (earlier in this post, in response to Confused_2) suggests that there should be a variation in intensity, from I/2 at maximum to I/4 at minimum, where I is the initial intensity before the light passes through the first filter.

QUOTE (->
 QUOTE Experiment (1)l ψ> -----> My(1) -----> QWP(2) ------> My(3).Where l ψ> is the unpolarized state of photons (Monochromatic or White Light)My = Linear polarizerQWP= Quarter wave plate1.1 Using Monochromatic LightYou would have ¼ the original intensity of l ψ>.The rotation of the QWP(2) has minimal effect (not perceptible to the naked eyes) on the intensity of light passing the three filters.

This is unexpected. My analysis (earlier in this post, in response to Confused_2) suggests that there should be a variation in intensity, from I/2 at maximum to I/4 at minimum, where I is the initial intensity before the light passes through the first filter.

1.2 Using White Light
No perceptible variation in the color of the light passing through the composite filters as we rotate the QWP(2).

Since a substantial amount of light is passed through and the variation in the QWP behavior with frequency is small, this is what I would expect.

QUOTE

[Note: For want of a better name, I will continue to refer QWP as a filter in spite of Mr. Homm objection]

Well, I don't really care what you call it, as long as we all understand its properties and behavior.

QUOTE (->
 QUOTE [Note: For want of a better name, I will continue to refer QWP as a filter in spite of Mr. Homm objection]

Well, I don't really care what you call it, as long as we all understand its properties and behavior.

If you conduct this other experiments:
Experiment (2)
l ψ> -----> My(1) -----> QWP(R2) ------> QWP(R3)(inverted 180 deg.)------> My(4).

2.1 Using Monochromatic Light
You should obtain the same result as the experiment --had you used a mirror. The only difference, is that you may get a higher intensity passing through this set of filters compared with when you uses the mirror. It is not quite as dark compared to the experiment using the mirror.
The rotation of QWP(2) relative to QWP(3) causes a variation in the intensity of light passing through the filters that is perceptible to the naked eyes.

How was the first QWP oriented relative to the linear polarizers. If it was at a 45 degree angle, then rotating the second one should vary the effect between complete cancellation (as if there were no QWPs) or a half-wave plate. A half wave plate reverses the direction of polarization relative to the HWP axis, which would convert y polarized light to x polarized light, which would not get through the second linear polarizer. In that case, I would expect substantial variation in light intensity. If the angle is not precisely 45 degrees, there would still be variation in light intensity, but not so much. The result you got here is pretty much what I would expect.

QUOTE

2.2 Using White Light
The chromaticity of the white light passing through the set of filters vary as we rotate one QWP(R3) relative to QWP(R2) as well as when we rotate both QWP relative to both the Linear Polarizer.

This is also as expected, since the presence of two QWPs will magnify the effect of frequency dependence and produce stronger variation in behavior as a function of light color.

QUOTE (->
 QUOTE 2.2 Using White LightThe chromaticity of the white light passing through the set of filters vary as we rotate one QWP(R3) relative to QWP(R2) as well as when we rotate both QWP relative to both the Linear Polarizer.

This is also as expected, since the presence of two QWPs will magnify the effect of frequency dependence and produce stronger variation in behavior as a function of light color.

Finally, if we were to conduct this last experiment:
Experiment (3)
l ψ> -----> My(1) -----> QWP(R2) ------> QWP(L3)------> My(4).

3.1 Using Monochromatic Light
We will see that there will be a greater intensity of photons passing through all the filters than in the case for Experiment (2).
The rotation of QWP(L3) relative to QWP(R2) causes some perceptible changes to the intensity of the monochromatic light passing through it. Similar changes is also recorded as we rotate both the QWP relative to the Linear Polarizers (where we fix it).

3.2 Using White Light
The chromaticity of the white light passing through the set of filters vary as we rotate one QWP(L3) relative to the other QWP(R2) as well as when we rotate both QWP relative to both the Linear Polarizer (where they are fixed).

The only difference I can see between experiment 2 and 3 is that you have labeled the second QWP as QWP(L3) instead of QWP(R3). What exactly the difference between these QWPs? As I said, I do not understand what you mean by different types of QWPs. In the concrete case of the experiment here, how do you know that they are different? What tests told you that one was L and one was R?

QUOTE
I hope you, Mr Homm or some other members who happen to have these apparatus could also independently verify the observation that I have described above.

I would love to try this experiment myself, but I do not own the necessary apparatus, and right now I can't afford to buy it. Sometime, I will try it, when I get a little money and free time.

I'll stop this (very long) post at this point and send it. I will immediately start working on another post, so that I can catch up to the rest of you on the list. Only 12 more days to go to catch up to TODAY!

--Stuart Anderson
mr_homm
@hexa, Nov. 6
QUOTE
Please do not mistake my replies to Confused2 as saying that you have been less than accurate in stating Quantum Theory. On the contrary, your command of Quantum Theory has been impeccable. You were able to distinguish the different shades of grey.  This can only be the hallmark of a true master who knows Quantum Theory inside out.

Thank you!

QUOTE (->
 QUOTE Please do not mistake my replies to Confused2 as saying that you have been less than accurate in stating Quantum Theory. On the contrary, your command of Quantum Theory has been impeccable. You were able to distinguish the different shades of grey.  This can only be the hallmark of a true master who knows Quantum Theory inside out.

Thank you!

But that does not mean that Quantum Theory represents the Gospel Truth of Nature. As what Richard Feynman had said, Quantum Theory is build on---to paraphrase him--- the ruins of Logic and Common sense. In the absence of Determinism (which you disputed my assertion), and an over reliance on mathematics (Quantum Mechanics), do you see the danger that in the absence of a Logical Phenomenological account of Nature, we run the risk of predicting an outcome that may be contrary to experiment that is far remote from Reality? Can we learn anything from the allegory of Plato’s Cave?

I agree that as the theory becomes increasingly abstract, there is increasing difficulty in interpreting it and in making concrete predictions. Thus the practitioners of the theory may end up in the position of either being unable to do the math to make a prediction, or of having so many competing interpretations of the theory that it is hard to know which prediction the theory actually makes, if any. String theory currently has both these problems, in my opinion. If the theory can be tied to our concrete experience at many points, then the danger is much less, and this seems to be what you are trying to achieve.

As to the allegory of the cave, yes, all mathematical representation is a study of shadows. However, I don't see that we have much choice about using at least some mathematics, and if some, why not all. Again, there is of course a danger that most human minds may not be able to handle extremely high levels of abstraction, and then it is hard to see how these theories could be construed as explanations of physical reality. "Explain" means to "make something plain" and what the theory says is often not plain at all, even to those with some training in it.

QUOTE
I think you are mistaken, when you said:
QUOTE (->
 QUOTE I think you are mistaken, when you said:It is my OPINION that current QM gives a pretty good account of circular polarization, which agrees with experimental data.

Well, it IS my opinion. I wouldn't make a mistake about my own opinion, would I? OK, I know what you really meant. Perhaps QM does not agree with experimental data after all. I have not reviewed the data on circular polarization in a couple of decades. I should probably go track some down and have a look.

QUOTE

Prior to hearing your suggestion on what constitute a TRUE Right and a TRUE Left Circular Polarizer, all the experiments that I have conducted with Circular Polarizers does not agree with what was predicted by QM as stated in the Physics textbook. Even with the introduction of another QWP before the Circular Polarizer, ROTATION INVARIANCE continues to evade from my experimental observation. The other observation involves a heavy dose of discount before we can begin to infer the prediction made in QM with regards to Circular Polarization.

I sincerely hope you will be able to conduct the same experiments on Circular Polarization to satisfy yourself with regard to whether they are mere artefact or that there is something fundamentally wrong with the QM prediction.

Your finding that circular polarizers are not rotation invariant is very puzzling to me. I would LOVE to do this experiment myself, just as soon as I have time and money to do so.

QUOTE (->
 QUOTE Prior to hearing your suggestion on what constitute a TRUE Right and a TRUE Left Circular Polarizer, all the experiments that I have conducted with Circular Polarizers does not agree with what was predicted by QM as stated in the Physics textbook. Even with the introduction of another QWP before the Circular Polarizer, ROTATION INVARIANCE continues to evade from my experimental observation. The other observation involves a heavy dose of discount before we can begin to infer the prediction made in QM with regards to Circular Polarization.I sincerely hope you will be able to conduct the same experiments on Circular Polarization to satisfy yourself with regard to whether they are mere artefact or that there is something fundamentally wrong with the QM prediction.

Your finding that circular polarizers are not rotation invariant is very puzzling to me. I would LOVE to do this experiment myself, just as soon as I have time and money to do so.

To state that QM may be wrong on Circular Polarization, does not  automatically make my proposition to use CLASSICAL STATISTICAL Method as correct.
One of the cardinal tests for this alternative approach is that it must be able to account LOGICALLY MALUS Experimental Law for the passage of light through two linear polarizers inclined at an angle δ.  I will do this in my next post to show that Malus Law is only an approximation to what we will observe experimentally. There is a more fundamental Reality.

QUOTE
In this posting, I will only address your remarks that you request further clarification.

QUOTE (->
 QUOTE In this posting, I will only address your remarks that you request further clarification.Paragraph 1:Here is a central point that we must clarify. [1.1]QM states that a filter performs a measurement, which technically means just that it treats photons in different states differently, absorbing some states but not others. [1.2]Linear polarizing filters absorb different orientations of linear photon states differently, so they perform a measurement; hence they are filters by the technical definition.[1.3] On the other hand, a QWP delays the phase of one state relative to another state, [1.4]but does not absorb either state. [1.5]Every photon that goes into a QWP comes out the other side (except for a small amount of absorption because the crystal is not absolutely transparent -- but it absorbs all polarization states equally, [1.6]so it still doesn't distinguish between them); therefore the QWP is NOT a filter by the technical definition. [1.1] is accepted with qualification in [1.2].[1.2] may not be technically correct. The molecules making up the polarizer does not significantly ABSORB the photons. Most of these photons that does not pass through a Linear Polarizer is reflected away from it. You can verify this assertion using a laser beam.[1.3] can be accepted since the extraordinary ray takes a longer path. However there is nothing in the molecules of the QWP to suggest that the “PHASES” can be precisely control to depart from one another by exactly 90 deg. It is just not reasonable to make this assumption, with the knowledge that the molecules making up the QWP is constantly vibrating and oscillating.[1.4] and [1.5] may be accepted.[1.6] How do you account for the fact that a calcite crystal (which can be used as a QWP), split ONE Beam of photons into two DISTINCT beams (Ordinary and Extraordinary Beams) if it is unable to distinguish one photon from another?

1.1: We agree.

1.2: I think we are seeing two things here. Light does of course reflect from the front surface of the polarizing filter, just as it would form any other smooth plastic surface. I think that this is just ordinary reflection at the surface. Of the light that gets past the surface, some is absorbed and some is passed through, as I originally said. There is a simple experimental test to see what is really happening: shine the laser on the polarizer at nearly normal incidence, and then observe the reflected light with a second polarizer. If the first polarizer is reflecting one component and passing through the other (your explanation) then the light that reflects from it should be highly polarized, which can be easily detected by the second filter. On the other hand, if this is just ordinary surface reflection (my explanation) then it will not be polarized. In that case, my statement is correct that while there is some loss from the surface, the actual filtering action involves absorption. In the other case, you are right, and the filtering action is by reflection.

1.3: We disagree. First, when a calcite crystal is cut at the proper angle to make a QWP, there is no extraordinary ray. All the light travels through it on the same path. Second, although the atoms are constantly oscillating, their motion amplitude is less then the crystal unit cell spacing, which is on the order of a few nanometers. Visible light has a wavelength of around 500 nanometers, so these atomic motions are negligible in size in comparison. Also, there is no difficulty in controlling the phase difference to be exactly 90 degrees, because this is controlled by the thickness of the crystal. Both the ordinary and extraordinary refractive indices are easy to measure. Here is a link to the page of a company that sells optical calcite crystals. As you can see, the two refractive indices differ markedly. In order to delay one polarization by 1/4 wavelength relative to the other, it is only necessary to cut the crystal the the right thickness so that the crystal holds 1/4 more wavelength of one polarization than the other.

In this case, let T be the thickness of the crystal. Then for a vacuum wavelength L, the wavelength of one polarization state will be L/no and the other will be L/ne, where no and ne are the ordinary and extraordinary refractive indices. In that case, the number of wavelengths fitting into a thickness T will be T/(L/no) and T/(L/ne). The difference will then be (T/L)(no-ne). Since no-ne = 0.1705, the thickness of the crystal must be T = L/0.1705. For average visible light in the yellow range, L = 500nm, so T = 2,933nm. Although this is pretty thin, it is easily possible to cut the crystal and polish it to this dimension. After all, telescope mirrors are commonly polished to within an accuracy of 50nm, and their surfaces are CURVED. A flat surface can be polished more accurately than that, so that you can get the number of wavelengths to differ by 1/4 between the two polarizations, with an error of less than 1%.

As a matter of fact, calcite is not the best choice for making a QWP because it is so STRONGLY birefringent. The two refractive indices are so very different that only a very thin layer of calcite is needed, which means it has to be manufactured to fairly precise tolerances. As I just said above, this can be done. However, it would be much easier to make a QWP from a material whose refractive indices were less different, because then the thickness of the plate would be much greater and it would be easier to manufacture it, as less precise tolerances would be needed.

1.4, 1.5: We agree.

1.6: As I've mentioned before, the calcite is cut at an entirely different angle to make a QWP than to make a polarizing separator. In a QWP, the photons are NOT separated into two streams. In a polarizing separator, they are. Although calcite is CAPABLE of distinguishing photons of different polarizations, when cut as a QWP it does not do so. A filter distinguishes between states, forcing each photon to choose a state, and only one state appears in the output beam.

A LP filter clearly does this, because light in a mixture of polarization states is resolved into states polarized either parallel or perpendicular to the molecular alignment of the LP filter, and those photons parallel to the molecules are absorbed, while the perpendicular orientation passes through. Therefore, every photon that gets through is in the polarization state selected by the LP filter.

When calcite is cut at the proper angle, it will separate light into ordinary and extraordinary rays. Every photon in the ordinary ray has one polarization axis, and every photon in the extraordinary ray has a polarization axis perpendicular to that of the ordinary ray. Looking at just one beam or the other, you have a "pure" stream of photons in one state, and no others. Therefore the calcite is acting as a filter when cut this way.

When calcite is cut to be a QWP, the ordinary and extraordinary rays are not separated. All the light comes out on the same path. You are free to regard the QWP as resolving photons into two perpendicular polarizations (because vectors can ALWAYS be thought of as resolved into components; this is a mathematical, not a physical action, and you don't need a physical apparatus AT ALL to do this), but it DOES NOT separate them. Every photon in the exiting beam is NOT in the same polarization state, no photons have been absorbed or diverted to another path, so no separation or absorption of states has been performed. Every photon that goes in comes out (barring minor losses due to surface reflection). How can that be a filter? If I had a coffee filter that passed everything through, it would be the same as if I forgot to put a filter in the coffee maker!

Summary: Calcite is capable of being a polarization filter. When cut at one angle it IS, and when cut at a different angle, it ISN'T. A QWP ISN'T a filter.

QUOTE
QUOTE (->
 QUOTE Paragraph 2:[2.1]This means that the RCP is not actually a series of filters. [2.2]There is only one filter in the series, and the other two layers (the QWPs) alter the state without filtering it. [2.3]One way to see that this is true is to ask what would happen if you omitted the LP layer and kept just the two QWPs. They are turned 90 degrees to each other, so one will delay the |H> state and the other will delay the |V> state. Since these states form a basis for all photon states, and since they are both delayed equally, the net result is that the photon state as a whole is delayed, but neither component is delayed relative to the other. This is exactly what you would expect from plain old glass, since its refractive index slows, and hence slightly delays, photons. In other words,[2.4]if you omit the LP layer, the combination of the two QWPs does EXACTLY NOTHING to the light. Light would be delayed simply by traveling through space anyway, to the two QWPs are equivalent to simply letting the light travel a tiny extra distance forward. [2.5]This obviously does not affect the state of the light in any way. [2.1] is incorrect. This is where I will have to disagree with you on your proposition that QWP is not a filter based on the reason that I have stated in [1.6].[2.2] and [2.3] appears to differ from your earlier proposition that there are two types of QWP. One that rotates light in the clockwise direction, and the other in the counterclockwise direction. In each of these cases, what is it that are being rotated?[2.4] has a problem. According to you---in the set up involving two TRUE Right Circular Polarizers, the x-linearly polarized photon will have to pass through Two QWP (one rotates in one direction with the other in another direction), before passing through the next x-linear polarizer.On another experiment involving ONE TRUE Right Circular Polarizer followed by a TRUE Left Circular Polarizer, the x-linearly polarized photon will have to pass through Two QWP (one rotate in one direction with the other reinforcing the rotation), before passing through another x-linear polarizer.If both the QWP does nothing, how do we account for the fact that:A] one allows more Light to pass through both the Linear Polarizers with TWO QWP than when only ONE QWP is being used? AndB] the other cut-off a substantial parts of the light as if the two linear polarizers are aligned orthogonally to one another?Hence, I don’t think [2.5] is tenable.2.5: Try it out. Attach two QWPs together with their axes 90 degrees apart, making sure they are firmly attached together so that they cannot rotate relative to each other. Then set up LP ----> 2QWP package ----> LP. Rotate the second LP to any angle you like, then observe what happens when you rotate the two QWPs. Rotate the WHOLE UNIT of two QWPs stuck together, do not rotate them separately. You should observe that there is NO effect on the light that gets through the second LP, for all orientations of the second LP and for all orientations of the 2QWP package. The results should be the same as if you conducted the experiment with just LP ----> LP and no QWPs at all. (There will of course be a small amount of light reflected from the front surface of the 2QWP package, so the final intensity will be a few percent less than without the QWPs. However, this is just the same kind of loss you would see with any smooth surface, such as plain glass, and is not anything the QWPs specifically are doing.)Do your QWPs have the axis marked in some way so that this is easy to do, or do you need to locate the axis by a calibration procedure every time?

2.1: I stand by my assertion, and have provided further explanation at 1.6.

2.2, 2.3: I have never said that there were two types of QWPs. I said that you could get different effects by rotating QWPs to different orientations relative to a LP, to make RCP or LCP filters.

2.4: The two QWPs only cancel if their optic axes are turned 90 degrees apart. If you rotate to a different angle, they will NOT cancel out. The point I was making is that if there is even ONE angle where there effects cancel out, then the QWPs cannot be thought of as filters because their effect is REVERSIBLE, one can cancel the effect of the other. Nothing reversible can be a filter, because if the process is reversible, then nothing is lost, hence nothing has been filtered out.

QUOTE
QUOTE (->
 QUOTE Paragraph 3:[3.1]So you see that the only filtering action is provided by the LP layer. [3.2]The two QWPs process the incoming state (WITHOUT measuring it, so no uncertainty relations are involved) so that light that was initially circularly polarized becomes linear, so that the LP can act on it, and then processes the resulting light back into its original circular state (because, as I said in the above paragraph, the effect of the two QWPs cancels out i.e. one is the inverse of the other). The action of this filter is mathematically identical to a single layer of circularly polarizing material. [3.3]Now we don't happen to have single layer circularly polarizing materials to use in the experiment, but this is a technical limitation only, not part of the basic physics. It should be possible to create a circularly polarizing material, but the fact is that no one is likely to bother, since the QWP LP QWP sandwich already works well. [3.1] is accepted.[3.2] need to answer the question that I have raised in [2.4].[3.3] I remain skeptical as to whether we could construct a single layer of polarizing material based on how we define a Circular Polarizer.Please pardon me for my impudence. I hope you could continue to set aside sometime from your busy schedule to clarify some of the issues that I have raised here. I will attempt to provide an explanation on Malus Law using simple Classical Statistical Method after your clarification to the issues that I have raised here.

3.1: We agree.

3.2: To clarify regarding 2.4: When I said the two QWPs cancel out, I was talking specifically about the QWPs that are before and after the LP in the three layer true circular filter package. Because one of these QWPs is turned 45 degrees clockwise relative to the LP and the other is 45 degrees counterclockwise from the LP, they are 90 degrees from each other in axis orientation. If you open the true circular filter package and remove the LP layer, and replace the two QWPs in their original orientations, they you will have a package of 2QWPs with optic axes 90 degrees apart. It was this package that I said canceled out its effects. Again, this is NOT true if the QWPs are rotated at any other angle than 90 degrees from each other. The point I was making is that if you remove the LP layer from the true circular filter, you are left with a package of 2 QWPs at 90 degrees to each other, and this package does exactly nothing to the light. Therefore, the only filtering action is provided by the LP layer, not by the QWPs.

3.3: On the website I linked to a few paragraphs above, there were the following interesting and relevant links:
Waveplate description
More on waveplates (on a different site linked from the first site)
Circular polarization with diagrams
Circular dichroism.

The last link is the most important one, because it shows that there are many materials that DO absorb one circular polarization state more than the other one, and therefore, these materials COULD be used to make a ONE LAYER circular polarizing filter. The catch is, that they are not nearly as efficient as linear polarizing filters. A good linear filter will reject 99.99% of the perpendicular polarization and pass through essentially all of the parallel polarization state. On the other hand, these circularly dichroic materials only absorb a few percent more light in one circular polarization than in the other. This means that if you started with VERY intense light, and used a VERY thick layer of one of these materials, you would get pretty close to 100% circularly polarized light coming out, but it would be weak because much of the light in both components would be absorbed by the material (which is why you must start with a very bright light).

In other words, it would be technically difficult to make an EFFICIENT one layer circular polarizing filter, but NOT impossible. A one layer circular filter can definitely exist, but for purely practical reasons of cost and efficiency, it is easier to make a 3 layer filter as I have described.

More later!

--Stuart Anderson
"THEY"
QUOTE (mr_homm+Nov 16 2006, 07:15 PM)
I would love to try this experiment myself, but I do not own the necessary apparatus, and right now I can't afford to buy it.  Sometime, I will try it, when I get a little money and free time.

--Stuart Anderson

Stuart- due to time I have not been able to follow this thread well enough to know exactly what setup hexa is using, but I am more than willing to toss into the bin for your use what I have been collecting for "they"2's science fair project. I also do have a little extra cash flow at the moment to where I could buy calcite crystals or some other items if they are necessary for hexa's setup. What it would teach her would be worth the money if you would like to use my filters etc!
hexa
Hi They,

Great!
I must thank you from the bottom of my heart, for offering to set aside some cash to help independently verify the experiments that I have conducted.
Do send me a personal message if you need more details other than those that I will be sharing with everybody following our discussion. Alternatively, you can also post your queries here for the benefits of everybody.
For the benefits of everybody, I will try to be as detail as I could but I will also try to keep it simple and sweet at the same time.

Below are some of the apparatus that you may need:
QUOTE

1) 4 Nos. Linear Polarisers (Used by photographers);
2) 4 Nos. QWP
3) 4 Nos. Right Circular Polarizers (used by photographers).
4) 4 Nos. Left Circular Polarzers (Used by photographers).
5) 1 Red color filter (used by photographer).
5) 1 Lux. meter with a resolution of 1 lux. It must also be capable of reading up to 2000 lux.
6) 1 steady white light source.
7) 1 red laser source.
8) You also need a clean power supplies with minimum voltage fluctuation. But this is beyond our control unless you are prepared to invest heavily on a power supplies voltage regulator.
9) You will need to calibrate the filters. My recommendation is that you calibrate all your filters at an angle interval of 5.625 deg. It will simplify your experiments substantially.
Recommendation: Used Normal size filter of 55mm diameter.

Hope it is not too difficult for you to obtain these apparatus.
Just wonder whether any representative from other institutes are prepared to conduct these experiments as well?

Cheers.

Hi Mr Homm,

Thank you very much for your extremely interesting and important replies.
Not only were you concise and consistent in your replies, you were candid on your personal assessment of prevailing theories.
Initially, I thought you were like Schneibster. He stood steadfast in defending the Official Doctrine of mainstream Science without butting an inch. He left leaving the discussion hanging in mid-air without proceeding beyond what is contained in the Standard Text. He could not even tell me how to Construct a Left Circular Polarizer from a Right Circular Polarizer.

I was not surprised when I read your statements below. I was extremely, extremely surprised when I read these paragraphs. I almost fell off my chair. Immediately, I braced myself that what you said can only come from a TRUE MASTER who is extremely enlighten. Not only were you extremely brave and honest to accept that some part of what you previously though was true may not be quite correct, you were able to see beyond the current discussion into the larger implication of what we are discussing.
QUOTE (->
 QUOTE 1) 4 Nos. Linear Polarisers (Used by photographers);2) 4 Nos. QWP3) 4 Nos. Right Circular Polarizers (used by photographers).4) 4 Nos. Left Circular Polarzers (Used by photographers). 5) 1 Red color filter (used by photographer).5) 1 Lux. meter with a resolution of 1 lux. It must also be capable of reading up to 2000 lux. 6) 1 steady white light source.7) 1 red laser source.8) You also need a clean power supplies with minimum voltage fluctuation. But this is beyond our control unless you are prepared to invest heavily on a power supplies voltage regulator.9) You will need to calibrate the filters. My recommendation is that you calibrate all your filters at an angle interval of 5.625 deg. It will simplify your experiments substantially.Recommendation: Used Normal size filter of 55mm diameter.

Hope it is not too difficult for you to obtain these apparatus.
Just wonder whether any representative from other institutes are prepared to conduct these experiments as well?

Cheers.

Hi Mr Homm,

Thank you very much for your extremely interesting and important replies.
Not only were you concise and consistent in your replies, you were candid on your personal assessment of prevailing theories.
Initially, I thought you were like Schneibster. He stood steadfast in defending the Official Doctrine of mainstream Science without butting an inch. He left leaving the discussion hanging in mid-air without proceeding beyond what is contained in the Standard Text. He could not even tell me how to Construct a Left Circular Polarizer from a Right Circular Polarizer.

I was not surprised when I read your statements below. I was extremely, extremely surprised when I read these paragraphs. I almost fell off my chair. Immediately, I braced myself that what you said can only come from a TRUE MASTER who is extremely enlighten. Not only were you extremely brave and honest to accept that some part of what you previously though was true may not be quite correct, you were able to see beyond the current discussion into the larger implication of what we are discussing.

In other words, nearly all of physics since the year 1840 is simply wrong. So the stakes here are very high indeed.

Personally, I think you may have been overly concern here. I prefer to look at it from the perspective that we are standing on "the sholders of giants".
Please accept my sincere apology if I have in any way offended you by challenging some part of your believes. I SALUTE you for being a TRUE Scientist.

QUOTE

[1]Surprisingly perhaps, I am less accepting of uncertainty than you are. [2]I feel that the whole uncertainty idea represents a primitive interpretation of the theory, and is just a leftover from its early days. [3]My position is that there is fundamentally no uncertainty. [4]Instead, there are perfectly definite states AT ALL TIMES (which I think agrees with your position), but further, I think that these states are abstract (here is where I disagree with your position), and that [5]uncertainty is basically an illusion created by our expectations. [6]We expect to get separate answers for momentum and position for example, but for the particle, these are actually only ONE property. [7]We expect to get two different answers to one question -- of course it doesn't work. [8]In classical physics, there are so many particles in an object that we can ask the question twice in two different ways without disturbing the object much, so we can get the two answers we want, and we have gotten used to that, so we think it is our RIGHT now.

[9]So basically, my position is that every particle is always in a perfectly definite state, but it might not be a state that we are comfortable with from our classical physics experience. [10]Statements like "the particle doesn't have a definite position" are misguided attempts to express a more fundamental idea: position and momentum are points of view on a single underlying reality, just as are space and time, or energy and momentum. [11](BTW, I am not accusing you, hexa, of being misguided. It's the statements in popular accounts of QM (and in textbooks, even some of Feynman's) that I find misguided.

[1] "Surprising" ---is an understatement.
[2] Couldn't agree more.
[3] Agree.
[4] Yes.
[5] Agree.
[6] Agree.
[7] Agree.
[8] Agree. I have no fundamental disagreement with you for [5] to [8]. I was just not able to express it with the eloquence that you have done here.
[9] Agree.
[10] Agree.
[11] Fully Agree. When I first raised my objection on the Official Doctrine based on the Copenhagen Interpretation, I was given a dirty look. Some even tell me that I have a skull too thick for my own good. I got remarks like "Shut up and calculate".

Thanks for the assurance that even a Nobel Laureate, like Richard Feynman may also be MISGUIDED.

I will post the experiments later.
Thanks again.

Cheers.
mr_homm
@"THEY"

I'm departing from my habit of taking posts strictly in order to thank you for your very kind offer. It would certainly have been rude not to acknowledge this one right away. It looks like hexa has provided a shopping list, some parts of which you probably already have. I'll take a look around for good prices on the most essential items and see what I can contribute myself. Certainly I have a good collection of "raw" calcite crystals, which could be used as polarizing beam separators, but this would make the filtering somewhat awkward, so regular photographic polarizing filters would be easier.

As you might have gathered, I deeply distrust photographic circular polarizing filters for precise experimental work. It is much better and more flexible to have separate, high quality quarter wave plates and linear polarizers. I had also had the idea that rather than a lux meter, one could use a digital camera with a manually controllable shutter speed. Using very low light levels, the CCD array in a digital camera makes an excellent scintillation counter, and the photographs can be transferred directly to a computer, and the bright pixels counted automatically.

This is more complicated than a lux meter, but probably more precise. Of course, it depends on having such a camera. Currently I own a decent older digital camera, but it is of the "fool proof" variety that won't let you fiddle with it. If I can swing getting myself a new digital camera for Christmas (perhaps as an EARLY Christmas present) the I could use it instead of purchasing a separate lux meter. On the other hand a lux meter is a nice thing to have, and the experiment is certainly EASIER that way, and the precision is probably plenty anyway.

Again, thank you for the offer. Of course if I borrowed your equipment, I would write up my results with complete instructions, so that "they"2 could try them out herself after I gave the equipment back to you.

@hexa

I feel that you deserve an immediate response as well. I was very glad to get your last post, as I had started to suspect that you felt I was taking a reactionary position against you. That is of course not true! The reasons that I have confined my responses to describing current theory are:
1: I do not like to put myself forward. I have a sort of allergy to taking charge. I prefer to stay in the background and contribute. It seemed to me that this was basically YOUR thread about your experiments and ideas, and butting in with my own opinions would be rude. In other words, I did not want to hijack your thread (which is what a lot of people on physorg do, and which I find very annoying).
2: It seemed to me that since I am well versed in the standard theory, my best contribution to the discussion would be to provide the standard QM take on things as clearly as possible, as a baseline for discussion. Since you are undertaking a critique of current theory, it seemed that having the current theory laid out as clearly as possible would be the best starting point.
3: I am conceptually radical but procedurally conservative. There is always the hope of making a great discovery, and fearing that this hope will mislead me, I want to be ABSOLUTELY sure that there are no loopholes in the experiment. Everything must be triple checked and independently verified before I dare to believe it. Even then I won't totally trust it, because there may be something I've overlooked.

In fact, since EVERYTHING rests on the validity of the experiment, the only safe procedure is to make absolutely sure that the experimental results are BULLETPROOF. And the only way to do that is to try as hard as I possibly can to shoot down your experiment. If I CAN shoot it down, then it was not strong enough to support the theory anyway, and if I CANNOT shoot it down, then we can be confident that the basis of the theory is correct. You have to remember that I was trained as a mathematician at least as much as a physicist. My standards of proof are ABSOLUTE, and the slightest doubt completely invalidates an explanation for me. That's why I'm so careful about assumptions, description of equipment, procedures, error analysis, and so on.

To be perfectly honest, while I an pretty sure that there is SOMETHING wrong with QM or with our understanding of it, I am not yet convinced that your experiment has gotten to the basis of it. Maybe, maybe not. Let's analyze and replicate the experiment and FIND OUT. That's my basic procedural position. Of course, this experiment has PROBABLY been done many times, and if the results did not agree with theory, I would have heard about it. On the other hand, this reasoning is dangerous: what if everyone else also uses this reasoning and assumes the experiment must have been performed and must have agreed with the theory? Then no one would be motivated to do it, so maybe NO ONE has done it, or only a very few people.

Still, it's probable that there are published results on this experiment, but they are probably very old. This sort of experiment would have been preformed (without lasers of course) back in the 1850s or so (my guesstimate of when this part of optics was being developed). That makes the results kind of hard to look up, since they predate most of the current research journals' existence! So perhaps it's better to just try the experiment ourselves. It's good practice anyway, and a learning experience for "they"2.

--Stuart Anderson
mr_homm
@hexa, Nov. 6 (cont)

QUOTE
QUOTE (->
 QUOTE The result .. no change as the QWP is rotated between two vertical filters. Could this be that the QWP has only changed the z angle of the spin vector .. to which neither the filters nor the human eye are sensitive. A more sensitive test would be to start with the filters at right angles. I think that is an excellent suggestion.The insertion of the QWP would allow light to pass through the two linear polarizers that are orthogonal to one another. At first sight, the subsequent rotation of the QWP appears not to change anything (for Monochromatic and White Light) that is significant to the naked eyes. I was Wrong. I have discounted the fluctuation when I rotated the QWP as artefacts of the QWP when I gave you the earlier result in my previous post. On hindsight, this fluctuation is due to the permutation of the two molecular axes found in the QWP against the Single axis of each of the Linear Polarizer. This confirms unequivocally that Circular Polarizer is not ROTATION INVARIANT as what QM has predicted. I don’t think Mr Homm assertion that the QWP is not a filter is defensible.

Although you were talking with Confused_2 here, I hope you won't mind my interjecting a comment. If you are rotating a single QWP between two LP filters, then this is NOT testing rotation invariance for a circular polarizer. It is testing rotation invariance of a QWP. Classical EM, QM, and I myself have never said that a QWP is rotation invariant. If you want to place a circular polarizer (consisting of QWP+LP+QWP with the two QWPs optic axes turned 45 degrees in opposite directions from the LP polarizing axis as per my true circular polarizer description) between the two LP filters, and then rotate the WHOLE circular filter as a package, THEN you are testing for rotation invariance of the circular polarizer.

@hexa, Nov. 8

QUOTE
With your latest clarification, I now know that I have totally misinterpreted the meaning of the statement that you intend to convey. What you in fact said is that a Linear Polarizer somehow become a Right or Left Circular Polarizer if the optical axis of the QWP is rotated clockwise or anti-clockwise relative to the polarizing axis of the Linear Polarizer.
By the way:
1)What does this OPTICAL Axis of the QWP represent?
2)How is this related to the Molecular arrangement of the QWP?
3)Does the molecules of the QWP not determine how any PHOTON is going to interact with it?

1) The optical axis the direction the E field of the light must align with in order to create the extraordinary ray (the e-ray). When light is polarized so that its E field lines up with the optic axis, it propagates as an e-ray through the calcite, and when it is polarized so that its E field is perpendicular to the optic axis, it propagates through the calcite as an ordinary ray (o-ray).
2) About terminology: since calcite is a crystal, it does not strictly speaking have a molecular arrangement, since it is not composed of molecules. Or if you want to think of it that way, the whole crystal is one molecule, since every atom is bonded to neighboring atoms, there is no place where one molecule stops and another begins. But that is just a verbal quibble, so it's not too important. The important thing is that the crystal structure of calcite is asymmetrical. One dimension of the unit cell is a different length from the others, and this affects the electrical polarizability of the material in that direction.

(Note: electrical polarizability has NOTHING to do with optical polarization; it is just a coincidence of terminology. Electrical polarizability means that the material responds to an electric field by polarizing -- electrically -- in the sense that electrons are displaced slightly from their normal positions so that atoms become small electric dipoles.)

The net effect is that light travels either faster or slower in the e-ray compared to the o-ray, depending on whether the material in question is more or less polarizable along the optic axis than along other directions. Calcite happens to be less polarizable along the optic axis than along the plane perpendicular to the optic axis, so it interacts LESS with light whose E field is oriented along the optic axis. Therefore, it slows it LESS, and so the e-ray travels faster than the o-ray. See below for further comments about light slowing down.

3) Yes, the crystal structure determines how each photon will interact with the crystal. I have given above the classical EM picture of the process. On the individual photon level, the polarizability becomes a probability of absorbing and re-radiating a photon. The probability is higher (or lower, depending on the material) along the optic axis than in the plane perpendicular to it. Typically of QM, each individual photon is regarded as going into a superposition of states, one state (the dominant one) in which it did not scatter off an atom, and another state (with small amplitude) in which it did. The scattered state has its phase delayed, because there is a time lag between being absorbed and re-emitted by an atom. The sum of these states produces a state with a retarded phase (because the overall phase is a linear combination of the phases of the states), which gives the APPEARANCE that the light has slowed down, even though both photon states travel at speed C.)

By the way, somewhere in the thread it was mentioned that the slowing of light due to refractive index contradicts the constancy of the speed of light in Special Relativity. Well, yes, it certainly APPEARS to, but there is an explanation that reconciles the two. Here it is: If a crystal can be polarized, then when the E field of a light ray passes through the crystal, the atoms will become tiny dipoles. Since the E field is oscillating rather than steady, they will be oscillating dipoles. Now an oscillating dipole is a radio antenna (this is precisely how ordinary radio antennas work -- they are just oscillating electric dipoles-- except that they are made much larger in order to interact with radio waves, which are much longer than optical light waves).

Therefore, these oscillating dipoles radiate, and they do so at the same frequency as they oscillate, which is the same frequency that the E field is pushing them. Therefore, they become small sources of light at the same frequency as the original light beam. Their light is added to the original light. Of course, this does not make the light brighter than what originally came it -- you can't get something for nothing. The light from the radiators takes energy to produce, energy which the radiators got from the original light beam in the first place. So basically some energy is removed from the original light beam and then re-radiated back to it.

However, driven oscillators are never perfectly in phase with the driving force. They always lag behind a little bit, and so the re-radiated light is slightly out of phase with the original light, which means that its wave crest is slightly behind the wave crest of the original light as they travel through the crystal. If you add a small sine wave with a slight phase delay to a large sine wave, the result is a sine wave of slightly larger amplitude, with its crest delayed slightly. In other words, the net result is that the wave crest is not as far along as it should be. This process continues all through the light's passage through the crystal, with the wave crest getting farther and farther behind where it would have been. Thus the APPARENT effect is that the light traveled slower through the crystal than through vacuum. What is really happening is that some fraction of the light is absorbed and re-radiated with a delay by the polarizable atoms in the crystal. The net light thus appears delayed. However, EVERY BIT of the light has traveled at speed C at ALL TIMES. The delay is due to the absorption and re-emission by the atoms in the crystal.

By the way, I have personally seen a very convincing demonstration of this effect with water waves. A long rectangular tank of water is clear of obstructions for about a meter, then there is a section about a meter long where many thin vertical rods are spaced about 1cm apart, like bristles on a very large hairbrush sticking up out of the water, and then there is another meter long clear section. A wave is generated from one end of the tank by vibrating the end, and the wave travels along the water until it comes to the section with the rods. As the wave hits each rod, a small circular wave comes out from the rod, and these circular waves overlap and add to the original wave. The net effect is that the wave crests of the wave become VISIBLY closer together. It is very obvious because the wavelength is decreased to about 2/3 of its original length. It is also moving VISIBLY slower, about 2/3 o its original speed. Again, the effect is quite pronounced and obvious to the eye. When the waves leave the section with the rods, they resume their original wavelength and speed.

The surprising part is that if you look close up at the water between the small rods, you can see lots of little waves traveling every which way, and EVERY ONE OF THEM is moving at the ORIGINAL wave speed. It is only their overall effect, the combined wave, that appears to move slower. This demonstration was very convincing to me, and showed me exactly how it was possible for a wave to slow down and yet still be composed entirely of small waves traveling at the full normal wave speed. The analogy with light is clear, and the mechanism is very similar, especially since we KNOW that highly polarizable materials have high refractive indices.

QUOTE (->
 QUOTE With your latest clarification, I now know that I have totally misinterpreted the meaning of the statement that you intend to convey. What you in fact said is that a Linear Polarizer somehow become a Right or Left Circular Polarizer if the optical axis of the QWP is rotated clockwise or anti-clockwise relative to the polarizing axis of the Linear Polarizer.By the way:1)What does this OPTICAL Axis of the QWP represent?2)How is this related to the Molecular arrangement of the QWP?3)Does the molecules of the QWP not determine how any PHOTON is going to interact with it?

1) The optical axis the direction the E field of the light must align with in order to create the extraordinary ray (the e-ray). When light is polarized so that its E field lines up with the optic axis, it propagates as an e-ray through the calcite, and when it is polarized so that its E field is perpendicular to the optic axis, it propagates through the calcite as an ordinary ray (o-ray).
2) About terminology: since calcite is a crystal, it does not strictly speaking have a molecular arrangement, since it is not composed of molecules. Or if you want to think of it that way, the whole crystal is one molecule, since every atom is bonded to neighboring atoms, there is no place where one molecule stops and another begins. But that is just a verbal quibble, so it's not too important. The important thing is that the crystal structure of calcite is asymmetrical. One dimension of the unit cell is a different length from the others, and this affects the electrical polarizability of the material in that direction.

(Note: electrical polarizability has NOTHING to do with optical polarization; it is just a coincidence of terminology. Electrical polarizability means that the material responds to an electric field by polarizing -- electrically -- in the sense that electrons are displaced slightly from their normal positions so that atoms become small electric dipoles.)

The net effect is that light travels either faster or slower in the e-ray compared to the o-ray, depending on whether the material in question is more or less polarizable along the optic axis than along other directions. Calcite happens to be less polarizable along the optic axis than along the plane perpendicular to the optic axis, so it interacts LESS with light whose E field is oriented along the optic axis. Therefore, it slows it LESS, and so the e-ray travels faster than the o-ray. See below for further comments about light slowing down.

3) Yes, the crystal structure determines how each photon will interact with the crystal. I have given above the classical EM picture of the process. On the individual photon level, the polarizability becomes a probability of absorbing and re-radiating a photon. The probability is higher (or lower, depending on the material) along the optic axis than in the plane perpendicular to it. Typically of QM, each individual photon is regarded as going into a superposition of states, one state (the dominant one) in which it did not scatter off an atom, and another state (with small amplitude) in which it did. The scattered state has its phase delayed, because there is a time lag between being absorbed and re-emitted by an atom. The sum of these states produces a state with a retarded phase (because the overall phase is a linear combination of the phases of the states), which gives the APPEARANCE that the light has slowed down, even though both photon states travel at speed C.)

By the way, somewhere in the thread it was mentioned that the slowing of light due to refractive index contradicts the constancy of the speed of light in Special Relativity. Well, yes, it certainly APPEARS to, but there is an explanation that reconciles the two. Here it is: If a crystal can be polarized, then when the E field of a light ray passes through the crystal, the atoms will become tiny dipoles. Since the E field is oscillating rather than steady, they will be oscillating dipoles. Now an oscillating dipole is a radio antenna (this is precisely how ordinary radio antennas work -- they are just oscillating electric dipoles-- except that they are made much larger in order to interact with radio waves, which are much longer than optical light waves).

Therefore, these oscillating dipoles radiate, and they do so at the same frequency as they oscillate, which is the same frequency that the E field is pushing them. Therefore, they become small sources of light at the same frequency as the original light beam. Their light is added to the original light. Of course, this does not make the light brighter than what originally came it -- you can't get something for nothing. The light from the radiators takes energy to produce, energy which the radiators got from the original light beam in the first place. So basically some energy is removed from the original light beam and then re-radiated back to it.

However, driven oscillators are never perfectly in phase with the driving force. They always lag behind a little bit, and so the re-radiated light is slightly out of phase with the original light, which means that its wave crest is slightly behind the wave crest of the original light as they travel through the crystal. If you add a small sine wave with a slight phase delay to a large sine wave, the result is a sine wave of slightly larger amplitude, with its crest delayed slightly. In other words, the net result is that the wave crest is not as far along as it should be. This process continues all through the light's passage through the crystal, with the wave crest getting farther and farther behind where it would have been. Thus the APPARENT effect is that the light traveled slower through the crystal than through vacuum. What is really happening is that some fraction of the light is absorbed and re-radiated with a delay by the polarizable atoms in the crystal. The net light thus appears delayed. However, EVERY BIT of the light has traveled at speed C at ALL TIMES. The delay is due to the absorption and re-emission by the atoms in the crystal.

By the way, I have personally seen a very convincing demonstration of this effect with water waves. A long rectangular tank of water is clear of obstructions for about a meter, then there is a section about a meter long where many thin vertical rods are spaced about 1cm apart, like bristles on a very large hairbrush sticking up out of the water, and then there is another meter long clear section. A wave is generated from one end of the tank by vibrating the end, and the wave travels along the water until it comes to the section with the rods. As the wave hits each rod, a small circular wave comes out from the rod, and these circular waves overlap and add to the original wave. The net effect is that the wave crests of the wave become VISIBLY closer together. It is very obvious because the wavelength is decreased to about 2/3 of its original length. It is also moving VISIBLY slower, about 2/3 o its original speed. Again, the effect is quite pronounced and obvious to the eye. When the waves leave the section with the rods, they resume their original wavelength and speed.

The surprising part is that if you look close up at the water between the small rods, you can see lots of little waves traveling every which way, and EVERY ONE OF THEM is moving at the ORIGINAL wave speed. It is only their overall effect, the combined wave, that appears to move slower. This demonstration was very convincing to me, and showed me exactly how it was possible for a wave to slow down and yet still be composed entirely of small waves traveling at the full normal wave speed. The analogy with light is clear, and the mechanism is very similar, especially since we KNOW that highly polarizable materials have high refractive indices.

However, there is a BIGGER PROBLEM if the photons are not rotated clockwise or anti-clockwise relative to the linear polarizer as you now intended to mean. This is because you have also stated that it is the Linear Polarizer in the TRUE Circular Polarizer (QWP + LP + QWP) that will either allow more light to pass through or none at all. If it does not rotate the orientation of the photons, then How is the Linear polarizer going to do what it does, if it is the ONLY FILTER by your definition?

I am sure you are aware of this experiment.
Experiment-1
Place x-linear polarizer at position 1 and y-linear polarizer at position 3 along the z-axis.
Pass a beam of photons along the z-axis passing through the two linear polarizers.
What do you see?

Experiment-2
Place a linear polarizer (inclined at 45 deg. to the x-linear polarizer) at position 2 in between the x-linear polarizer at position-1 and y-linear polarizer at position 3.
What do you see?

How do you account for the fact that the photons can now pass through the polarizers in Experiment-2 but not in Experiment-1 if none of the photons are being rotated by the linear polarizer inclined at 45 degree to the x and y linear polarizers?

Let's be careful here. I never said that LPs do not rotate photons. I said that QWPs do not rotate photons. However, I'll say it now: LPs do not rotate photons either. Both the classical EM and the QM explanations involve vectors. In the EM explanation, it is the E field vector that the LP and QWP operate upon, and in the QM explanation, it is the photon state vector.

First let's talk about vectors in general. This is just math, not physics. Let's say that X and Y are unit vectors (vectors of length 1) in the x and y directions, and that X' and Y' are the unit vectors along the axes of a coordinate system rotated 45 degrees counterclockwise relative to x and y. In other words, X' points along the line y=x in the first quadrant, and Y' points along the line y=-x in the second quadrant.

The vectors X' = 1/√2*(X + Y) and Y' = 1/√2*(Y - X), which is obvious if you draw the picture, so X' and Y' clearly can be expressed in terms of X and Y. However, it is also true that X = 1/√2*(X' - Y') and Y = 1/√2*(X' + Y'), which is obvious either from the picture or by using the formulas for X' and Y' above, so X and Y clearly can be expressed in terms of X' and Y' as well. The relation is symmetrical, and either set of vectors can be used as a basis to express the other.

It is this fact about vectors that allows both classical EM and QM to provide calculated predictions of light behavior that agree with the experimental behavior of linear polarizers, including Malus's Law, WITHOUT having filters rotate the polarization angle. It is important to remember that both theories postulate that vector addition is a PHYSICAL law in addition to being a mathematical calculation. In other words, it is obvious MATHEMATICALLY that X' = 1/√2*(X + Y), but that by itself doesn't mean that an electric field E oriented along the x' direction, |E|*X', is the PHYSICALLY the same thing as having two electric fields |E|/√2*X and |E|/√2*Y at the same location. This is a physical assumption which forms the basis of a lot of physical theory: the assumption that when you have physical things represented by vectors (such as forces, momenta, angular momenta, velocities, electric magnetic and gravitational fields, etc.), these physical things really, PHYSICALLY combine in the same way that vectors combine mathematically. This just a long, detailed way of saying that "vectors are an accurate mathematical model of the behavior of certain physical quantities."

Taking this assumption as true (which is what all current physical theories do), you can explain the behavior of polarizers in the following way:

For experiment 1, unpolarized light hits the first LP. This light consists of electric fields whose vectors point in many different directions at different times, about equally. Since electric field is a vector, each individual E field within the light ray can be thought of as a sum of an E_x and E_y, the vector components in the x and y directions. This decomposition of the vector is both mathematically AND PHYSICALLY identical to the original E vector. Nothing either physical or mathematical is changed by doing this; the decomposition is done for clarity of exposition only.

Now look at the behavior of the first LP filter acting on this E field. The LP filter axis is along the x direction, so it absorbs any E field in the y direction and passes through E field in the x direction. Therefore, the E_y is removed by the filter and E_x passes through. Since the original E field was a combination of fields oriented in random directions and randomly changing with time, on average exactly half the E field will be in the x component and half in the y component, so the intensity that gets through the first filter is half the original intensity. This is the light that then hits the second filter. Since this filter's axis is oriented along the y axis, it absorbs any E_x that hits it, and passes through any E_y that hits it. Since ONLY E_x is present in the light that strikes the second LP filter, ALL of the light is absorbed and none passes through.

For experiment 2, the first stage is the same as experiment 1, and you have light of intensity I/2 composed of 100% E_x leaving the first LP filter. The second filter is oriented along the x' axis, 45 degrees from the first filter. Therefore, you decompose the E vector into its x' and y' components. Since E is oriented along the x axis, it is |E|*X when expressed as a magnitude and unit direction vector, and since X = 1/√2*(X' - Y'), it follows that E = |E|/√2*(X' - Y') = |E|/√2*X' + |E|/√2*(-Y'). Since the second LP filter absorbs any E field that is in the y' direction, the second component is absorbed, and the first component passes through. Therefore, the light exiting the second LP filter is has an E field E = |E|/√2*X'.

Now this light strikes the third LP filter, which has its polarizing axis oriented along the y direction. Therefore, you decompose the E vector into x and y components in order to see what the third filter will do do it. Since E = |E|/√2*X', and X' = 1/√2*(X + Y), it follows that E = |E|/√2*1/√2*(X + Y) = |E|/2*X +|E|/2*Y. The third filter absorbs the x component, so only the y component passes through. Therefore, the light passing through the third filter has E field E = |E|/2*Y. Therefore, the amplitude of the light has been reduced by a factor of 2. Since the intensity of light is proportional to E^2, the intensity has been reduced by a factor of 4 relative to what got through the first LP filter (which was already I/2, remember), so the intensity is 1/8 as great as the original unpolarized light. Therefore, light DOES get through the third filter, the polarization is along the y axis, and the intensity is I/8.

Something odd has happened here! The first polarizer discarded all y component, then the second filter discarded all y' component, and this caused some y component to REAPPEAR. This is the light that gets through the third filter. This seems like magic at first, but it is just HOW VECTORS WORK, and there is no way around that because its in the math, not the physics. In fact, physical vectors must work this way, too. If they did not, then even basic things like Newton's three laws of motion would be wrong. I for one am not really keen on rewriting physics all the way back to the year1687, so I'm going to assume we've got this one RIGHT: physical vectors DO work this way.

Notice that none of the polarizers actually ROTATES any light. All they do is absorb one component and pass through another. However, the net effect of these processes is that the light appears to be rotated. So you could say that the net effect is to rotate the light and reduce its intensity, but the method by which this effect is achieved involves only selective absorption. So I would say that the physical action of LP filters is not a rotation, but that their apparent effect upon polarized light is a rotation and intensity reduction.

I'm out of time again. In my next post I will address the question of the classical EM and QM account of exactly what a QWP does, and how it can allow light to get through two perpendicular LPs.

--Stuart Anderson
Confused2
Hi hexa, Mr homm, THEY(2) et al,

The reason I suggested LP QWP LP was more to test hexa's QWP rather than theory. With hindsight a better test would seem to be LP QWP mirror QWP LP as suggested by a manufacturer some time back. I don't think we have that result for the true circular polarizer setup.

Many thanks to all , C2.

(psi)^2 .. oops, of course
hexa
Hi Mr. Homm,

Thanks you for all your clarifications.
I fully concur with the approach that you have adopted.

Initially, I thought that believing in something that you also believe:
QUOTE

there are perfectly definite states AT ALL TIMES (which I think agrees with your position),

is considered naive. This is because main-stream physicists will tell their students that it is Totally Wrong to harbour such idea. It must be discarded if we are to learn the TRUTH about Nature.

Thanks for sharing your inner thought as well as in sharing this profound thought that I think deserve more clarification:

QUOTE (->
 QUOTE there are perfectly definite states AT ALL TIMES (which I think agrees with your position),

is considered naive. This is because main-stream physicists will tell their students that it is Totally Wrong to harbour such idea. It must be discarded if we are to learn the TRUTH about Nature.

Thanks for sharing your inner thought as well as in sharing this profound thought that I think deserve more clarification:

[5]uncertainty is basically an illusion created by our expectations.
[6]We expect to get separate answers for momentum and position for example, but for the particle, these are actually only ONE property.
[7]We expect to get two different answers to one question -- of course it doesn't work.

I wonder whether you could put it in simpler words for the benefit of everybody, just in case I may have misinterpreted what you had intended to convey.

In the meantime, I will proceed to state Malus Law more fundamentally, as it is the key to understanding all the other properties surrounding Circular Polarization of Light. You will see “how the failure to understand this topic more fundamentally has led to many incredulous proposition in Science”. You will see that the debate on EPR Experiment; Quantum Entanglement; Bohmian Mechanics, Aspect Experiment; Quantum Computing, etc, etc is directly or indirectly build on the foundation of Polarization of Light. Unfortunately, our understanding on the topic of Linear and Circular Polarization of Light is hopelessly imprecise that many theoretical physicists continue to build huge and impressive Castles resting on this foundation. Some appear to be like building another leaning Tower of Pisa.

Hence, it is futile to make any speculation if the Experiment does not speak for itself.

Cheers.

Hi Confused2,

I will try to provide you with my observation that you have requested before bringing you through the painful process of understanding the Experiment more fundamentally. It will be quite difficult to understand Circular Polarization without first understanding Linear Polarization and how Malus Law Operates.
QUOTE

With hindsight a better test would seem to be LP QWP mirror QWP LP as suggested by a manufacturer some time back. I don't think we have that result for the true circular polarizer setup.

The result is as stated by the manufacturer. In other words, the light reflected from the mirror after passing through the Right Circular Polarizer (linear polarizer followed by the QWP) will pass through the QWP but is stopped by the same Linear polarizer.
It appears that the combination of a QWP followed by a Linear Polarizer in this situation involving a mirror will behave as a Left Circular Polarizer (if we assume that the first polarizer is a Right Circular Polarizer).

Unfortunately, a Left Circular Polarizer is not defined as a QWP followed by a Linear Polarizer, which Mr. Homm had helped to established. This is where I thought his proposition of a TRUE Right Circular Polarizer [QWP(-45) LP + QWP (+45)] and a TRUE Left Circular Polarizer [QWP(+45) +LP+QWP(-45)was extremely innovative.

QUOTE (->
 QUOTE With hindsight a better test would seem to be LP QWP mirror QWP LP as suggested by a manufacturer some time back. I don't think we have that result for the true circular polarizer setup.

The result is as stated by the manufacturer. In other words, the light reflected from the mirror after passing through the Right Circular Polarizer (linear polarizer followed by the QWP) will pass through the QWP but is stopped by the same Linear polarizer.
It appears that the combination of a QWP followed by a Linear Polarizer in this situation involving a mirror will behave as a Left Circular Polarizer (if we assume that the first polarizer is a Right Circular Polarizer).

Unfortunately, a Left Circular Polarizer is not defined as a QWP followed by a Linear Polarizer, which Mr. Homm had helped to established. This is where I thought his proposition of a TRUE Right Circular Polarizer [QWP(-45) LP + QWP (+45)] and a TRUE Left Circular Polarizer [QWP(+45) +LP+QWP(-45)was extremely innovative.

True left circular filter = TLCF = QWP(+45) + LP + QWP(-45)

True right circular filter = TRCF QWP(-45) + LP + QWP(+45)

Photographic left circular polarizer = PLCP = LP + QWP(-45)

Photographic right circular polarizer = PRCP = LP + QWP(+45)

Photographic left circular analyzer = PLCA = QWP(+45) + LP

Photographic right circular analyzer = PRCA = QWP(-45) + LP.

Unfortunately, this arrangement does not mean that the Circular Polarizer is Rotation Invariant . You can try putting two True Right Circular Polarizers {[QWP(-45) LP + QWP (+45)] + [QWP(-45) LP + QWP (+45)]}. Chances is that the intensity of light passing through two Right Circular Polarizers is not going to be ½ the intensity from the source which is predicted by QM. It is ¼.
Similarly, if you pass light through a True Right followed by a True Left Circular Polarizer, you are not going to get zero intensity compared to the source as predicted by QM.

Further, if you rotate the second circular polarizer relative to the first, the intensity of the light from the source passing through the two polarizers is going to fluctuate. If white light is used, you will see changes to the color of the light passing through both the circular polarizers.

If a monochromatic source is used, then the fluctuation in intensity become discernible to the eyes. I will give you the variation in lux. later.

I hope you can now see why I had so much problem trying to verify the prediction stated in QM for Circular polarization of light.

Dissatisfied that QM could not provide a logical explanation on how Malus Law works, coupled with this problem on Circular Polarization, it drove me to make a totally different proposition of what essentially is a photon. This is based on the proposition that Mr. Homm had stated “perfectly definite states AT ALL TIMES”.

I went on to HYPOTHESIZE that a photon is a “deck of cards” as opposed to a box of marbles. This proposition appears to be more suited to explain both Linear and Circular Polarization much better than QM. Most significantly, this proposition allows me to explain Malus Law fundamentally without having to resort to some abstract mathematical postulates.

It is for this reason that I have raised the question whether a PHOTON found in a Circular Polarized State, can be distinguished from another found in another Circular or any of the Two Linearly polarized state.
If so, How?

I will provide you the readings that I have obtained for you to evaluate whether the inference that I had made is reasonable. Do provide me your esteem opinion after you have digested the data. The same invitation is extended to all the other members following this thread.

Cheers.
hexa
Hi Mr. Homm, Confused2, Montec, They, etc,

Let me start by providing you the comparison between what I observed and what is predicted by Malus Law (which is what QM will predict).

Can anyone please advise me on how to post the Excel Table on this forum page? In the meantime, I will do it the clumsy way.

Take a look at this set of data:
QUOTE

Experiment 1
Angle θ (measured in degree) against Intensity of light (measured in lux) versus the values predicted by Malus Law for two linear polarizers:

Column[1]  Column[2]        Column[3]            Column[4]    Column[5]
1) 00.00 deg. = 346 lux. ; Malus Law = 346 lux.; Diff=0 lux.;  Percent=0.00%
2) 11.25 deg. = 335 lux. ; Malus Law = 333 lux.; Diff=2 lux.;  Percent=0.60%
3) 22.50 deg. = 302 lux. ; Malus Law = 295 lux.; Diff=7 lux.;  Percent=2.37%
4) 33.75 deg. = 244 lux. ; Malus Law = 239 lux.; Diff=5 lux.;  Percent=2.09%
5) 45.00 deg. = 177 lux. ; Malus Law = 173 lux.; Diff=4 lux.;  Percent=2.31%
6) 56.25 deg. = 113 lux. ; Malus Law = 107 lux.; Diff=6 lux.;  Percent=5.61%
7) 67.50 deg. =  59 lux. ; Malus Law =    51 lux.; Diff=8 lux.;  Percent=15.69%
8) 78.75 deg. =  23 lux. ; Malus Law =    13 lux.; Diff=10 lux.; Percent=76.92%
9) 90.00 deg. =  11 lux. ; Malus Law =    0 lux.; Diff=11 lux.;  Percent=Infinity

Interpretation of the data:

1) Column [1] shows the angle θ;
2) Column [2] shows the readings in lux for light passing through the two polarizers;
3) Column [3] shows the prediction using Malus Law {based on (cos(θ))^2};
4) Column [4] shows the difference between prediction against observation;
5) Column [5] shows the percentage of the difference against the prediction based on Malus Law.

QUOTE (->
 QUOTE Experiment 1Angle θ (measured in degree) against Intensity of light (measured in lux) versus the values predicted by Malus Law for two linear polarizers:  Column[1]  Column[2]        Column[3]            Column[4]    Column[5]1) 00.00 deg. = 346 lux. ; Malus Law = 346 lux.; Diff=0 lux.;  Percent=0.00%2) 11.25 deg. = 335 lux. ; Malus Law = 333 lux.; Diff=2 lux.;  Percent=0.60%3) 22.50 deg. = 302 lux. ; Malus Law = 295 lux.; Diff=7 lux.;  Percent=2.37%4) 33.75 deg. = 244 lux. ; Malus Law = 239 lux.; Diff=5 lux.;  Percent=2.09%5) 45.00 deg. = 177 lux. ; Malus Law = 173 lux.; Diff=4 lux.;  Percent=2.31%6) 56.25 deg. = 113 lux. ; Malus Law = 107 lux.; Diff=6 lux.;  Percent=5.61%7) 67.50 deg. =  59 lux. ; Malus Law =    51 lux.; Diff=8 lux.;  Percent=15.69%8) 78.75 deg. =  23 lux. ; Malus Law =    13 lux.; Diff=10 lux.; Percent=76.92%9) 90.00 deg. =  11 lux. ; Malus Law =    0 lux.; Diff=11 lux.;  Percent=Infinity

Interpretation of the data:

1) Column [1] shows the angle θ;
2) Column [2] shows the readings in lux for light passing through the two polarizers;
3) Column [3] shows the prediction using Malus Law {based on (cos(θ))^2};
4) Column [4] shows the difference between prediction against observation;
5) Column [5] shows the percentage of the difference against the prediction based on Malus Law.

Experiment 2
Angle θ (measured in degree) against Intensity of light (measured in lux) versus the values predicted by Malus Law for three linear polarizers; the angle θ is the same between any two adjacent linear polarizers:

Column[1]    Column[6]          Column[7]        Column[8]    Column[9]
1) 00.00 deg. = 346 lux. ; Malus Law = 346 lux.; Diff=0 lux.;  Percent=0.00%
2) 11.25 deg. = 328 lux. ; Malus Law = 320 lux.; Diff=8 lux.;  Percent=2.50%
3) 22.50 deg. = 267 lux. ; Malus Law = 252 lux.; Diff=15 lux.; Percent=5.95%
4) 33.75 deg. = 177 lux. ; Malus Law = 165 lux.; Diff=12 lux.; Percent=7.27%
5) 45.00 deg. =  96 lux. ; Malus Law =    87 lux.; Diff=9 lux.;  Percent=10.34%
6) 56.25 deg. =  40 lux. ; Malus Law =    33 lux.; Diff=7 lux.;  Percent=21.21%
7) 67.50 deg. =  13 lux. ; Malus Law =      7 lux.; Diff=6 lux.;  Percent=85.71%
8) 78.75 deg. =    4 lux. ; Malus Law =      1 lux.; Diff=3 lux;  Percent=300.00%
9) 90.00 deg. =    3 lux. ; Malus Law =      0 lux.; Diff=3 lux;  Percent=Infinity

Interpretation of the data:

1) Column [1] shows the angle θ;
2) Column [6] shows the readings in lux for light passing through the three polarizers;
3) Column [7] shows the prediction using Malus Law {based on (cos(θ))^4};
4) Column [8] shows the difference between prediction against observation;
5) Column [9] shows the percentage of the difference against the prediction based on Malus Law.

INFERENCES:
1) Looking at Column [2] we can infer that as angle θ increases, the intensity of light passing through the two linear polarizers decreases.
2) Similarly, looking at Column [6] we can infer that as angle θ increases, the intensity of light passing through the three linear polarizers also decreases.
3) Looking at Column [5], we can infer that as angle θ increases, the relative intensity of light passing through the two linear polarizers compared to that predicted by Malus Law increases.
4) Comparing Column[5] with Column [9], we can infer that as angle θ increases, the relative intensity of light passing through the three linear polarizers increases at a faster rate compared to when only two linear polarizers are used. The base comparison is against the prediction using Malus Law.
5) This indicates that the statistical distribution of the photons passing through any single linear polarizer differs slightly from the Cosine law. It is only a statistical bell-curve that have some resemblance to the cosine curve.
6) More importantly, we can infer that the closer we get to the polarizing axis of the polarizer, the higher will be the probability of photons passing through it.

I will stop here for you to ponder on the implication of this set of data before I continue with the proof of Malus Law.

Cheers.

"THEY"
Hexa- what kind of circular polarizer lenses are you using and how do you determine right and left hand?

Would you suggest different lenses/setup for a 12 year old performing this test?

HAPPY HOLIDAYS TO ALL!
Confused2
Hi hexa,Mr Homm, THEY, Montec et al,

hexa, minor point, it seems a bit fierce to classify poor old Malus as infinitely wrong because 3.0% of the light passes at 90 degrees .. I'd be tempted to blame the filter manufacturer. That none-total stoppage would affect the 45 degree point too .. say 1.5% error ? which puts Malus within about 1% .. not too bad?

Surely there must be some loss with the filters inserted .. 10% ?

Holiday? I can't imagine what that's all about. Have a nice one anyway.

Best wishes,

-C2.
hexa
Hi They,

The Circular Polarizer that I am using are those produced by the makers of camera lenses. Unfortunately, manufacturers of these lenses does not bother to make any distinction between a Right and a Left Circular Polarizer. There is no necessity as the photographers essentially get the same effect from a right and a left circular polarizer.

To understand what is happening when light passes through a QWP, let me use the analogy of a clock with both the front and the back visible to you. If you look at the hands of the clock from the front, the hands of the clock move in the clockwise direction. If you look at the same clock from the rear, the hands are moving in the anti-clockwise direction.

Unlike a linear polarizer, a QWP plate is essentially a piece of material that has two axes instead of one. I gave the analogy that the QWP has two doors instead of one. It will align the photons passing through it along two principal axes that are generally orthogonal to one another. Please note that this is my hypothesis and not a statement that you will find it in any textbook. However, I do have the experimental result to support this claim which I will share with you and the rest of the members a little later. A "photographic circular polarizer" essentially laminate a linear polarizer with a QWP together. The axes of the QWP is placed at 45 degree from the polarizing axis of the linear polarizer. This allows the QWP to disperse the photons in the clockwise as well as in the anti-clockwise directions.

In order for us to observe the cancelling of light passing through a left followed by a right circular polarizer, it is necessary that in the construction of a right circular polarizer, you use the same batch of material and laminate the QWP with the linear polarizer in EXACTLY the same angle that it was done for the left circular polarizer. The only difference is that you laminate the opposite face (like the back of a clock) to the linear polarizer. This is the only way you can make a set of "perfect" right and left "photographic circular polarizer".

Mr Homm suggestion to make a TRUE Right and a TRUE Left Circular Polarizer is correct. Unfortunately, you are unlikely to be able to find a set of Right and Left Photographic Polarizers that is produced in the way that I have described.

The only way out is to purchase some linear polarizers and some QWP from the same manufacturer to construct your own Circular Polarizers.

Alternative, you may want to consider using a mirror in the experimental setup if you are only able to obtain the commercially available photographic circular polarizers.

I hope the above explanation helps.

Cheers.
hexa
Hi Confused2,

You are correct to make that assessment.
The error does seem to be small.

However, if you compare the relative percentage against what is predicted, you will notice that the error can be quite substantial.
Take a look at the variation between what you will observe against what is predicted by Malus at 45 degree. If you use two linear polarizers, the error is 2.31%. If you use 3 linear polarizers, the error climb to 10.34%. Imagine what you will get if you use 4 or 5 linear polarizers?
Next, take a look at angle θ=56.25 degree. With two polarizers, the error is 5.61%. With three polarizers, the error is 21.21%.
If we use angle θ=67.5 degree, the error for two polarizers is 15.69%. With three polarizers, the error climb to 85.71%.
Are these errors considered insignificant by your assessment?
This is where I hope a third party could also confirm the validity of my result.

The point which I was trying to make is that the distribution of the photon intensity against the angle θ is a BELL CURVE and not one that follows the cosine curve perfectly. We can amplify the difference by placing a third, a fourth and a fifth linear polarizer with each inclined at the same common angle θ to one another.

It is this Bell curve distribution of the photons passing through EACH linear polarizer that give rise to the cosine square observation by Malus. There is no intention on my part to prove that Malus Law is wrong.

Apparently, QM uses Malus Experimental Result but makes no attempt to provide a more fundamental explanation on why the probability of light passing through two linear polarizer inclined at an angle θ is given as a square of the wave function, which in this case happen to be the cosine function and not any other trigonometrical function.

I hope the above explanation is acceptable to you.

Cheers.
hexa
Hi They,

To add to my earlier post, if you are doing it for your 12 years old son/daughter you should consider getting some perspect sheet and some plastic materials.
If you stress these materials, you will be able to see some changes to the colorful patterns as you look through these polarizers.

Tell her that there are practical applications playing around with these polarizers.
Engineers uses x-ray instead of ordinary light to study the stress pattern of mechanical parts. It can anticipate any failure of the parts before they fail.

Cheers
Confused2
Hi hexa,

This is Mr Homm's territory really ..

Your initial population is randomly polarised
After first LP are they all (say 90 degrees) vertically polarised or is there (say) a gaussian distribution about the 90 degrees... of width ?
The 45 degree LP is picking from this distribution and may be giving a more distorted distribution .. which gets passed on to the next .. could that be part of the explanation?

Best wishes,

C2.
hexa
Hi Confused2,

You may be correct to assume that the error could be amplified if we pass on to the next stage. But what is really important for us to note here is that the photons passing through A SINGLE Linear Polarizer obey the Gaussian Distribution or Bell curve which I had stated earlier. It does not matter whether it is exactly a cosine curve or not. Afterall, the cosine curve also belong to the Set of curves described by the Gaussian Distribution.

In other words, if we assume that every Photon has a unique orientation where it can be defined by an angle θ on the x-y plane with the photon translating along the z-axis, then the probability of the photons passing through the linear polarizer can be described by the Gaussian Distribution with respect to the polarizing axis of Each Polarizer.

I certainly agree with you that Mr. Homm input at this stage is very important. He will be able to guide us on whether I had committed any logical error in presenting the results as stated in this post ( http://forum.physorg.com/index.php?showtop...ndpost&p=144893 ). I certainly look forwad to his comment as well.

Cheers.
hexa
Hi Mr. Homm, Confused2, Montec, They, Peter Robert, Maltida, Dr. Brettmann, Schneibster, etc,

Mr Homm was correct to reject the proposition that a photon can be described by the generic angle θ on the x-y plane unless there is some way that we can prove that such an angle exist. How are we going to do this when, unlike an electron (where we can use a Stern Gerlach Apparatus), a photon does not respond to the electric or magnetic field that our Apparatus may be designed to measure?

To provide the proof that such an angle exist, we need to understand how Malus Law operate at a more fundamental level. Continuing with the proof of Malus Law, let us imagine that there are 20 doors on a sliding wall with each door placed at an interval of 1 meter apart. There are two sliding walls to this experiment. We construct the two walls parallel to one another such that all twenty doors of both walls are aligned directly to one another. Let us label the doors for wall-X with the notation X(n), where n is an integer 1 to 20. For the doors in wall-Y, we will use the notation Y(n), where n is an integer 1 to 20.
QUOTE

Experiment-1
We get a group of children and instruct them to run through the doors along a straight line that is drawn perpendicular to the two walls. We further instruct them that they can only pass through the door at the rate of 1 child in every twenty seconds.
With these conditions, we will now determine the number of children passing through the doors of both walls after every 20 seconds:
1) Open X(1) to X(20) and  Y(1) to Y(20) – Observation = 20
2) Open X(1) to X(20) and  Y(1) to Y(10) – Observation = 10
3) Open X(1) to X(20) and Y(11) to Y(20)– Observation = 10
4) Open X(1) to X(10) and  Y(1) to Y(20) – Observation = 10
5) Open X(11) to X(20) and Y(1) to Y(20)– Observation = 10
6) Open X(1) to X(10) and Y(11) to Y(20)– Observation = 0
7) Open X(11) to X(20) and Y(1) to Y(10)– Observation = 0
8) Shut X(1) to X(20) and Y(1) to Y(20)– Observation = 0

QUOTE (->
 QUOTE Experiment-1We get a group of children and instruct them to run through the doors along a straight line that is drawn perpendicular to the two walls. We further instruct them that they can only pass through the door at the rate of 1 child in every twenty seconds. With these conditions, we will now determine the number of children passing through the doors of both walls after every 20 seconds:  1) Open X(1) to X(20) and  Y(1) to Y(20) – Observation = 202) Open X(1) to X(20) and  Y(1) to Y(10) – Observation = 103) Open X(1) to X(20) and Y(11) to Y(20)– Observation = 104) Open X(1) to X(10) and  Y(1) to Y(20) – Observation = 105) Open X(11) to X(20) and Y(1) to Y(20)– Observation = 106) Open X(1) to X(10) and Y(11) to Y(20)– Observation = 07) Open X(11) to X(20) and Y(1) to Y(10)– Observation = 08) Shut X(1) to X(20) and Y(1) to Y(20)– Observation = 0

Experiment-2
Next, consider the situation where we slide the entire wall-Y to the right and leave all the doors open. Determine the numbers of children passing through the doors of both walls at an interval of 20 seconds:
1) If Y(1) coincide with X(1) – Observation = 20
2) If Y(1) coincide with X(2) – Observation = 19
3) If Y(1) coincide with X(3) – Observation = 18
4) If Y(1) coincide with X(4) – Observation = 17
………………………………….
18) If Y(1) coincide with X(19) – Observation = 2
19) If Y(1) coincide with X(20) – Observation = 1
20) If none of the doors coincide with one another– Observation = 0

QUOTE

Experiment-3
Next, we instruct the children that for doors 10 and 11 (irrespective of whether it is Wall X or Wall-Y), they can pass through the door at the rate of 20 children at every 20 seconds; for doors 9 and 12, they can do so at the rate of 18 for every 20 seconds; for doors 8 and 13 at the rate of 16 for every 20 seconds; for doors 7 and 14 at the rate of 14 for every 20 seconds:  for doors 6 and 15 at the rate of 12 for every 20 seconds:  for doors 5 and 16 at the rate of 10 for every 20 seconds:  for doors 4 and 17 at the rate of 8 for every 20 seconds: for doors 3 and 18 at the rate of 6 for every 20 seconds:  for doors 2 and 19 at the rate of 4 for every 20 seconds: and for doors 1 and 20 at the rate of 2 for every 20 seconds.
The walls are reinstated to the original position, with X(1) aligned to Y(1) and X(20) aligned to Y(20).
Again, we want to determine the numbers of children passing through the doors of both walls after every 20 seconds:

1) Open X(1) to X(20) and  Y(1) to Y(20) – Observation = 220
2) Open X(1) to X(20) and  Y(1) to Y(10) – Observation = 110
3) Open X(1) to X(20) and Y(11) to Y(20)– Observation = 110
4) Open X(1) to X(10) and  Y(1) to Y(20) – Observation = 110
5) Open X(11) to X(20) and Y(1) to Y(20)– Observation = 110
6) Open X(1) to X(10) and Y(11) to Y(20)– Observation = 0
7) Open X(11) to X(20) and Y(1) to Y(10)– Observation = 0
8) Shut X(1) to X(20) and  Y(1) to Y(20) – Observation = 0

QUOTE (->
 QUOTE Experiment-3Next, we instruct the children that for doors 10 and 11 (irrespective of whether it is Wall X or Wall-Y), they can pass through the door at the rate of 20 children at every 20 seconds; for doors 9 and 12, they can do so at the rate of 18 for every 20 seconds; for doors 8 and 13 at the rate of 16 for every 20 seconds; for doors 7 and 14 at the rate of 14 for every 20 seconds:  for doors 6 and 15 at the rate of 12 for every 20 seconds:  for doors 5 and 16 at the rate of 10 for every 20 seconds:  for doors 4 and 17 at the rate of 8 for every 20 seconds: for doors 3 and 18 at the rate of 6 for every 20 seconds:  for doors 2 and 19 at the rate of 4 for every 20 seconds: and for doors 1 and 20 at the rate of 2 for every 20 seconds.The walls are reinstated to the original position, with X(1) aligned to Y(1) and X(20) aligned to Y(20).Again, we want to determine the numbers of children passing through the doors of both walls after every 20 seconds:1) Open X(1) to X(20) and  Y(1) to Y(20) – Observation = 2202) Open X(1) to X(20) and  Y(1) to Y(10) – Observation = 1103) Open X(1) to X(20) and Y(11) to Y(20)– Observation = 1104) Open X(1) to X(10) and  Y(1) to Y(20) – Observation = 1105) Open X(11) to X(20) and Y(1) to Y(20)– Observation = 1106) Open X(1) to X(10) and Y(11) to Y(20)– Observation = 07) Open X(11) to X(20) and Y(1) to Y(10)– Observation = 08) Shut X(1) to X(20) and  Y(1) to Y(20) – Observation = 0

Experiment-4
Next, we repeat Experiment-3 but shift the entire wall-Y to the right and leave all the doors open. Determine the numbers of children passing through the doors of both walls after every 20 seconds:
1) If Y(1)  coincide with X(1) – Observation = 220
2) If Y(1) coincide with X(2) – Observation = 200
3) If Y(1) coincide with X(3) – Observation = 180
4) If Y(1) coincide with X(4) – Observation = 162
5) If Y(1) coincide with X(5) – Observation = 144
………………………………….
16) If Y(1) coincide with X(17) – Observation = 12
17) If Y(1) coincide with X(18) – Observation = 8
18) If Y(1) coincide with X(19) – Observation = 4
19) If Y(1) coincide with X(20) – Observation = 2
20) If none of the doors coincide with one another – Observation = 0

From the observations, we can infer that Experiment-2 varies linearly in relation to the shifting of the wall while Experiment-4 does not. We may have no information of the instructions that was given to the children in running through these doors or any information as to which particular door the children actually passed through in each of the experiment. But from the result in recording the TOTAL numbers of children passing through the doors of both the walls as we slide wall-Y to the right, we can make the following inferences:
I] the children passes through each door at the same rate in Experiment-2
II] more children passes through the doors at the center than those at each ends of the wall.
The above inference can be made purely from the Total numbers of children passing through both walls and the knowledge that the entire Wall-Y is shifted at an interval of 1 meter to the right.

From this simplistic illustration, we will attempt to draw the same inference when we rotate the polarizing axis of one linear polarizer at an angle σ from the others. But this requires us to make an important ASSUMPTION that each photon can be described physically by a generic angle θ. We will make the assumption that if the photon is translating along the z-axis, this angle θ can then be defined on the x-y plane. Instead of doors in our simple experiments, we can replace the specific door with the angle σ, where σ is measured from the polarizing axis. If the rate is similar to that described in Experiment-2 when the angle σ is increased, then we can infer that the photons pass through the polarizers uniformly. In other words, the photons have equal probability to be found at any angle θ. This is in fact the case for a source of unpolarized light.
On the other hand if the rate is similar to that described in Experiment-4 when the angle σ is increased, then we must infer that the photons passes through the polarizer at a higher rate when angle σ is small compared to when the angle σ is large. We also notice that at a certain angle σ =90 deg., the intensity of any photon passing through the two linear polarizers approaches zero. This would further reaffirm our ASSUMPTION that A PHOTON must have this PHYSICAL attribute where it can be described by an angle θ on the x-y plane. Hence, from the measurement of the total intensity of photons passing through both the linear polarizers against the angle σ that one polarizer is rotated from the other, we can infer that the photons passing through any one polarizer obey the Gaussian Distribution. It has the shape of a bell. It may resemble the cosine curve.

In conclusion, I hope I have conveyed to you how Malus Law can be understood more fundamentally. More importantly, I hope I was able to convey to you the particle nature of A PHOTON. From the proof of Malus Law, I hope I was also able to convey to you that A PHOTON behave more like a Deck of Cards as opposed to a Box of marbles and has this physical attribute that we can define using the angle θ.

I will stop here for you to ponder as to the reasonableness of the above propositions before proceeding to account for the observation of Photons passing through the Circular Polarizers.
It will be quite futile to proceed further unless we can agree to the proposition that Each PHOTON has a Generic angle θ and that there is a distinct molecular axis in the linear polarizer that governs how A PHOTON passes through it.
Do raise your objection if you are not entirely convinced on these propositions.

Cheers.

Note: If you are confused by my usage of angle θ and angle σ, please refer to my earlier post where I clarify the usage of these two notations ( http://forum.physorg.com/index.php?showtop...ndpost&p=142652 ) based on the question raised by Mr. Homm.
mr_homm
@hexa, Nov.8 (continued)

Classical EM description of the action of a QWP:

The QWP has an "optic axis" at some angle, and slows (or speeds up, depending on the material) the passage of light that is plane polarized with its E filed aligned with the optic axis. Now consider two LP filters one with its polarization axis at 0 deg and the other with its axis at 90 deg. Place a QWP between them with its optic axis at 45 deg.

For this experiment, the first stage is the same as experiment 1, and you have light of intensity I/2 composed of 100% E_x leaving the first LP filter. The QWP axis is oriented along the x' axis, 45 degrees from the first filter. Therefore, you decompose the E vector into its x' and y' components. Since E is oriented along the x axis, it is |E|*X when expressed as a magnitude and unit direction vector, and since X = 1/√2*(X' - Y'), it follows that E = |E|/√2*(X' - Y') = |E|/√2*X' + |E|/√2*(-Y'). Since the QWP delays any E field that is in the y' direction, the second component is delayed relative to the first. In order to express this delay, it is necessary to give more detail about |E|. Since a QWP only works correctly for a narrow range of wavelengths, we should look at a monochromatic E field, i.e. |E| = E_0*cos(kz-wt). The action of the QWP on the y component is therefore to change this |E| into |E'| = E_0*sin(kx-wt). Therefore, the light exiting the QWP is has an E field E = |E|/√2*X' + |E'|/√2*(-Y').

Now this light strikes the third LP filter, which has its polarizing axis oriented along the y direction. Therefore, you decompose the E vector into x and y components in order to see what the third filter will do do it. Since E = |E|/√2*X'+ |E'|/√2*(-Y'), and X' = 1/√2*(X + Y), and Y' = 1/√2*(-X + Y) it follows that E = |E|/√2*1/√2*(X + Y) + |E'|/√2*(-1/√2*(-X + Y))= (|E|+|E'|)/2*X +(|E|-|E'|)/2*Y. The third filter absorbs the x component, so only the y component passes through. Therefore, the light passing through the third filter has E field E = (|E|-|E'|)/2*Y. In order to find the amplitude of the light that gets through, you need to combine the two E contributions. Since it is an elementary trig identity that cos(x) + sin(x) = √2sin(x+45deg), the net field is √2|E|/2*Y = |E|/√2*Y with a 45 deg phase delay. Therefore, the amplitude of the light has been reduced by a factor of √2. Since the intensity of light is proportional to E^2, the intensity has been reduced by a factor of 2 relative to what got through the first LP filter (which was already I/2, remember), so the intensity is 1/4 as great as the original unpolarized light. Therefore, light DOES get through the third filter, the polarization is along the y axis, and the intensity is I/4.

At this point, something may be puzzling. I have said that taking vectors apart into components makes no physical difference, so why do I need a QWP at all? Can't I just arbitrarily decide to write the E field in terms of X' and Y' (after all, it makes no difference), and then let these field components hit the second polarizer? The answer is, yes I can do this, and the answer will come out just like experiment 1. The reason is that without the delay, |E'| = |E|, and so the y component exiting the second polarizer is just (|E|-|E'|)/2*Y = 0, which is the same result I got when I DIDN'T break the E field up into the new components. So you can see that it truly doesn't matter whether I take the vector apart or not; it is only a matter of calculational convenience to do so.

I should also mention that the QM approach is identical to the classical EM one. Just substitute |X> for E_x*X and |Y> for E_y*Y, and so on. The QM operators do the exact same thing to the state vectors that the EM theory does to the E field, namely resolve into components, absorb a component, or delay a component. All the math is the same, you just apply it to state vectors instead of E field vectors, so I won't go through the description again. If you want to read the QM version, just cut and paste |X> for |E|*X and so on; it really is word for word the same.

Now on to further topics:

On your answers to my questions about how you regard photons as passing through filters, thank you. Your hypothesis is clear to me now. Perhaps there is more you have not yet stated, but what you have said so far is understood.

QUOTE
The angle θ of a SINGLE PHOTON cannot be measured physically and is unlikely that we can measure it definitively in the near future. This is because a PHOTON is a boson. Unlike fermion, a boson is not affected by magnetic field or electric field. Hence, it is impossible to measure the angle θ with the precision that we can measure for the spin of an electron or any other fermion. I could be wrong, but I don't see how one could measure this angle θ definitively, given the limitation that I have mentioned above.
But that does not mean that we cannot infer the range of angle θ from its group behavior.

I'm not sure I buy the explanation that the angle is unmeasurable because photons are bosons rather than fermions. This is a spin property, not a charge property. Photons are not affected by electric or magnetic fields because they are uncharged. There are charged bosons (W+ and W- bosons that mediate the weak nuclear force), uncharged bosons (photons, Z boson that also mediates the weak nuclear force), charged fermions (electrons, protons), and uncharged fermions (neutrons, neutrinos). So, you are right that we cannot measure the spin of a photon as easily as an electron, but it is because one is uncharged and the other is charged, not because one is a boson and the other is a fermion. The examples I have cited show that these properties are not correlated.

QUOTE (->
 QUOTE The angle θ of a SINGLE PHOTON cannot be measured physically and is unlikely that we can measure it definitively in the near future. This is because a PHOTON is a boson. Unlike fermion, a boson is not affected by magnetic field or electric field. Hence, it is impossible to measure the angle θ with the precision that we can measure for the spin of an electron or any other fermion. I could be wrong, but I don't see how one could measure this angle θ definitively, given the limitation that I have mentioned above.But that does not mean that we cannot infer the range of angle θ from its group behavior.

I'm not sure I buy the explanation that the angle is unmeasurable because photons are bosons rather than fermions. This is a spin property, not a charge property. Photons are not affected by electric or magnetic fields because they are uncharged. There are charged bosons (W+ and W- bosons that mediate the weak nuclear force), uncharged bosons (photons, Z boson that also mediates the weak nuclear force), charged fermions (electrons, protons), and uncharged fermions (neutrons, neutrinos). So, you are right that we cannot measure the spin of a photon as easily as an electron, but it is because one is uncharged and the other is charged, not because one is a boson and the other is a fermion. The examples I have cited show that these properties are not correlated.

The Local Hidden Variable Theory made the assumption that the angle θ of the photons are evenly distributed. This is an incorrect assumption which I will explain when I provide you the proof for Malus Law.
Bell’s theorem is made on this erroneous premises. This has led to the ludicrous presumption that Locality is violated and that it is possible to communicate information faster than the speed of light. No. The claim is even more preposterous. It is instant communication irrespective of whether the two communicating parties may be half a Universe away from one another. This is the current claim of Quantum entanglement.

My understanding of Bell's theorem is that it does not depend on ANY special assumptions such as the one you mention. The theorem is supposed to hold if you assume that the world is CAUSAL, LOCAL, and DETERMINISTIC (in the sense that quantum uncertainty represents our lack of knowledge about a definite physical state, rather than an inherent indefiniteness in the state). Could you please give me a reference where the assumption of equal angle probability is used? I'd like to see how it figures into the theorem, since I was unaware of this assumption.

QUOTE
1)The polarizing axis of first Linear polarizer is aligned at 0 degree.
2)The second linear polarizer is aligned at 45 degree.
3)The third linear polarizer is aligned at 90 degree.
Question:
Determine the probability intensity of light passing through all the three linear polarizers.

Done above; the answer is 1/8, assuming ideal polarizers.

@ Peter Robert, Nov. 9

Thanks for the kind words. I can never understand mott.carl either, so I just skip him.

@ hexa, Nov. 10

That was an interesting and informative post by GoodElf in the other thread. I think I've already addressed all the questions you brought up in this post, so I have nothing to add here. Just mentioning it so you will know I haven't skipped ahead while trying to catch up!

@ Confused2, Nov. 11

Yes, you can rotate the vector instead of the filter as this is a mathematically equivalent way to calculate the result. The trouble you found with the value is that you have calculate the E field AMPLITUDE, while the intensity is proportional to the square of the amplitude. Therefore, you actually get an intensity reduction of 1/2, which agrees with Malus. (BTW, I saw in a later post that you already found the trouble. I'm just taking posts in strict order, so I'm answering here anyway.)

@ hexa, Nov. 11

On your points 1 through 4, I agree. This is exactly how I would calculate it.

QUOTE (->
 QUOTE 1)The polarizing axis of first Linear polarizer is aligned at 0 degree.2)The second linear polarizer is aligned at 45 degree.3)The third linear polarizer is aligned at 90 degree.Question:Determine the probability intensity of light passing through all the three linear polarizers.

Done above; the answer is 1/8, assuming ideal polarizers.

@ Peter Robert, Nov. 9

Thanks for the kind words. I can never understand mott.carl either, so I just skip him.

@ hexa, Nov. 10

That was an interesting and informative post by GoodElf in the other thread. I think I've already addressed all the questions you brought up in this post, so I have nothing to add here. Just mentioning it so you will know I haven't skipped ahead while trying to catch up!

@ Confused2, Nov. 11

Yes, you can rotate the vector instead of the filter as this is a mathematically equivalent way to calculate the result. The trouble you found with the value is that you have calculate the E field AMPLITUDE, while the intensity is proportional to the square of the amplitude. Therefore, you actually get an intensity reduction of 1/2, which agrees with Malus. (BTW, I saw in a later post that you already found the trouble. I'm just taking posts in strict order, so I'm answering here anyway.)

@ hexa, Nov. 11

On your points 1 through 4, I agree. This is exactly how I would calculate it.

The point that I wanted to highlight by this illustration is that QM essentially took Malus Law as another confirmation of its validity even though QM provide no generic explanation. By the way, Malus Law also do not have a generic explanation.
QM simply states that the state vector of photons passing through a polarizer inclined at an angle θ from an earlier linear polarizer as:

(5) lx'> = cosθlx> + sinθly>

Eliminating sinθ and retaining cosθ based on the quantum rule that l<xlx>l = 1
and l<ylx>l=0, we end up with the wave function of cosθ.
The square of the imaginery wave function l<θlx>l= cosθ will then give us the probability of the intensity predicted by Malus Law. Looks to me like QM is engaging in tautology.

Here I must disagree with you. QM was mostly derived from considerations about atoms initially (along with black body radiation and the photoelectric effect). The QM of atoms already implied that photons carried angular momentum. (This was known because certain energy transitions were NOT observed experimentally, so it was deduced that some physical effect was blocking them. It turned out that all the missing transitions corresponded to changes of electron configuration that involved NO change of angular momentum. This could be explained if photons had angular momentum, because then no photon could be produced without changing the atom's angular momentum.)

Since the photoelectric effect shows that light is composed of photons, and since classical EM theory (and experiments) show that light carries angular momentum if and only if it is circularly polarized, it was pretty clear that circularly polarized light in the classical sense consists of photons selected to all spin the same way, so that their angular momenta add up instead of canceling out. Since classical EM also shows that the superposition of equal right and left circularly polarized beams produces a linearly polarized beam, the only possible photon interpretation is that the linearly polarized state is an equal superposition of opposite circularly polarized states.

Since the whole idea of states being vectors had already been created by Heisenberg (again, with reference to atoms, not starting from light), and since the left and right circularly polarized states form a basis for the vector space (known because all physically measurable light properties can be realized in experiments by appropriate linear combinations of these two states), it follows that the state space is 2 dimensional, and that any two distinct LINEAR polarizations could equally well be used as a basis (by application of a fundamental theorem of linear algebra). Since a calcite crystal can separate two perpendicular linear states cleanly, they MUST be orthogonal in the vector space. Otherwise, according to fundamental tenets of QM, anything that would let one polarization through would necessarily let some of the other through as well.

Once you have all this (a 2-d vector space, orthogonal basis of x and y linear polarization states), you can calculate from the theory that Malus's law must be true. This is 100% based on other parts of QM which DO NOT use Malus's law or even talk about photons. Therefore, QM DOES give a generic explanation of Malus's law, and it is not a tautology. This makes the stakes much higher, because if Malus's law is untrue, then the rest of QM must also be wrong, INCLUDING the basic parts that I mentioned above. This puts us back to about 1926 in terms of understanding how things work. If Malus's law is untrue, then we don't even know what stops atoms from collapsing, because even the very basic parts of QM that explain that are suspect. Of course, it would also mean that classical EM is wrong, as I've mentioned before.

QUOTE
I hope you and the other members following this thread could now comment on Eq(4). Is this a valid test before I make an attempt to state the prediction using a deterministic approach that maintain photon as a real physical entity. One that has the following physical attributes, such as:
1) having a physical axis in our 3D-Space;
2) where we could use θ (on the x-y plane) to describe its orietation while translating through space along the z-axis;
3) where it will interact with molecules making up the polarizers as if they are real particles even though we are unable to measure its mass and charge (a key attributes that is associated with particle) but not forgetting that we can physically measure the momentum and energy associated with EACH photon;
4) and how the photons passing through a polarizer is guided statistically by the alignment of the molecular axis given by the angle σ relative to each photon;
5) and how angle σ determine the range of angles θ' that will in turn determine how they will pass through a subsequent polarizer inclined at another angle σ'.

This should be a valid test of Malus's law. One thing to worry about is that any imperfections in the experimental equipment will also be magnified by the use of multiple LP filters. I will calculate later what to expect from non-ideal filters. In the meantime, I have a question and a suggestion:

Are you planning to measure many different angles with multiple filters, or mainly at 45 deg?

And, you might want to try to confirm the experiment by using optical calcite or Bragg angle scattering to do your LP filtering. These methods are reputed to be much "cleaner" than the polymer (Polaroid) LP filters. The manufactures of these filters say that they may let through up to 3% of the light with the wrong polarization. They also reduce the overall intensity of the light more than you would expect, because they also have a non-polarizing absorption. In other words, the manufacturers of the filters say that, if |E|X + |E|Y hits a Polaroid LP filter with its axis at 0 deg, the light output will be about 0.9|E|X + 0.03|E|Y. This must be taken into account in interpreting the experimental results.

More later.

--Stuart Anderson
dboots
Schneibster

Could you please look at the topic I posted last night
"a magnetic field caught on camera?". I am not sure, but the
way you described the light movement, might be exactly what I caught on camera last night in my back yard, using a flashlight.
Nick
If light is electro-MAGNETIC then why doesn't it influence a compass?

Mitch Raemsch
hexa
Hi Nick,

QUOTE

If light is electro-MAGNETIC then why doesn't it influence a compass?

This is a relevant question.
Perhaps, Mr Homm, Confused2, or those familiar with QM would like to provide the answer from the Classical as well as the QM perspective?

Much as I would like to provide you with the answer at this stage using the proposition that I am advocating, it may be futile for me to try to explain to you until we are able to agree with the way we should perceive each photon in relation to how it passes through a linear or circular polarizer.
In the meantime, I will confine my answer which I had stated in my earlier post ( http://forum.physorg.com/index.php?showtop...ndpost&p=142652 )

QUOTE (->
 QUOTE If light is electro-MAGNETIC then why doesn't it influence a compass?

This is a relevant question.
Perhaps, Mr Homm, Confused2, or those familiar with QM would like to provide the answer from the Classical as well as the QM perspective?

Much as I would like to provide you with the answer at this stage using the proposition that I am advocating, it may be futile for me to try to explain to you until we are able to agree with the way we should perceive each photon in relation to how it passes through a linear or circular polarizer.
In the meantime, I will confine my answer which I had stated in my earlier post ( http://forum.physorg.com/index.php?showtop...ndpost&p=142652 )

3) If it is a particle, why is it that we are unable to measure its mass or charge?
Answer: It is simply because the APPARATUS that we can devise relies on electric field and magnetic field to measure mass or charge. Photon does not feel the effect of either of these fields BECAUSE of the Relativistic Effect. I will discuss this topic a little later.

I hope you will be patient. I promise you that I will return to this important question of yours after we have thoroughly explore all the issues surrounding the Polarization of Light.
Do raise it again, but only after we have explore the Polarization of Light and the Doubleslits Experiments.

Cheers.
Maltida
Hi Mr Homm & Hexa,

Thanks Hexa for raising this topic and your advocacy in wanting to look at A PHOTON in Simpler Light (figuratively speaking).

To Mr Homm, I must salute you for standing on the side of Classical and Quantum Mechanics (based on the Copenhagen Interpretation(CI)) that appears to have stood the test of Time and against giants like Einstein, de Broglie, Schrodinger, etc even though you have indicated that you may not agree with CI in its entirety. In fact, I was very surprised that you are also quite a radical yourself when you shared your inner thoughts.
Nevertheless, you seem quite happy to embrace QM notwithstanding the problem which Hexa is saying with regards to Circular Polarization of Light.

My only appeal is for Mr. Homm to keep his post as current as his time permit.
I find it a little bit disjointed when he is commenting on the earlier post without relating to the latest discussion. Are his comments on the earlier posts to be taken in the context of the most current posts by members participating on this thread?

Whatever my comment, I must thank both of you for showing us the Light.

Yours humbly,

Maltida.

mr_homm
@ hexa, Nov. 14

QUOTE
The problem arises from my attempt to see whether we could visually distinguish one photon in one polarized state from another even though we may never know the details of the bolts and nuts that goes into the making of a Single Photon. This stem from my personal belief that if a Photon is Real, then it must also have a PHYSICAL existence that is capable of being described like a marble, a plate, a ball or a planet. It must also have a shape, a size and a mass even though the means available to measure any of these attributes are not available to us. Thanks for highlighting this difficulties in your latest post.

I agree that the photon is real and has a definite physical existence that is capable of being described. I am not committed one way or the other to its having a size and shape, since it is outside the range of natural human perception to perceive the details of a single photon. It may be an unwarranted assumption that everything on all size scales looks basically like it does on the scale we have evolved to perceive. On the other hand, it may be an unwarranted assumption that it does NOT look basically like what we have evolved to perceive. On the question of mass, I agree, the photon has a definite mass, zero, on relativistic grounds. (The answer to a question being zero is quite different from that question not having an answer.)

QUOTE (->
 QUOTE The problem arises from my attempt to see whether we could visually distinguish one photon in one polarized state from another even though we may never know the details of the bolts and nuts that goes into the making of a Single Photon. This stem from my personal belief that if a Photon is Real, then it must also have a PHYSICAL existence that is capable of being described like a marble, a plate, a ball or a planet. It must also have a shape, a size and a mass even though the means available to measure any of these attributes are not available to us. Thanks for highlighting this difficulties in your latest post.

I agree that the photon is real and has a definite physical existence that is capable of being described. I am not committed one way or the other to its having a size and shape, since it is outside the range of natural human perception to perceive the details of a single photon. It may be an unwarranted assumption that everything on all size scales looks basically like it does on the scale we have evolved to perceive. On the other hand, it may be an unwarranted assumption that it does NOT look basically like what we have evolved to perceive. On the question of mass, I agree, the photon has a definite mass, zero, on relativistic grounds. (The answer to a question being zero is quite different from that question not having an answer.)

Before we attempt to visualize a photon, perhaps you may want to ask the following questions:
1) Is Light a particle or a wave?
Answer: I think the answer has been pretty much decided by the Michelson and Morley Experiment; Max Planck account of the Black body radiation and Einstein account of the photoelectric effect. Light is a PARTICLE.

I agree that the last two experiments show that light has particle properties. However, the Michelson/Morley experiment was based on interference, and so it would seem to me to be evidence for wave properties rather than particle properties. In my opinion, it doesn't matter what we call it; the photon has a certain list of observed properties, which define its behavior. Some of those properties match those we associate with waves, and some match those of particles. Concluding that the photon must be one thing or the other has no basis in experiment, but represents our attempt to fit the photon into our existing conceptual framework. As such, this is a philosophical, rather than a physical question.

There is a story I heard once about a logician. He is riding on a train, when the train passes some sheep. His friend asks, "what color are the sheep?" The logician responds, "they are white ON THE SIDE FACING US." By refusing to jump to the conclusion that they are the same color on the unobserved side, the logician opens up the possibility that these sheep represent something that can't be categorized as either black or white. Of course, in the story the logician's attitude is absurd, because sheep are a part of collective human experience, and we all know they are the same color on both sides. However, particles in the subatomic realm are NOT part of our collective experience, and it is not good to make unwarranted assumptions about them. The only judge of truth is experiment, and all the experiments give inconclusive, conflicting results. It cannot be that the universe itself is confused, so the problem must lie with our conceptual categories

QUOTE

2) If it is a particle, how do you account for the observation in the Double Slits Experiment?
Answer:This is a Topic by itself. You may want to refer to the discussion in another thread. But if you want to know what I think about this topic Now, you can backtrack to my earlier discussion with Schneibster on the experiment conducted by the scientists in Hitachi Research Lab. I will return to this topic after we have thoroughly explored Polarization of Light.

Yes, this is part of the core weirdness of QM and definitely deserves a full discussion in its own thread.

QUOTE (->
 QUOTE 2) If it is a particle, how do you account for the observation in the Double Slits Experiment?Answer:This is a Topic by itself. You may want to refer to the discussion in another thread. But if you want to know what I think about this topic Now, you can backtrack to my earlier discussion with Schneibster on the experiment conducted by the scientists in Hitachi Research Lab. I will return to this topic after we have thoroughly explored Polarization of Light.

Yes, this is part of the core weirdness of QM and definitely deserves a full discussion in its own thread.

3) If it is a particle, why is it that we are unable to measure its mass or charge?
Answer: It is simply because the APPARATUS that we can devise relies on electric field and magnetic field to measure mass or charge. Photon does not feel the effect of either of these fields BECAUSE of the Relativistic Effect. I will discuss this topic a little later.

QUOTE

We are able to measure its mass and charge.  They are both known to be zero.  I do not know what you mean about the Relativistic Effect.  Relativity does not make things immune to electric or magnetic fields; in fact the electromagnetic field tensor transforms under the Lorenz transformation and is valid in all reference frames.  It is true that you cannot have a reference frame traveling along with the light (it would not be connected to slower reference frames by any Lorenz transformation) but that is not necessary.  If light had ANY electric charge at all, it would be bent by a strong magnetic field the same way it is known to be bent by a gravitational field.  It is observed not to bend, so the charge is zero.

4) Would it be reasonable to assume that one photon that has exactly the same amount of energy or momentum would look exactly the same as the next photon that has exactly the same energy or momentum?

I agree, although I would want it to have the same energy AND momentum AND angular momentum AND phase. I think any two photons that have all these four things the same would be identical. (Phase is not really so important, because phase is different at different places and times, so it is really just a timing issue, i.e. are the photons synchronized, rather than any more fundamental internal property.)

QUOTE (->
 QUOTE We are able to measure its mass and charge.  They are both known to be zero.  I do not know what you mean about the Relativistic Effect.  Relativity does not make things immune to electric or magnetic fields; in fact the electromagnetic field tensor transforms under the Lorenz transformation and is valid in all reference frames.  It is true that you cannot have a reference frame traveling along with the light (it would not be connected to slower reference frames by any Lorenz transformation) but that is not necessary.  If light had ANY electric charge at all, it would be bent by a strong magnetic field the same way it is known to be bent by a gravitational field.  It is observed not to bend, so the charge is zero.  4) Would it be reasonable to assume that one photon that has exactly the same amount of energy or momentum would look exactly the same as the next photon that has exactly the same energy or momentum?Answer: Why not?

I agree, although I would want it to have the same energy AND momentum AND angular momentum AND phase. I think any two photons that have all these four things the same would be identical. (Phase is not really so important, because phase is different at different places and times, so it is really just a timing issue, i.e. are the photons synchronized, rather than any more fundamental internal property.)

5) Can we visually distinguish one photon that has more energy or momentum than another photon like a deck of cards or a box of marbles?
Answer: I think it is more probable that it has the appearance of a deck of cards based on the information on polarization of light.

I'm not sure I understand your analogy to a deck of cards vs. box of marbles. The only thing I can think of is determinate randomness (the cards are in a definite predetermined order, but we don't know what that order is) vs. indeterminate randomness (which marble you pull from a box is not predetermined by anything, so there is no predetermined order for us to know). Is that what you are getting at, or am I missing your point?

QUOTE

6) If we assume that a photon is more like a deck of cards than a box of marbles, can we then attach a PHYSICAL AXIS that is NORMAL to the face of the cards to describe the orientation of the cards in Euclidean space?
Answer: Why not? Mathematically, that is how we define a plane.

Now the cards look like an actual geometric metaphor for polarization, so I'm less sure I interpreted part 5 correctly. Anyway, there is nothing wrong with the axis you are setting up, in my opinion. It can describe the polarization of linearly polarized photons. It must be determined from experiment whether it is adequate to account for all photon states.

QUOTE (->
 QUOTE 6) If we assume that a photon is more like a deck of cards than a box of marbles, can we then attach a PHYSICAL AXIS that is NORMAL to the face of the cards to describe the orientation of the cards in Euclidean space?Answer: Why not? Mathematically, that is how we define a plane.

Now the cards look like an actual geometric metaphor for polarization, so I'm less sure I interpreted part 5 correctly. Anyway, there is nothing wrong with the axis you are setting up, in my opinion. It can describe the polarization of linearly polarized photons. It must be determined from experiment whether it is adequate to account for all photon states.

7) If that can be done, are we able to describe the orientation of a photon in Cartesian coordinates that translate along the z-axis?

I agree, this axis set-up can describe the orientation of a linearly polarized photon traveling along the z axis.

QUOTE

8) Since it is a deck of cards, is it reasonable to assume that the photon looks exactly the same if we flip the cards by 180 degree?

The phase of the photon will be reversed if you do this. We know that strong light beams have phase classically, and rotating them 180 degrees around the z axis will reverse the E field direction and therefore the phase. Either photons have phase, and strong light beams inherit their phase from the constituent photons, or photons do not have phase and it arises in strong light beams by some collective action of the photons, like temperature in thermodynamics. In the first case, rotating the beam will reverse the phase of each photon in the beam, which will account for the phase reversal of the whole beam. In the second case, where photons do not have phase, reversing each individual photon will not change it, as you suggest in your answer. However, then there is no easy explanation for how the phase of the whole light beam could reverse. So perhaps photons do have a direction (unlike playing cards, more like trading cards) and it is noticeable when they are upside down.

QUOTE (->
 QUOTE 8) Since it is a deck of cards, is it reasonable to assume that the photon looks exactly the same if we flip the cards by 180 degree?Answer: Sound reasonable, isn’t it?

The phase of the photon will be reversed if you do this. We know that strong light beams have phase classically, and rotating them 180 degrees around the z axis will reverse the E field direction and therefore the phase. Either photons have phase, and strong light beams inherit their phase from the constituent photons, or photons do not have phase and it arises in strong light beams by some collective action of the photons, like temperature in thermodynamics. In the first case, rotating the beam will reverse the phase of each photon in the beam, which will account for the phase reversal of the whole beam. In the second case, where photons do not have phase, reversing each individual photon will not change it, as you suggest in your answer. However, then there is no easy explanation for how the phase of the whole light beam could reverse. So perhaps photons do have a direction (unlike playing cards, more like trading cards) and it is noticeable when they are upside down.

9) If this is possible, how are we going to distinguish a packet of photon that passes through a x-linear polarizer from another that passes through a y-linear polarizer.
Answer: If we define each photon as having an angle θ that this PHYSICAL AXIS makes on the x-y plane, then we can describe a ray of unpolarized photons as having angles that are distributed evenly from 0 deg < θ <360 deg.

OK, this is a reasonable assumption, and is pretty much the same thing that classical EM assumes about the E field in unpolarized light.

QUOTE

The presence of a x-linear polarizer with its molecular axis aligned along the x-axis will allow photons with angles 0 deg < θ <45 deg. 135 deg < θ <225 deg. 315 deg < θ <360 deg. to pass through the x-linear polarizer. The distribution of the photon through the x-linear polarizer is not uniform. It has a bell curve distribution with a higher concentration for those closer to the x-axis. I will discuss this in greater details in my next post. In the meantime, please take it as correct. This is also important for us to understand why Malus Law works even though it is only an approximation.
With this proposition, you can see that a random population can be neatly divided into the Xs or the Ys. But makes no mistake that one photon in this X vector state may be different from another photon in the same X vector state.
With this, you can see that prediction using this visual proposition will also obtain the QM predictions of l<Xl X>l = 1 and l<YlX>l=0.

Yes, your hypothesis is clear, and yes, it does reproduce the QM and classical EM predictions.

QUOTE (->
 QUOTE The presence of a x-linear polarizer with its molecular axis aligned along the x-axis will allow photons with angles 0 deg < θ <45 deg. 135 deg < θ <225 deg. 315 deg < θ <360 deg. to pass through the x-linear polarizer. The distribution of the photon through the x-linear polarizer is not uniform. It has a bell curve distribution with a higher concentration for those closer to the x-axis. I will discuss this in greater details in my next post. In the meantime, please take it as correct. This is also important for us to understand why Malus Law works even though it is only an approximation.With this proposition, you can see that a random population can be neatly divided into the Xs or the Ys. But makes no mistake that one photon in this X vector state may be different from another photon in the same X vector state.With this, you can see that prediction using this visual proposition will also obtain the QM predictions of ll = 1 and ll=0.

Yes, your hypothesis is clear, and yes, it does reproduce the QM and classical EM predictions.

10) How are we going to distinguish one Right Circularly polarized photon from a Left circularly polarized photon?
Answer: We Can’t! We can’t distinguish it for a SINGLE PHOTON. Collectively, a circularly polarized group of photons is more organized than a beam of unpolarized photon. It has both the populations of the Xs and the Ys. The only difference, is that the Xs is concentrated along the x-molecular axis and the Ys is concentrated along the y-molecular axis. The two molecular axes found in the QWP need not be orthogonal.

Here's a suggestion for a possible experiment to distinguish single RCP photons from single LCP photons. First, set up a double slit experiment, and put a true RCP filter in between the light source and the two slits. Just after ONE slit, place a small container of pure water with flat glass sides. Slowly add fructose sugar to the water and observe the interference pattern as a function of sugar concentration. It will shift, because the refractive index of the water is changing. Now repeat the experiment with a true LCP filter. You will find that the refraction pattern shifts by a different amount. This is because the refractive index of fructose in solution is different for RCP or LCP light (known fact from chemistry). Now reduce the light intensity until only one photon at a time is passing through the device. You will now find that the speckle pattern of individual photons builds up an interference pattern just as before, and that the shift is still there. Conclusion: individual RCP photons behave differently than individual LCP photons.

On the other hand, if you want a single test that can be performed just ONCE and will definitively tell a RCP photon from a LCP photon without building up a behavior pattern, there is no such thing. In fact, there is no such thing in classical physics, or in all of science. Behavior is associated with classes of objects, not with individuals. Without replication of the experiment until you have a good set of statistics, you don't know whether the behavior you are seeing is a glitch or a fundamental property.

QUOTE

11) How do you explain that a Left Circular polarizer will cut off the photons coming out from a Right Circular Polarizer?
Answer: The short answer is that there is no generic Circular Polarizer. It need the Linear Polarizer to do the job. The QWP can’t play that role. It merely direct the X and Y populations along the two molecular axes. Since you have played around with calcite crystal before, I am sure that you must be aware that it is quite difficult to recombine the ordinary and extraordinary ray after it has been split by a previous calcite crystal.

Yes, it is technically difficult to get it to work right. It does work, but it's hard. You need another calcite crystal identical to the first, cut the same way, and rotated 180 degrees around the z axis.

QUOTE (->
 QUOTE 11) How do you explain that a Left Circular polarizer will cut off the photons coming out from a Right Circular Polarizer?Answer: The short answer is that there is no generic Circular Polarizer. It need the Linear Polarizer to do the job. The QWP can’t play that role. It merely direct the X and Y populations along the two molecular axes. Since you have played around with calcite crystal before, I am sure that you must be aware that it is quite difficult to recombine the ordinary and extraordinary ray after it has been split by a previous calcite crystal.

Yes, it is technically difficult to get it to work right. It does work, but it's hard. You need another calcite crystal identical to the first, cut the same way, and rotated 180 degrees around the z axis.

To answer this question, I will use the standard apparatus that involves the use of a mirror. The forward path of a ray of light (unpolarized) passing through the x-linear polarizer(M1) followed by the QWP(M2) is then reflected back to the QWP (M3) before passing through the original x-linear polarizer (M4).
This is what happen:
A] lψ> -----> M1 -----> lx>
B] lx> -----> M2 ----> lX> + lY>
C] lX> + lY> -----> M3 ----> ly>
D] ly> -----> M4 ----> 0
Notes: The X and Y in [C] is laterally inverted. The M3 will further rotate the photons into the ly> vector state.

Yes, I agree with this account.

QUOTE

From the above explanation, you can see that if we were to rotate M4, then it is unlikely that we will be able to stop the ly> state photons from passing through the linear polarizer. The experiment that I have carried out using two different sets of circular polarizers (based on your suggestion of a TRUE Right and a TRUE Left Circular Polarizer) confirmed this proposition. It is NOT ROTATION INVARIANT as what is suggested in QM. Please verify my result.

But the light striking M4 is not circularly polarized any more. The second QWP has turned it back into LP light, which we already know is not rotation invariant. As to replicating the result, I might be able to do that, since THEY has kindly offered to find some of the equipment. However, I barely have time to answer the posts here, and it won't be until Christmas break at the earliest that I will have ANY free time at all. I'm just completely saturated with obligations right now, and there's no point in doing a quick-and-dirty test, because then the results won't be convincing.

QUOTE (->
 QUOTE From the above explanation, you can see that if we were to rotate M4, then it is unlikely that we will be able to stop the ly> state photons from passing through the linear polarizer. The experiment that I have carried out using two different sets of circular polarizers (based on your suggestion of a TRUE Right and a TRUE Left Circular Polarizer) confirmed this proposition. It is NOT ROTATION INVARIANT as what is suggested in QM. Please verify my result.

But the light striking M4 is not circularly polarized any more. The second QWP has turned it back into LP light, which we already know is not rotation invariant. As to replicating the result, I might be able to do that, since THEY has kindly offered to find some of the equipment. However, I barely have time to answer the posts here, and it won't be until Christmas break at the earliest that I will have ANY free time at all. I'm just completely saturated with obligations right now, and there's no point in doing a quick-and-dirty test, because then the results won't be convincing.

[1] I am afraid you may have confused the terms used in classical optics with our discussion here.
I think many physicists also over-simplifies the problem by not looking deep enough into the Construction of the APPARATUS. If you ask an expert in material science, he will tell you that there are many arrangements within a crystal. There could be the AX crystal structure as well as the ABX crystal structure. The packing arrangement could be the Simple cubic, FCC or BCC. Next, we need to consider the shape of each unit of crystal: cubic, hexagonal, tetragonal, rhombohedral, orthorhombic, monoclinic and triclinic. Each of these molecular arrangements will mean that the photon interacting with it will emerge from the array of atoms differently. I am SUGGESTING that there are TWO distinct axes that are present in the QWP that ROTATES the photons one way or the other.

OK, I understand this. However, the crystal structure of calcite is known to me, and I agree that it is the asymmetry of this structure that allows it to interact with photons differently when they have different polarizations.

QUOTE
[2] I don’t think it is technically correct to suggest that light “slow down”. It does not. This is the fallacy of the Fermat Principle. I think the classical explanation on refraction of light is also incorrect. Light being light will always travels at the speed c. It can be made to take a longer path that will give rise to the perception that light “slow down”. Like refraction of different frequency light through a prism. Hence, what decide that one photon take the vertical path while another take the horizontal path, must be decided by the ATOMS interacting with it. The only reasonable explanation is that their paths are determined by their molecular alignment together with the physical state of the photons prior to interacting with the APPARATUS. In the case of a QWP, there are two DISTINGUISHABLE molecular axes that will interact with an unpolarized light. Figuratively, there are TWO doors in QWP instead of one in the Linear polarizer.

I have discussed in my answer to your previous post the way to see that light can apparently slow down even while individual photons continue to travel at speed C. For the rest of your point, I agree.

QUOTE (->
 QUOTE [2] I don’t think it is technically correct to suggest that light “slow down”. It does not. This is the fallacy of the Fermat Principle. I think the classical explanation on refraction of light is also incorrect. Light being light will always travels at the speed c. It can be made to take a longer path that will give rise to the perception that light “slow down”. Like refraction of different frequency light through a prism. Hence, what decide that one photon take the vertical path while another take the horizontal path, must be decided by the ATOMS interacting with it. The only reasonable explanation is that their paths are determined by their molecular alignment together with the physical state of the photons prior to interacting with the APPARATUS. In the case of a QWP, there are two DISTINGUISHABLE molecular axes that will interact with an unpolarized light. Figuratively, there are TWO doors in QWP instead of one in the Linear polarizer.

I have discussed in my answer to your previous post the way to see that light can apparently slow down even while individual photons continue to travel at speed C. For the rest of your point, I agree.

[4] They are generally reflected than absorbed. You can test this using a laser beam.

I've suggested a test for this in my response to your earlier post.

QUOTE

[5] Disagree—please refer to the reason stated in [2]. But you are correct to state that the time it takes to emerge from the QWP is different from another photon that takes the other path. The phase factor is an irrelevant consideration.

Perhaps I should have said "apparent slower travel" of the light, because that is of course what I meant. This is just the same thing as saying the light takes longer to emerge, so we are in agreement about the facts, if not the terminology. The relevancy of the phase factor depends on your point of view. By your hypothesis for explaining polarization, it is clearly irrelevant. However, from the classical EM or QM point of view, its relevance is clear, since it is central to their explanations of all QWP actions.

QUOTE (->
 QUOTE [5] Disagree—please refer to the reason stated in [2]. But you are correct to state that the time it takes to emerge from the QWP is different from another photon that takes the other path. The phase factor is an irrelevant consideration.

Perhaps I should have said "apparent slower travel" of the light, because that is of course what I meant. This is just the same thing as saying the light takes longer to emerge, so we are in agreement about the facts, if not the terminology. The relevancy of the phase factor depends on your point of view. By your hypothesis for explaining polarization, it is clearly irrelevant. However, from the classical EM or QM point of view, its relevance is clear, since it is central to their explanations of all QWP actions.

[6] I don't think speed is a correct consideration.

Speed determines phase upon exit, which as I said in [5] above, is relevant for QM but not for your hypothesis.

QUOTE

Again, please accept my apology for not stating it clearly.
I have used angle θ to define the generic state of a photon. The angle σ is used to define the orientation of the photon relative to the molecular axis of the atoms making up the linear polarizer. A photon may have a generic angle of θ=80 deg. But if the molecular axis (polarizing axis) of a linear polarizer is positioned at 60 deg., then the angle σ of the photon relative to the molecular axis is 20 degree. It is this angle that determine whether or not this particular photon will emerge from this linear polarizer. Not the generic angle θ.

If instead of a linear polarizer, we now use a QWP with two molecular axes.
This single photon will have two angles σ that are approximately orthogonal to one and the other. Let us use σ1 and σ2 to distinguish the two angles of ONE photon relative to the TWO axes. If σ1= 30 deg and σ2=60 deg, then this PHOTON will emerge from the QWP by taking the path of least resistance, ie. the one that it makes an angle of σ1= 30.
If the above explanation can be accepted, then we can look at the ellipticity of the QWP. Basically, the alignment of the two molecular axes in a QWP need not be orthogonal. The more acute the angle that one axis makes with the other, the greater will be the ellipticity of the QWP.
I am sorry for the confusion that I have generated.
I hope with the above explanation you can now better critique what I will be proposing to examine the issue surrounding Circular Polarization.

Yes, your ideas are now clear to me.

QUOTE (->
 QUOTE Again, please accept my apology for not stating it clearly.I have used angle θ to define the generic state of a photon. The angle σ is used to define the orientation of the photon relative to the molecular axis of the atoms making up the linear polarizer. A photon may have a generic angle of θ=80 deg. But if the molecular axis (polarizing axis) of a linear polarizer is positioned at 60 deg., then the angle σ of the photon relative to the molecular axis is 20 degree. It is this angle that determine whether or not this particular photon will emerge from this linear polarizer. Not the generic angle θ.If instead of a linear polarizer, we now use a QWP with two molecular axes.This single photon will have two angles σ that are approximately orthogonal to one and the other. Let us use σ1 and σ2 to distinguish the two angles of ONE photon relative to the TWO axes. If σ1= 30 deg and σ2=60 deg, then this PHOTON will emerge from the QWP by taking the path of least resistance, ie. the one that it makes an angle of σ1= 30.If the above explanation can be accepted, then we can look at the ellipticity of the QWP. Basically, the alignment of the two molecular axes in a QWP need not be orthogonal. The more acute the angle that one axis makes with the other, the greater will be the ellipticity of the QWP.I am sorry for the confusion that I have generated.I hope with the above explanation you can now better critique what I will be proposing to examine the issue surrounding Circular Polarization.

Yes, your ideas are now clear to me.

Finally, please pardon me for seeking this clarification:
QUOTE

It is my OPINION that current QM gives a pretty good account of circular polarization, which agrees with experimental data.

Can I assume that your OPINION is not based on the experiments that you have conducted personally with regards to Circular Polarization of Light?

I performed some but not all of these experiments long ago in college. The results I got then agreed with the classical and QM predictions, but I will admit that I did not test for exactly the behavior you have measured, so as far as my personal experience goes, I must consider this an open question.

Out of time once again. I'll continue trying to catch up to the current discussion as time permits.

--Stuart Anderson
hexa
Hi Mr Homm,

QUOTE
Mr Homm:
QUOTE (->
 QUOTE Mr Homm:Quote Hexa:The problem arises from my attempt to see whether we could visually distinguish one photon in one polarized state from another even though we may never know the details of the bolts and nuts that goes into the making of a Single Photon. This stem from my personal belief that if a Photon is Real, then it must also have a PHYSICAL existence that is capable of being described like a marble, a plate, a ball or a planet. It must also have a shape, a size and a mass even though the means available to measure any of these attributes are not available to us. [1] I agree that the photon is real and has a definite physical existence that is capable of being described. [2] I am not committed one way or the other to its having a size and shape, since it is outside the range of natural human perception to perceive the details of a single photon. [3] It may be an unwarranted assumption that everything on all size scales looks basically like it does on the scale we have evolved to perceive. [4] On the other hand, it may be an unwarranted assumption that it does NOT look basically like what we have evolved to perceive. [5] On the question of mass, I agree, the photon has a definite mass, zero, on relativistic grounds. (The answer to a question being zero is quite different from that question not having an answer.)

[1] Thanks for agreeing to this. It is a key assumption if we are to find any common ground to what I am advocating in this thread.

[2] I am inclined to accept that there is a shape and size attached to a PHOTON notwithstanding that it is outside the range of natural human perception. But I do agree with you that we can never be sure because any material object also emits “FIELD” that does not fit into the same definition of a physical entity that obey the Law of Conservation.
Wasn’t it, not too long ago, that the size of an ATOM was also beyond human perception? Now we have fixed the size at around 10E-10m.
Wasn’t the size of the nucleus of atom beyond human perception? Now we have it at around 10E-15m.
Lastly, wasn’t the size of a PROTON also beyond human perception? Now we have it at around 10E-17m. We could even infer the guts (the quarks) that goes into the construction of a proton.
Again, not too long ago, the shape of an Atom was also beyond human perception. At the beginning of the 20th century, we had the plum pudding model proposed by J.J.Thomson who discovered the electron as a particle. This was corrected by Rutherford from his experiment in bombarding a gold foil with alpha particles. NOW, I do not think there is any doubt in majority of the peoples' mind who have learned some basic science on how they ought to perceive the shape of a SINGLE ATOM.
Similarly, I think the common consensus on the shape of elementary particles like electron, proton and neutrons would generally be that of a marble as opposed to something else.
Science needed to start with a Model before it can attempt to put in the numbers to describe the particles under consideration. Without a realistic Model, the mathematics involved will be quite meaningless--just like the plum pudding Model of the atom proposed by J.J. Thomson.
This is where I find the Model based on Copenhagen Interpretation that led to the development of Quantum Mechanics unsatisfactory. It makes no apology on why nature behave so illogically as long as the number is right. I tend to believe that QM is incomplete rather than incorrect. It needed some modification to the Model if it can be used to fully describe Nature.
QM can’t be totally wrong if it is able to predict the fine structure constant that has an agreement with experiment to an accuracy of 11 decimal places. On the same note, Classical Physics cannot be totally wrong when QM and Einstein Relativity seek to displace it. In fact, 90% of what is described in contemporary physics continue to be based on the foundation of Classical Physics. What I am advocating here is that it needs to be modified-- and this has to start with the Model. I think understanding Polarization of Light more fundamentally is a cheap and effective approach to exploring and establishing a more effective Model to describe Nature. The Accelerators in CERN or Fermilab, etc is fine if you have deep pocket. Otherwise, I think there is no less physics involved in trying to understand the Science of Circular Polarization more fundamentally.

[3] I disagree with this statement in favour of [4].

[4] I think it makes more sense and is a lot easier to describe something that has a PHYSICAL attribute than to do without.

[5] There is some problem with the way Einstein had presented his Theory of Relativity although he is correct to make the connection between Matter and Energy. All credit goes to Einstein.
On a strict interpretation of E=mc^2, it must mean that matter in one frame that moves at a velocity v (less than c) will allow an observer to measure its mass. The mass measured in one inertial frame can be related to the mass measured in another using Lorentz Transformation as long as the speed of light, c is not exceeded.
Next, consider the fact that if we were to move the same mass in this blob of matter to the speed of light c. Does it not then becomes Energy, given by Einstein’s hallmark equation?

To answer this question we need to ask ourselves this basic question. How do we measure Mass?

At the macro level, the weight of an object is not written on the object. It must be inferred from the displacement that the mass of an object will exert on a spring or any device that will provide a displacement where measurement can be made. In fact all the APPARATUS known to Man that measure the fundamental units of measurement of Mass and Time rely on our ability to measure DISPLACEMENT which is the unit of Length.
Similarly, at the scale of an atom, a proton, an electron or a photon, we also need to measure the displacement that the electric or magnetic field exerts on these particles. If electric or magnetic field is unable to exert any influence on the particle to cause it to displace differently for different mass, then we will have no means to determine the mass of these particles.
This explains why neutron was not detected until James Chadwick overcame this difficulty by transferring the momentum of a neutron to a proton. By measuring the momentum of the proton that received the momentum from the neutron, he could then infer the existence of the neutron. Similarly, we cannot measure the mass of a neutral atom if it does not respond to the effect of electric and magnetic field. We need to convert it into an ion before we can measure its mass using a mass spectrometer. On the same basis, a PHOTON does not respond directly to the stimulus of electric and magnetic field in a Mass spectrometer because it is traveling at the speed of light, c.. This is where I think it is incorrect to make the assumption that a PHOTON has “Zero Mass”.
To extend Relativity to imply that Two different photons (carrying different energy and momentum) has the same “zero mass” will cause us to run foul of the Law of Conservation of Matter. This Law essentially means that we cannot create something from nothing and neither can we cause something to vanish into nothingness.
There are more to what I mean by relativistic effect. I will not go into the details at this stage, as it would be totally incomprehensible without first agreeing to some basic propositions that I have posted here.

Let me also address the question that you have raised:
QUOTE
Quote Mr Homm:
QUOTE (->
 QUOTE Quote Mr Homm:Quote Hexa:3) If it is a particle, why is it that we are unable to measure its mass or charge?Answer: It is simply because the APPARATUS that we can devise relies on electric field and magnetic field to measure mass or charge. Photon does not feel the effect of either of these fields BECAUSE of the Relativistic Effect. I will discuss this topic a little later. We are able to measure its mass and charge. They are both known to be zero. I do not know what you mean about the Relativistic Effect. Relativity does not make things immune to electric or magnetic fields; in fact the electromagnetic field tensor transforms under the Lorenz transformation and is valid in all reference frames. It is true that you cannot have a reference frame traveling along with the light (it would not be connected to slower reference frames by any Lorenz transformation) but that is not necessary. If light had ANY electric charge at all, it would be bent by a strong magnetic field the same way it is known to be bent by a gravitational field. It is observed not to bend, so the charge is zero.

I will want to defer providing the explanation for the same reason that I have given Nick.
It will be quite futile until we can clearly establish the particle nature of photon as a deck of cards as opposed to a box of marbles.

In pursuance to this objective, I will also defer discussing your proposition of alternative experiments to a little later until after we have analysed the data of light passing through a Circular Polarizer followed by a Linear Polarizer.
However, there is some confirmation that I need from you based on my proof of Malus Law.
Can we agree in principle to the followings:
QUOTE

1) That the photons passing through a Linear Polarizer obey the Gaussian Distribution about the polarizing axis of the linear polarizer?
2) That, it is plausible to assume that a photon in the unpolarized state has the probability to be found at any angle θ where 0 deg.<θ<360 deg ;
3) That, it is plausible to describe a PHOTON in the state vector lx> as a photon that has the probability to be found at any angle θ where 0 deg.<θ<45 deg; 135 deg.<θ<225 deg; 315 deg.<θ<360 deg;
4) That, it is plausible to describe a photon in the state vector ly> as a photon that has the probability to be found at any angle θ where 45deg.<θ<135 deg; 225 deg.<θ<315 deg.

I hope I have stated my case with sufficient details to solicit in principle agreement from you. And that the above propositions are plausible and that it is not some far fetch idea too ridiculous for consideration.

Cheers.
hexa
Hi Mr. Homm,

It is OK to state that you do not agree to any of these propositions at this juncture.
This is an important feedback because it will signal to me on where I have erred and what are the areas I need to clarify to state my proof more explicitly before looking at the data on the experiments that I have conducted with Circular Polarizers.

I hope you will pardon me if I had used words and terms that may not be entirely comfortable to you.

I look forward to some comment on the points that I have raised in my last post.

Cheers.
hexa
Hi Mr. Homm,

Looks like you have been pretty busy catching up on the other threads.
I thoroughly enjoy your analysis that you put forth in the thread on Superposition and Electromagnetism. I hope to expand on the discussion a little later.

In the meantime let me discuss on this point that you have put forward pertaining to the story about the logician:

QUOTE

In my opinion, it doesn't matter what we call it; the photon has a certain list of observed properties, which define its behavior. Some of those properties match those we associate with waves, and some match those of particles. Concluding that the photon must be one thing or the other has no basis in experiment, but represents our attempt to fit the photon into our existing conceptual framework. As such, this is a philosophical, rather than a physical question.

There is a story I heard once about a logician. He is riding on a train, when the train passes some sheep. His friend asks, "what color are the sheep?" The logician responds, "they are white ON THE SIDE FACING US." By refusing to jump to the conclusion that they are the same color on the unobserved side, the logician opens up the possibility that these sheep represent something that can't be categorized as either black or white. Of course, in the story the logician's attitude is absurd, because sheep are a part of collective human experience, and we all know they are the same color on both sides. However, particles in the subatomic realm are NOT part of our collective experience, and it is not good to make unwarranted assumptions about them. The only judge of truth is experiment, and all the experiments give inconclusive, conflicting results. It cannot be that the universe itself is confused, so the problem must lie with our conceptual categories

Yes, I fully agree that as astute as the logician, one should simply sit on the fence. It is the safest choice. Unfortunately, life is about making choices. Science would not have progressed if nobody makes any decision to turn right or left. Life are full of cross-roads and T-junctions. Life would be a COMPLETE STANDSTILL if nobody makes any decision when they come to a cross-road or T-junction.

Similarly, progress in Science is made by deciding on what is the best description of Nature not by sitting on the fence. Take Light as an example. Through the ages, man has looked upon light with mythical awe. When Science had progressed to the stage when we were able to give it a proper technical term, we named it as WAVE. Then Newton came along and pronounce it as PARTICLE which he called CORPUSCLE. Next, Thomas Young conducted the experiment using a Double-slits that showed light as a WAVE. Afterwhich, Einstein push the pendulum back to the PARTICLE corner based on his Account of the Photoelectric Effect.
The PARTICLE nature of Light is further reinforced by the same experiment using the double-slits that pronounced Light as a Wave. It was shown unmistakenly that the photon arrive on the screen ONE AT A TIME. It is not one half or a quarter of a photon. This can only suggest that Light is a PARTICLE. What is not Understood at this Juncture in Science is why STATISTICALLY, they seem to be able to act in concert with one another to manifest the fringes that appears to have an answer based on the assumption that light is a wave. Similarly, known Particles that has mass and charge like the electrons also manifest the interference pattern when they are made to pass through the Double-slits. This is where QM came into the picture by providing the mathematics to allow prediction to be made based on the ASSUMPTION that these Quantum entities also has this wave properties. But we must not forget that this is based on an incomplete understanding of what Light and the rest of the Quantum entities is really all about. This is where I find the Uncertainty Principle, the Complementary Principle and the Superposition Principle only provide us an intermediate account of Nature and not one that is cast in stone.

By my post ( http://forum.physorg.com/index.php?showtop...ndpost&p=147725 ), I hope to establish whether we could make the assumption base on the discussion that we have soldiered since you came on to this thread.
I hope to establish whether it is reasonable to make these assumptions before proceeding to make further analysis on the data I have obtained with regards to Circular Polarization of Light. It will be quite futile to built on a faulty foundation if it can be shown irrevocably that it is hopelessly wrong.

QUOTE (->
 QUOTE In my opinion, it doesn't matter what we call it; the photon has a certain list of observed properties, which define its behavior. Some of those properties match those we associate with waves, and some match those of particles. Concluding that the photon must be one thing or the other has no basis in experiment, but represents our attempt to fit the photon into our existing conceptual framework. As such, this is a philosophical, rather than a physical question.There is a story I heard once about a logician. He is riding on a train, when the train passes some sheep. His friend asks, "what color are the sheep?" The logician responds, "they are white ON THE SIDE FACING US." By refusing to jump to the conclusion that they are the same color on the unobserved side, the logician opens up the possibility that these sheep represent something that can't be categorized as either black or white. Of course, in the story the logician's attitude is absurd, because sheep are a part of collective human experience, and we all know they are the same color on both sides. However, particles in the subatomic realm are NOT part of our collective experience, and it is not good to make unwarranted assumptions about them. The only judge of truth is experiment, and all the experiments give inconclusive, conflicting results. It cannot be that the universe itself is confused, so the problem must lie with our conceptual categories

Yes, I fully agree that as astute as the logician, one should simply sit on the fence. It is the safest choice. Unfortunately, life is about making choices. Science would not have progressed if nobody makes any decision to turn right or left. Life are full of cross-roads and T-junctions. Life would be a COMPLETE STANDSTILL if nobody makes any decision when they come to a cross-road or T-junction.

Similarly, progress in Science is made by deciding on what is the best description of Nature not by sitting on the fence. Take Light as an example. Through the ages, man has looked upon light with mythical awe. When Science had progressed to the stage when we were able to give it a proper technical term, we named it as WAVE. Then Newton came along and pronounce it as PARTICLE which he called CORPUSCLE. Next, Thomas Young conducted the experiment using a Double-slits that showed light as a WAVE. Afterwhich, Einstein push the pendulum back to the PARTICLE corner based on his Account of the Photoelectric Effect.
The PARTICLE nature of Light is further reinforced by the same experiment using the double-slits that pronounced Light as a Wave. It was shown unmistakenly that the photon arrive on the screen ONE AT A TIME. It is not one half or a quarter of a photon. This can only suggest that Light is a PARTICLE. What is not Understood at this Juncture in Science is why STATISTICALLY, they seem to be able to act in concert with one another to manifest the fringes that appears to have an answer based on the assumption that light is a wave. Similarly, known Particles that has mass and charge like the electrons also manifest the interference pattern when they are made to pass through the Double-slits. This is where QM came into the picture by providing the mathematics to allow prediction to be made based on the ASSUMPTION that these Quantum entities also has this wave properties. But we must not forget that this is based on an incomplete understanding of what Light and the rest of the Quantum entities is really all about. This is where I find the Uncertainty Principle, the Complementary Principle and the Superposition Principle only provide us an intermediate account of Nature and not one that is cast in stone.

By my post ( http://forum.physorg.com/index.php?showtop...ndpost&p=147725 ), I hope to establish whether we could make the assumption base on the discussion that we have soldiered since you came on to this thread.
I hope to establish whether it is reasonable to make these assumptions before proceeding to make further analysis on the data I have obtained with regards to Circular Polarization of Light. It will be quite futile to built on a faulty foundation if it can be shown irrevocably that it is hopelessly wrong.

1) That the photons passing through a Linear Polarizer obey the Gaussian Distribution about the polarizing axis of the linear polarizer?
2) That, it is plausible to assume that a photon in the unpolarized state has the probability to be found at any angle θ where 0 deg.<θ<360 deg ;
3) That, it is plausible to describe a PHOTON in the state vector lx> as a photon that has the probability to be found at any angle θ where 0 deg.<θ<45 deg; 135 deg.<θ<225 deg; 315 deg.<θ<360 deg;
4) That, it is plausible to describe a photon in the state vector ly> as a photon that has the probability to be found at any angle θ where 45deg.<θ<135 deg; 225 deg.<θ<315 deg.

I do look forward to your comment, even if you do not agree to the above propositions.

By the way, on your remarks:
QUOTE

I agree that the last two experiments show that light has particle properties. However, the Michelson/Morley experiment was based on interference, and so it would seem to me to be evidence for wave properties rather than particle properties.

I do have the explanation of the MM Experiment based purely on the fact that Light is a PARTICLE. There is no need to assume a priori that light is a WAVE before we can observe the interference fringes using the MM Apparatus.

Cheers.
Peter Robert
Hi Hexa,

I feel very uneasy based on your comments on Quantum Mechanics and Relativity.
Yet I cannot find anything that you had said so far that seem to contradict logic and common sense. In fact, I find your propositions so much more persuasive than the prevailing theories of contemporary physics.

I find your latest post replying to Mr Homm remarks on what the logician said quite illuminating. If I may add, quantum mechanics appears to be telling us that at the cross-roads and T-junctions, you need to split youselves into two or three and move in all directions simultaneously. This appears to be the conventional wisdom governing quantum mechanics. I know it is nonsensical philosophically. But the mathematics appears to agree very well with experiments that allows engineers to consturct all the devices and apparatus that you see in the 20th and 21st century.

While we are waiting for Mr. Homm to catch up on some of the issues raised in this thread as well as the others found in this forum, I would appreciate that you move on to state your experiments on Circular Polarization. I don't see how Mr. Homm could disagree with your propositions:
QUOTE

1) That the photons passing through a Linear Polarizer obey the Gaussian Distribution about the polarizing axis of the linear polarizer?
2) That, it is plausible to assume that a photon in the unpolarized state has the probability to be found at any angle θ where 0 deg.<θ<360 deg ;
3) That, it is plausible to describe a PHOTON in the state vector lx> as a photon that has the probability to be found at any angle θ where 0 deg.<θ<45 deg; 135 deg.<θ<225 deg; 315 deg.<θ<360 deg;
4) That, it is plausible to describe a photon in the state vector ly> as a photon that has the probability to be found at any angle θ where 45deg.<θ<135 deg; 225 deg.<θ<315 deg.

But it is extremely disturbing to anyone including myself who had been taught quantum mechanics and relativity to agree with you unless there are evidence to the contrary.

I hope that after you have thoroughly explore this issue on polarization of light, we could move on to discuss the Double-slits issue and then the topic on Relativity which you claimed is different from what Einstein had proposed. Here, I must commend you for your insight on MEASUREMENT which many of us have taken for granted. Most theoretical physicsits have taken the results that the experimental physicists had measured as correct since the published result are generally corroborated by other physicists. With this insight, I think it augers well to question the values of "Experimental Results" with greater scrutiny.

There are a few outstanding issues that you promised to discussed. One by Nick, the other my Montec and severals by Mr Homm.

I am curious to know how your proposition of a "Deck of Cards" as opposed to a "Box of Marbles" for the PHOTONS would eventually materialise into matters??

Peter Robert
Zephir
QUOTE (Peter Robert+Dec 5 2006, 04:59 AM)
I hope that after you have thoroughly explore this issue on polarization of light, we could move on to discuss the Double-slits issue

By AWT the explanation of circular polarization of light is simple. The AWT supposes, the vacuum is massive environment, composed from particle density fluctuations, recursively. This gives the vacuum character of nested foam, the spongy character of condensing supercritical vapor is basically the same stuff.

The foamy character of vacuum explains the transversal wave character of light, but it's polarisation, too. The light is passing along the shape of mutually perpendicular foam membranes, so it can transfer just not the normal momentum, but angular momentum, too. Simply because the phase interphase is the place, where two standing waves interferring together
Confused2
Hi hexa,

Re Gaussian distribution after a linear polarizing filter .. I'm a bit worried about the tails of the Gaussian preventing total cancellation at 90 degrees. The test with LP+QWP Mirror QWP+ LP was an indirect test of 90 degree cancellation. It seems not unlikely that the transform of LP + QWP giving RHCP light could easily be the perfect inverse transform for LHCP ( generated by reflection in the mirror of the RHCP) regardless of any errors of alignment etc .. even so .. the result .. good cancellation .. seems to suggest all might be well with QM. Jury out.

Best wishes,

-C2.
hexa
Hi Mr Homm, Peter Robert, Zephir, Confused2, Montec, Maltida, They,etc,

I agree with Peter that I should proceed to state the results of the experiments so that those following this thread could assess the validity of the data.
Without wasting anymore time, let me state the observations of the experiments that I have conducted:

1. Reading of lux. meter without any intervening polarizer = 850 lux.
2. Reading of lux. meter with one linear polarizer = 296 lux.
3. Reading of lux. meter with one circular polarizer (LP+QWP) = 265 lux.
4. Column 3 shows the reading with the apparatus placed as follow:
Source of light ---- > {QWP1+LP1(0 deg) }+LP2(θ)
Note: QWP1 and LP1 is part of the circular polarizer; Linear polarizer, LP2(θ) is rotated relative to LP1 of the circular polarizer.
5. Column 4 shows the reading with the apparatus placed as follow:
Source of light ---- >{ LP1(0 deg) + QWP1}+LP2(θ)
Note: LP2(θ) of linear polarizer is rotated relative to the LP1 of the first circular polarizer.
6. Column 5 shows the reading with the apparatus placed as follow:
Source of light ---- >{ LP1(0 deg) + QWP1}+{ QWP3 + LP3(θ) }
Note: LP3(θ) of second circular polarizer is rotated relative to the LP1 of the first circular polarizer.
7. Column 6 shows the reading with the apparatus placed as follow:
Source of light ---- >{ LP1(0 deg) + QWP1}+{ LP3(θ) + QWP3}
Note: LP3(θ) of second circular polarizer is rotated relative to the LP1 of the first circular polarizer.

QUOTE

Column 1    Column2    Column 3   Column 4     Column 5      Column6
(Deg.)       (lux.)        (lux.)              (lux.)           (lux.)
1                      0.00        178             96                 158               87
2                    11.25         170            92                 158               83
3                    22.50         153            87                 158               79
4                    33.75         122            84                 159               76
5                    45.00           88            81                 158               75
6                    56.25           55            81                 159               75
7                    67.50           28            83                 160               76
8                    78.75           10            86                 160               80
9                    90.00             3            89                 161               84
10                101.25           10            94                 161               87
11                112.50           29            99                 161               90
12                123.75           58          101                 160               93
13                135.00           89          104                 160               95
14                146.25         124          104                 159               95
15                157.50         151          103                 158               92
16                168.75         170          100                 158               90
17                180.00         177            96                 157               86

INFERENCES

1. Column 3 shows the result that when both the LP1 and LP2 are aligned at 0 degree, the lux meter will register the highest intensity. Conversely, when LP2(θ) =90 degree, the intensity will be minimum at 3 lux. compared to 178 lux. when LP2(θ) = 0 degree.
Result:
1.1 Malus Law/Classical Optics = Observed;
1.2 QM = Observed;
1.3 My proposition = Observed.

2. Column 4 shows that there is a minimum intensity of 81 lux. at LP3(θ) = 45 degree and a maximum of 104 lux. at LP3(θ) = 135 degree.
This observation is consistent with the hypothesis that I am making with regards to linear polarizer and circular polarizer.
Unfortunately, this is where QM or classical optics will not be able to make the same prediction consistent with this observation.
Result:
2.1 Malus Law/Classical Optics = Not Observed;
2.2 QM = Not Observed;
2.3 My proposition = Observed

3. Column 5 shows that there is no significant variation in intensity when the LP3(θ) of the second circular polarizer is rotated relative to the linear polarizer of the first circular polarizer.
Result:
3.1 Malus Law/Classical Optics = Not Observed;
3.2 QM = Not Observed;
3.3 My proposition = Observed

4. Column 6 shows that there is a minimum intensity of 75 lux. at LP3(θ) = 45 degree and a maximum of 95 lux. at LP3(θ) = 135 degree.
This observation is consistent with the hypothesis that I am making with regards to linear polarizer and circular polarizer.
Unfortunately, this is where QM or classical optics again will not be able to make the same prediction consistent with this observation.
Result:
4.1 Malus Law/Classical Optics = Not Observed;
4.2 QM = Not Observed;
4.3 My proposition = Observed

Questions:
1. Are these result due to the artefacts of photographic circular polarizers that render the entire experiment invalid?
2. If acceptable, is there an explanation of the observation based on QM or classical optics?

Cheers.

To Peter Robert,

QUOTE (->
 QUOTE Column 1    Column2    Column 3   Column 4     Column 5      Column6                    (Deg.)       (lux.)        (lux.)              (lux.)           (lux.)1                      0.00        178             96                 158               872                    11.25         170            92                 158               833                    22.50         153            87                 158               79            4                    33.75         122            84                 159               765                    45.00           88            81                 158               756                    56.25           55            81                 159               757                    67.50           28            83                 160               768                    78.75           10            86                 160               809                    90.00             3            89                 161               8410                101.25           10            94                 161               8711                112.50           29            99                 161               9012                123.75           58          101                 160               9313                135.00           89          104                 160               9514                146.25         124          104                 159               9515                157.50         151          103                 158               9216                168.75         170          100                 158               9017                180.00         177            96                 157               86

INFERENCES

1. Column 3 shows the result that when both the LP1 and LP2 are aligned at 0 degree, the lux meter will register the highest intensity. Conversely, when LP2(θ) =90 degree, the intensity will be minimum at 3 lux. compared to 178 lux. when LP2(θ) = 0 degree.
Result:
1.1 Malus Law/Classical Optics = Observed;
1.2 QM = Observed;
1.3 My proposition = Observed.

2. Column 4 shows that there is a minimum intensity of 81 lux. at LP3(θ) = 45 degree and a maximum of 104 lux. at LP3(θ) = 135 degree.
This observation is consistent with the hypothesis that I am making with regards to linear polarizer and circular polarizer.
Unfortunately, this is where QM or classical optics will not be able to make the same prediction consistent with this observation.
Result:
2.1 Malus Law/Classical Optics = Not Observed;
2.2 QM = Not Observed;
2.3 My proposition = Observed

3. Column 5 shows that there is no significant variation in intensity when the LP3(θ) of the second circular polarizer is rotated relative to the linear polarizer of the first circular polarizer.
Result:
3.1 Malus Law/Classical Optics = Not Observed;
3.2 QM = Not Observed;
3.3 My proposition = Observed

4. Column 6 shows that there is a minimum intensity of 75 lux. at LP3(θ) = 45 degree and a maximum of 95 lux. at LP3(θ) = 135 degree.
This observation is consistent with the hypothesis that I am making with regards to linear polarizer and circular polarizer.
Unfortunately, this is where QM or classical optics again will not be able to make the same prediction consistent with this observation.
Result:
4.1 Malus Law/Classical Optics = Not Observed;
4.2 QM = Not Observed;
4.3 My proposition = Observed

Questions:
1. Are these result due to the artefacts of photographic circular polarizers that render the entire experiment invalid?
2. If acceptable, is there an explanation of the observation based on QM or classical optics?

Cheers.

To Peter Robert,

I am curious to know how your proposition of a "Deck of Cards" as opposed to a "Box of Marbles" for the PHOTONS would eventually materialise into matters??

You appear to be skeptical as to whether it is possible to describe Nature more simply and logically with simple macro metaphor like a “Deck of Cards”. Instead you seem to think that Nature must be a lot more complex and is capable of description only if we use complex mathematics (that are privy to only a selected few) that characterize contemporary physics.
Yes, I was also of this opinion when I first begin my search. But I come to realize the IMPOSSIBILITY of Nature to organize itself with the pervasive uniformity if we have too many components. Take the atom as an example. If we have more than four entities: Proton, neutron, electron and photons, it will probably be impossible to have the kind of uniformity that we observe in Nature. I will show later that the neutron is One particle TOO MANY in the construction of the atom.
If instead or a few basic components, we assume that an atom is like a WATCH with a few thousand parts. Is it possible for a few thousand parts to organize themselves with such consistency that every single carbon atom is precisely identical to every other carbon atoms with the same atomic mass? This also applies to the hydrogen and oxygen atoms from which life evolves.

At the level of the PHOTON, I also wonder whether it will have the same consistency if each individual Photon has more than a SINGLE component. I reckon that this is less probable if light or photon is going to be emitted in such abundance throughout the entire universe and is capable of translating at the speed, c. So I ended with the choice between perceiving a SINGLE photon as a marble or a plate (or card). The phenomena relating to Polarization convince me that light must come in the form of a Card as opposed to a Marble. Hence, one photon can be distinguished from another photon (with different energy and momentum) by the number of cards that goes into the construction of a packet of photon.

Please comment on the experiments that I have stated in this post.

Cheers.

To Zephir,

I just love your graphics and animation.
But I am not sure I can agree with your AWT theory because of my own belief that Light are Photons that are essentially Particles and not Waves.

One of the problem with the assumption of Light as a Wave is the speed of propagation.
From the study of wave, for anything to be transmitted through a medium, the propagator must convey its energy to the medium. I suppose you call your medium aether. The section of the aether that first received the energy from the propagator needs to convey the same energy to the next section of medium and so on.
Unfortunately, such a process takes too much time to propagate from one point to another. This will unduly retard the speed of propagation. It is highly improbable for Light to travel at the speed, c if it is some kind of a wave.
By the way, I am sure you are aware that an electron (a particle) may be accelerated in a synchrotron to close to the speed of light, c. I just wonder whether it is possible to accelerate a sound wave that is already in mid-flight through a fluid?

Although I disagree with your proposition (based on aether) that Light travels through space at the speed, c, I will not disagree with you if you were to state that the Field (Electric, Magnetic and Gravitational) is propagated like a wave through space at the speed c. This is because, FIELD unlike photon has no momentum or energy. I will call a PHOTON a PARTICLE but not FIELD (although field is also a physical entity). FIELD appears not to obey the Laws of Conservation unlike a PHOTON. FIELD and the PARTICLE that emits it are two separate entities that are distinguishable from one another.

I hope to defer the discussion on FIELD after we have explored the polarization of light and has clearly establish the case for photon as a "Deck of Cards" or a "Wave" including “Your AWT Wave” as you may have preferred.

Cheers.

To Confused2,

I think there is no problem with the tails if we are to assume the Gaussian Distribution. The cut-off angle from the axis of the linear polarizer is 45 degree in the clockwise or anti-clockwise directions. Beyond 45 degree, each photon will perceive the molecules forming the polarizing axis as another orthogonal axis. The Gaussian Distribution will continue to apply to how the photons will pass through a linear polarizer without we worrying about the tail effect.

Do comment on the Result of the Experiment that I have posted here.

Cheers.
mr_homm
Hello again everyone,

I have now finished up several projects that were taking up all my time, and so it is possible for me to catch up with the discussion. For the last month, I have been trying to catch up, but I have had only about 1/2 hour a week of free time (yes, not even lunch breaks most days), so it has been all I could do just to not fall further behind. Responding to a recent post by Maltida, who was hoping that I could respond to CURRENT posts instead of two-week-old posts: I agree that it has been confusing, but I did not want to skip any of the earlier comments that seemed to require a response. Now I finally should be able to catch up, and the problem will go away.

@hexa, Nov.16:

Thank you for the references. I have not yet read the first two, but I read the third (which was easiest because of the link). This paper is about a technique for fabricating LP filters using an application of photoactive dyes conductive polymer molecules, and laser light. This essentially replaces the original Land technique of simply stretching the polymer while to hardened. The new technique should produce more efficient LP filters.

However, it has nothing whatever to do with QWPs, since the whole paper discusses nothing but fabrication techniques for LP filters. QWPs are not constructed in this way, as you know, but are cut from calcite or other birefringent materials. These materials are inorganic crystals, and so they are not formed by arrangements of polymer molecules. Therefore the optic axis discussed in the paper is that of an LP filter, not that of a QWP. This does not of course disprove your hypothesis about the operation of QWPs, but it does not really discuss them at all. It may have provided you with the seed of an idea, or an analogy which gave rise to your hypothesis.

QUOTE
Having said that, I must concede that what I have proposed in our discussion here is an ALTERNATIVE HYPOTHESIS to the postulates used in Quantum Mechanics. You may call it hand waving if you like. It is an assumption on how QWP might work which I have investigated based on EXPERIMENT that I have conducted. As I have stated earlier, the experiment that I had conducted based on QM prediction does not seem to agree with my observation.

OK, let's adopt this as a working hypothesis subject to further testing.

QUOTE (->
 QUOTE Having said that, I must concede that what I have proposed in our discussion here is an ALTERNATIVE HYPOTHESIS to the postulates used in Quantum Mechanics. You may call it hand waving if you like. It is an assumption on how QWP might work which I have investigated based on EXPERIMENT that I have conducted. As I have stated earlier, the experiment that I had conducted based on QM prediction does not seem to agree with my observation.

OK, let's adopt this as a working hypothesis subject to further testing.

Let me share with you the experimental data that I have obtained using a circular polarizer followed by a linear polarizer that act as an analyzer.
QUOTE

Objective
To investigate the intensity of light passing through a circular polarizer followed by a linear polarizer when the linear polarizer is rotated relative to the circular polarizer.
The Apparatus:
M1 = linear polarizer ; M2 = QWP; M3=QWP and a Lux. meter with a resolution of 1 lux.
The Procedures
The polarizing axis of M1 is set along the x-axis.
Pass a steady source of Light (unpolarized) through M1, M2 and M3.
Rotate the polarizing axis of M3 starting from 0 degree by giving it an anti-clockwise rotation of 11.25 deg.
Measure the corresponding intensity using a lux. meter.

QUOTE (->
 QUOTE ObjectiveTo investigate the intensity of light passing through a circular polarizer followed by a linear polarizer when the linear polarizer is rotated relative to the circular polarizer.The Apparatus:M1 = linear polarizer ; M2 = QWP; M3=QWP and a Lux. meter with a resolution of 1 lux.The ProceduresThe polarizing axis of M1 is set along the x-axis.Pass a steady source of Light (unpolarized) through M1, M2 and M3.Rotate the polarizing axis of M3 starting from 0 degree by giving it an anti-clockwise rotation of 11.25 deg.Measure the corresponding intensity using a lux. meter.

1) 0 deg. = 315 lux
2) 11.25 deg. = 298 lux.
3) 22.50 deg. = 283 lux.
4) 33.75 deg. = 273 lux.
5) 45.00 deg. = 266 lux.
6) 56.25 deg. = 264 lux. (Minimum)
7) 67.50 deg. = 267 lux.
8) 78.75 deg. = 276 lux.
9) 90.00 deg. = 287 lux.
10) 101.25 deg. = 299 lux.
11) 112.50 deg. = 313 lux.
12) 123.75 deg. = 320 lux.
13) 135.00 deg. = 326 lux.
14) 146.25 deg. = 329 lux. (Maximum)
15) 157.50 deg. = 326 lux.
16) 168.75 deg. = 318 lux.
17) 180.00 deg. = 309 lux.

I am a little confused by your description of this experiment. You say at the beginning that you are measuring the passage of circularly polarized light through a linear polarizer, but when you describe the equipment, M3 is a QWP. Shouldn't it be a LP?

Your readings look like M3 was a LP, so I'll assume that unless you tell me otherwise. Besides that, your readings pretty clearly show that rotation invariance is not perfect, which was one of the things you mentioned in other posts. The max and min readings are 90 deg apart, as expected if M3 is a LP, since its filtering behavior should be opposite at orientations 90 deg apart.

The standard physics explanation of this is that the LP filter is not 100% perfect, or the QWP M2 is slightly off from a 45 deg orientation, or that the light wavelength used is not the one for which the QWPs produce an exact 1/4 wave effect. The ratio of max to min lux is 1.246, so assuming the imperfections are in the LP, I'll compute the degree of imperfection needed to explain this data.

A small leakage of polarization component perpendicular to the LP axis would produce a small mixture of opposite orientation circular polarized light, e.g. some LCP mixed with the dominant RCP. The max lux value occurs where these interfere constructively, and the min where they interfere destructively. In that case, max intensity is proportional to (E_RCP + E_LCP)^2 and min intensity to (E_RCP - E_LCP)^2. Letting r = E_LCP / E_RCP be the amplitude ratio, this reduces to 1.246 =[(1+r)/(1-r)]^2, so taking square roots and rearranging you get 1.11634(1-r) = 1+r, which solves to 2.11634r = 0.11634, so r = .055. In other words, the LP filter is letting through about 5.5% of light polarized in the wrong direction.

How does this compare with manufacturer's claims for their filters? I looked at specifications from a lot of manufacturers (You can get lots of information centrally through globalspec.com, which links to manufacturer's specifications for thousands of scientific and technical products. I found them while websearching just today, and I immediately registered with them, and found their site incredibly helpful. Highly recommended!). The bottom line is, most cheap quality LP filters are advertised to let through less than 1% of the wrong polarization. The good quality ones (for research) let through less than .01%, and the highly specialized laser filters (based on calcite) let through less than .001%. Photographic polarizers are undoubtedly the cheap kind (the .01% type cost roughly \$300 each and that's for a small size, much less than 50mm!), because photography does not require the high precision of the scientific filters. Even those, however, will not let 5.5% through, so the rotational variance in intensity CANNOT be blamed on the LP.

Let's look at the orientation of the QWP. Since this is not a feature of the plate itself, I have no way of knowing how accurately you (or the photographic filter manufacturer) have aligned it. Of course its fast axis and slow axis must be oriented exactly 45 deg from the polarization axis of the LP. I'll just assume you were careful and got this just right, because I have no way to know. So I can't really assess how much error contribution this might have made, except that it is probably small.

Finally, looking at the QWP itself, there seems to be something going on. Looking at various manufacturers via globalspec.com, I found this . Look at the graph at the bottom of the page to see the important information. The graph shows the difference in behavior between zero-order and multiple order QWPs. Zero-order plates produce exactly 1/4 wavelength delay, whereas multiple order ones produce 1+1/4, 2+1/4, or more wavelength delays. Optically, the effect is the same, but the multiple order QWPs are MUCH more sensitive to the wavelength of the light. The graph shows that if your wavelength is off by 6% from the one the QWP is designed for, the wave could be delayed by as much as an extra +/- 1/4 wavelength. This would be enough to change it into a 1/2 wave plate, or into a do-nothing plate with NO phase delay at all. This would completely destroy your circular polarization.

The circular polarizers for cameras are certainly the multiple order QWPs, because these are much cheaper (it is much harder to make the material very thin and still perfectly even, so manufacturing the zero order plates is much more expensive) and photography doesn't need the effect to be very exact for its purposes. Now if you know exactly what the designed wavelength for your QWP is, there IS a way to adjust it by tilting the QWP. I found instructions here telling you how to do it and how much to tilt the QWP. However, it appears that you can only get good results with monochromatic light because of the QWP's extreme sensitivity to wavelength. One difficulty is that the manufacturer of your photographic circular polarizers probably doesn't tell you what the design wavelength is, because what photographer would care? That makes the adjustment instructions kind of hard to follow. I suppose you could use the trick of holding the photographic circular polarizer up to a mirror, and then slowly tilting it until the image in the mirror was completely dark and recording the angle. You would have to use the laser as the light source for this, of course, so you'd be looking into the reflection of the laser beam . . . not recommended!

Now just how far off would the wavelength need to be from the design wavelength in order to give you the observed results? If x polarized light of amplitude E strikes the QWP, it will resolve into fast and slow components, and the slow component will be delayed by some amount phi (which SHOULD be pi/2, but won't be exactly that if the wavelength is wrong). Therefore, the field exiting the QWP will be E/sqrt(2[(cos(kx-wt)X' + cos(kx-wt+phi)Y'] where X' and Y' are the unit vectors along the +/- 45 deg directions.

The maximum value of E will occur at a time that is midway between the times when each component reaches its own wave crest, so kx-wt must be -phi/2, and the max amplitude must be E/sqrt(2)|cos(-phi/2)X' + cos(phi/2)Y'| = E/sqrt(2)*cos(phi/2)|X'+Y'| = Ecos(phi/2). The minimum amplitude must occur midway between the times when one wave reaches its crest and the other its trough, so kx-wt must be pi/2-phi/2. This makes the amplitude be E/sqrt(2)|cos(pi/2-phi/2)X + cos(pi/2+phi/2)Y| = E/sqrt(2)|-sin(phi/2)X + sin(phi/2)Y| = E/sqrt(2)sin(phi/2)|-X+Y| = Esin(phi/2). Since the ratio of max to min amplitudes is then cot(phi/2), this gives 1.11634 = cot(phi/2), so phi = 2*41.85 degrees = 0.2325*2pi radians, which is 0.2325 wavelengths. Since this differs by -.0175 wavelengths from the correct value of 0.25, the chart on the retarder plate webpage I referenced above shows that the wavelength only needs to be about 0.4% too high for this to happen.

In other words, a VERY MINOR mismatch between the design wavelength and the actual wavelength would produce the observed deviation from circular polarization in your data. It appears that the QWP is extremely sensitive to wavelength, and you cannot get the results that the theory predicts unless the wavelength is matched EXACTLY to the QWP design wavelength. This means that in order for your results to be experimentally convincing, you need to fine tune the calibration of your QWP using the tilting method described in the Edmund Optics website above.

It's now late and past my bedtime, but I really wanted to finish this analysis before quitting tonight. Originally I had intended to plow through as many posts as I could, trying to catch up, but it seems that I've done a very in-depth analysis of just this one post instead. I think this was important to do, so I'll just have to catch up next time.
hexa
Hi Mr Homm,

Glad to hear that you can spend a bit more time on the forum.
I am sure all of us will cherish your presence.
I am also confused by the time lag. I would sincerly appreciate that you could keep your post current where time permit.
Thanks again for all your posts.

QUOTE

Objective
To investigate the intensity of light passing through a circular polarizer followed by a linear polarizer when the linear polarizer is rotated relative to the circular polarizer.
The Apparatus:
M1 = linear polarizer ; M2 = QWP; M3=QWP and a Lux. meter with a resolution of 1 lux.

Thanks for highlighting the error. M3 is a linear polarizer based on what I have written.
I have incorrectly annotated it as QWP. I did notice the error and had attempted to get the moderator to modify the error--but to no avail.
Anyway the same experiment was repeated in my latest post ( http://forum.physorg.com/index.php?showtop...ndpost&p=151504 ) where I restate the data in Column 4.
The distribution of the intensity is almost similar to the one I have conducted earlier.

The reference I have given earlier ( http://www.opticsexpress.org/DirectPDFAcce...CFTOKEN=1471927 ) is to illustrate the relevance of the molecular axis in relation to the polarization process. This is the basis where I made my hypothesis that the QWP has two molecular axes as opposed to one in the case of a linear polarizer.
In the case of a QWP, the two axes are aligned at 45 degree in the clockwise and anti-clock wise direction relative to the axis of the linear polarizer. If they are aligned at a different angle relative to the axis of the linear polarizer, then it will no longer behave as a Circular polarizer.

QUOTE (->
 QUOTE ObjectiveTo investigate the intensity of light passing through a circular polarizer followed by a linear polarizer when the linear polarizer is rotated relative to the circular polarizer.The Apparatus:M1 = linear polarizer ; M2 = QWP; M3=QWP and a Lux. meter with a resolution of 1 lux.

Thanks for highlighting the error. M3 is a linear polarizer based on what I have written.
I have incorrectly annotated it as QWP. I did notice the error and had attempted to get the moderator to modify the error--but to no avail.
Anyway the same experiment was repeated in my latest post ( http://forum.physorg.com/index.php?showtop...ndpost&p=151504 ) where I restate the data in Column 4.
The distribution of the intensity is almost similar to the one I have conducted earlier.

The reference I have given earlier ( http://www.opticsexpress.org/DirectPDFAcce...CFTOKEN=1471927 ) is to illustrate the relevance of the molecular axis in relation to the polarization process. This is the basis where I made my hypothesis that the QWP has two molecular axes as opposed to one in the case of a linear polarizer.
In the case of a QWP, the two axes are aligned at 45 degree in the clockwise and anti-clock wise direction relative to the axis of the linear polarizer. If they are aligned at a different angle relative to the axis of the linear polarizer, then it will no longer behave as a Circular polarizer.

Column 1    Column2    Column 3  Column 4    Column 5      Column6
(Deg.)      (lux.)        (lux.)              (lux.)          (lux.)
1                      0.00        178            96                158              87
2                    11.25        170            92                158              83
3                    22.50        153            87                158              79
4                    33.75        122            84                159              76
5                    45.00          88            81                158              75
6                    56.25          55            81                159              75
7                    67.50          28            83                160              76
8                    78.75          10            86                160              80
9                    90.00            3            89                161              84
10                101.25          10            94                161              87
11                112.50          29            99                161              90
12                123.75          58          101                160              93
13                135.00          89          104                160              95
14                146.25        124          104                159              95
15                157.50        151          103                158              92
16                168.75        170          100                158              90
17                180.00        177            96                157              86

Look at Column 4 of my latest post. The minimum and maximum intensity are located at 45 deg. and –45 deg.(135 deg.) respectively relative to the linear polarizer (at 0 deg.) that make up the Circular polarizer.
In the absence of a QWP, the intensity of light will be distributed in accordance with the readings as shown in Column 3.
Note the following comparison:
At 0 deg, : Column 3 = 178 lux. ; Column 4 = 96 lux.
45 deg, : Column 3 = 88 lux. ; Column 4 = 81 lux. (Minimum)
90 deg, : Column 3 = 3 lux. ; Column 4 = 89 lux.
135 deg, : Column 3 = 89 lux. ; Column 4 =104 lux. (Maximum)

This is where I infer that a QWP has two molecular axes based on the analysis of intensity passing through the Linear polarizer that act as an analyzer.

Let me address your concern on the type of filters used, and how this may affect the readings that we can make using a photographic grade rather than the scientific grade filters. I am under no illusion that there will be some deviation between these two grades of equipments.
I am less concern with the absolute intensity that I may be able to observe but more on the general behavior of how a Linear or Circular Polarizer would behave. You may have noticed that without any filter, the lux. meter register a reading of 850 lux. The presence of a linear or circular polarizer reduces the intensity to less than half at 296 lux. and 265 lux. respectively.
Further, I am also not concern because the readings in Column 4 is less than half the intensity of the light that passes through a Sincle Circular Polarizer.

Similarly, I have also taken the precaution to distinguish the result based on a white light source or a monochromatic source. The variation using a monochromatic source will be more pronounced compared to a source using white light.
You are correct to state that different color light APPEARS to pass through the polarizers at different speed and hence the relative intensity will vary differently at one angle for one monochromatic light compared to another angle. But this does not negate the observation that the intensity will fluctuate around the two axes found in the QWP.

For your information, the readings of the experiments that I have last posted is based on White Light.

With these results, I will like to know how you would infer from these observations.

Is it reasonable to make these ASSUMPTIONS that I have stated in my earlier post?
I hope you are not faulting it because the experiments are not conducted using the premium grade apparatus.

QUOTE

1) That the photons passing through a Linear Polarizer obey the Gaussian Distribution about the polarizing axis of the linear polarizer?
2) That, it is plausible to assume that a photon in the unpolarized state has the probability to be found at any angle θ where 0 deg.<θ<360 deg ;
3) That, it is plausible to describe a PHOTON in the state vector lx> as a photon that has the probability to be found at any angle θ where 0 deg.<θ<45 deg; 135 deg.<θ<225 deg; 315 deg.<θ<360 deg;
4) That, it is plausible to describe a photon in the state vector ly> as a photon that has the probability to be found at any angle θ where 45deg.<θ<135 deg; 225 deg.<θ<315 deg.

I hope with the above clarifications, it is sufficient for you to comment on the reasonableness of these ASSUMPTIONS.

Cheers.
Zephir
QUOTE (hexa+Dec 7 2006, 06:32 AM)
But I am not sure I can agree with your AWT theory because of my own belief that Light are Photons that are essentially Particles and not Waves.

By AWT the photon is the wave packet, resulting from interference of the light wave with the waves beneath the surface of quantum foam. Such waves are having the wavelength of the average Planck size, from this the size of photon can be computed.

The average wavelength of vacuum fluctuation corresponds the Planck length (approximately 10-35 m). The interference pattern frequency corresponds the wavelength ratio, for example at the case of light of wavelength 10-9 meters (soft X-ray radiation) the corresponding photon size will be 10-9 x 10-9 / 10-35 = 10-17 meters (slightly above atom nuclei diameter range 10-18 m).
hexa
Hi Zephir,

I just love your graphics. I certainly would like to take a lesson from you on how to do all these wonderful animations.
Personally, I will credit you with the graphic and animation. But I don’t think I can agree with most of all that you have said. Maybe, I am bias in favor of my personal belief that light come as a stream of particles. I tend to agree with Planck and Einstein that light are quanta and are essentially PARTICLES. But I can't seem to agree with the Copenhagen Interpretation that require us to simultaneously turn in all directions at the "cross roads and T-junctions" that Peter Robert has succintly put it. It is simply ILLOGICAL. This is where I was pleasantly surprised to find agreement with Mr. Homm who appears to stood for QM.

To understand you a little better, I would appreciate if you could help me with a little question pertaining to the wave pattern displayed on an oscilloscope:
QUOTE

Is the sinusoidal curves that you see on the phosphor screen the result of wave or particle?

One of the most serious problems in hypothesizing that light is a form of wave start at the door of the propagator.
How is light propagated?
To try to answer this question, let us take a look at how sound wave is propagated underneath the surface of water. The propagator must be fed with a continuous stream of energy. The only reasonable means of propagation is for the membrane or the sound propagator to compress the immediate medium adjacent to it. The energy gained from this section of the medium is then conveyed to the next section, and the next section, etc, etc. until it reaches the receiver or any point in the medium. This must then be followed by rarefaction. This is where it give rise to the entity of wavelength and frequency of the waveform. In other words, the wave is of the LONGITUDINAL Waveform based on Compression and Rarefaction of the medium.
How about the waves that are propagated on the surface?
The wave on the surface is a traverse wave unlike the longitudinal sound wave that is propagated beneath the surface. It travels a lot slower than the sound wave that is propagated beneath it. To do that, it requires that the medium has a certain value of Young’s modulus. In other words, the chain of water molecules that serve as the communicating medium, bobbing up and down, must be able to withstand the vertical shear stress for the wave energy to be communicated TRAVERSELY from one molecule to the next molecule.
You can attempt to send TRAVERSE Wave through the surface on sand of a beach. I think you will realize how difficult to send a traverse wave across the surface of sand.

From all that you have stated, I believe your AWT wave is a TRAVERSE Wave.
I just can’t imagine that empty space is filled with lots and lots of this AWT stuffs and yet does not impede the motion of stars, planets, moons, meteorites, and other charged and uncharged particles that move at tremendous speed through space???

I hope you are not invoking more dimensions to resolve these difficulties?
Since more dimensions are something that neither you nor anyone could ever prove, I think I will rather adopt Aristotle's ONE WORLD Universe as opposed to his teacher, Plato's TWO World Universe proposition. This is a topic in philosophy and not PHYSICAL Science. I don't think there will ever be any agreement to indulge in such philosophical debate that is Subjective and beyond the ability of Science to ever measure it Objectively.

QUOTE (->
 QUOTE Is the sinusoidal curves that you see on the phosphor screen the result of wave or particle?

One of the most serious problems in hypothesizing that light is a form of wave start at the door of the propagator.
How is light propagated?
To try to answer this question, let us take a look at how sound wave is propagated underneath the surface of water. The propagator must be fed with a continuous stream of energy. The only reasonable means of propagation is for the membrane or the sound propagator to compress the immediate medium adjacent to it. The energy gained from this section of the medium is then conveyed to the next section, and the next section, etc, etc. until it reaches the receiver or any point in the medium. This must then be followed by rarefaction. This is where it give rise to the entity of wavelength and frequency of the waveform. In other words, the wave is of the LONGITUDINAL Waveform based on Compression and Rarefaction of the medium.
How about the waves that are propagated on the surface?
The wave on the surface is a traverse wave unlike the longitudinal sound wave that is propagated beneath the surface. It travels a lot slower than the sound wave that is propagated beneath it. To do that, it requires that the medium has a certain value of Young’s modulus. In other words, the chain of water molecules that serve as the communicating medium, bobbing up and down, must be able to withstand the vertical shear stress for the wave energy to be communicated TRAVERSELY from one molecule to the next molecule.
You can attempt to send TRAVERSE Wave through the surface on sand of a beach. I think you will realize how difficult to send a traverse wave across the surface of sand.

From all that you have stated, I believe your AWT wave is a TRAVERSE Wave.
I just can’t imagine that empty space is filled with lots and lots of this AWT stuffs and yet does not impede the motion of stars, planets, moons, meteorites, and other charged and uncharged particles that move at tremendous speed through space???

I hope you are not invoking more dimensions to resolve these difficulties?
Since more dimensions are something that neither you nor anyone could ever prove, I think I will rather adopt Aristotle's ONE WORLD Universe as opposed to his teacher, Plato's TWO World Universe proposition. This is a topic in philosophy and not PHYSICAL Science. I don't think there will ever be any agreement to indulge in such philosophical debate that is Subjective and beyond the ability of Science to ever measure it Objectively.

Quote Zephir:
[1]By AWT the photon is the wave packet, [2]resulting from interference of the light wave with the waves beneath the surface of quantum foam.[3] Such waves are having the wavelength of the average Planck size, from this the size of photon can be computed.

[1] What do you mean by WAVE-PACKET?
How big is this wave-packet? Where does it begins and where does it ends? Has it got a physical shape that we can distinctly describe one packet as having a vertical orientation that we can distinguish another that is in the horizontal orientation which is so important to the discussion on the phenomena on Polarizationof Light?
[2] What do you mean by LIGHT WAVE? What constitute QUANTUM FOAM? If it is a foam, then can I assume that there will be empty space between one foam entity and another foam entity as well as there are plenty of empty space inside each foam?
At what angle must one TRAVERSE light wave interfere with another to yield this PHOTON you called a wave packet? Can two traverse wave that is orthogonal to one another INTERFERE with one another? What do you mean by beneath the surface? Where is the demarcation between what is above and what is below?
[3] Planck length is roughly equal to 1.6 x 10E-35 m. HOW do you propose that the size of a photon can be related to this Planck length?

QUOTE
Quote Zephir:
The average wavelength of vacuum fluctuation corresponds the Planck length (approximately 10-35 m). The interference pattern frequency corresponds the wavelength ratio, for example at the case of light of wavelength 10-9 meters (soft X-ray radiation) the corresponding [4]photon size will be 10-9 x 10-9 / 10-35 = 10-17 meters (slightly above atom nuclei diameter range 10-18 m).

[4] You made a very interesting statement in stating the size of a photon.
Does photons (of different momentum, energy, wavelength and frequency) have different sizes?
How is the size of a Photon compare to the size of an Electron?

I hope you will answer each of these questions as concisely as you could.
I hope you are not going to unload everything that you have already stated in your personal website before you can answer these questions.
I hope you will remain objective in answering these questions.

In the mean time, I also hope that Mr Homm as well as the other members could comment on the questions that I have raised in my last post ( http://forum.physorg.com/index.php?showtop...ndpost&p=151892 ).

Cheers.
mr_homm
Now I'm back to catching up on older posts.

@hexa, Nov. 20:
QUOTE
Thanks for sharing your inner thought as well as in sharing this profound thought that I think deserve more clarification:
QUOTE (->
 QUOTE Thanks for sharing your inner thought as well as in sharing this profound thought that I think deserve more clarification:[5]uncertainty is basically an illusion created by our expectations.[6]We expect to get separate answers for momentum and position for example, but for the particle, these are actually only ONE property.[7]We expect to get two different answers to one question -- of course it doesn't work. I wonder whether you could put it in simpler words for the benefit of everybody, just in case I may have misinterpreted what you had intended to convey.

I wrote more extensively about this in another thread. Here's the link, so I don't have to type it all in again. In that post, I placed a further link to an even earlier post of mine about uncertainty. The earlier post is a fuller description, but please read them both together. It certainly bears more discussion than this, perhaps after I catch up.

For now, let's defer comment on the qualitative description of your observations later in this Nov. 20 post, because the quantitative data will enable a much fuller discussion later. I would appreciate some clarification on the following point:

QUOTE
I went on to HYPOTHESIZE that a photon is a “deck of cards” as opposed to a box of marbles. This proposition appears to be more suited to explain both Linear and Circular Polarization much better than QM. Most significantly, this proposition allows me to explain Malus Law fundamentally without having to resort to some abstract mathematical postulates.

It is pretty clear that you have some specific behavior in mind with the deck of cards vs box of marbles analogy, but I am not getting it. In exactly what way is a photon like a deck of cards or box of marbles? I'm sure I'm missing something obvious here.

@hexa, Nov.22
I won't cut and paste all your data sets, but I have looked carefully at them and I am bearing them in mind as I respond to your comments in the Nov. 22 post:
QUOTE (->
 QUOTE I went on to HYPOTHESIZE that a photon is a “deck of cards” as opposed to a box of marbles. This proposition appears to be more suited to explain both Linear and Circular Polarization much better than QM. Most significantly, this proposition allows me to explain Malus Law fundamentally without having to resort to some abstract mathematical postulates.

It is pretty clear that you have some specific behavior in mind with the deck of cards vs box of marbles analogy, but I am not getting it. In exactly what way is a photon like a deck of cards or box of marbles? I'm sure I'm missing something obvious here.

@hexa, Nov.22
I won't cut and paste all your data sets, but I have looked carefully at them and I am bearing them in mind as I respond to your comments in the Nov. 22 post:
INFERENCES:
1) Looking at Column [2] we can infer that as angle θ increases, the intensity of light passing through the two linear polarizers decreases.
2) Similarly, looking at Column [6] we can infer that as angle θ increases, the intensity of light passing through the three linear polarizers also decreases.
3) Looking at Column [5], we can infer that as angle θ increases, the relative intensity of light passing through the two linear polarizers compared to that predicted by Malus Law increases.
4) Comparing Column[5] with Column [9], we can infer that as angle θ increases, the relative intensity of light passing through the three linear polarizers increases at a faster rate compared to when only two linear polarizers are used. The base comparison is against the prediction using Malus Law.
5) This indicates that the statistical distribution of the photons passing through any single linear polarizer differs slightly from the Cosine law. It is only a statistical bell-curve that have some resemblance to the cosine curve.
6) More importantly, we can infer that the closer we get to the polarizing axis of the polarizer, the higher will be the probability of photons passing through it.

1) through 4): Agree. This is very clear from the data.
5): This is certainly what your experiment has observed. However, it is good to remember that this MAY be an effect of the particular LPs you are using. If so, then doing the experiment with different equipment will produce different results, if not, then your results will be replicated in experiments with varying equipment.
6): Agree, although both the cosine and Gaussian share this property, so it doesn't distinguish between them.

Now as to the data itself, let's see if this can be explained by assuming some degree of imperfection in the polarizing filters. As I mentioned in my previous posts, many polarizing filters let through on the order of 1% light of the perpendicular polarization, although there are of course higher grade polarizers that let through much less than this. How will this affect the expected light intensity in the 2 and 3 polarizer experiments?

Suppose that the polarizer lets through 100% of the E field oriented along its axis and a small fraction p (stands for perpendicular) of the E field perpendicular to its axis, and suppose that all 3 polarizers are equally good. Then when unpolarized light strikes the first polarizer (with axis assumed to be at 0 degrees), you can think of the light as having equal but incoherent components polarized along the x and y axes. Since they're incoherent, you should treat each one separately as it goes through the filters, and then add the intensities at the end (never the amplitudes; that's only for coherent light).

The filters are 3 LPs with angles 0, Θ, and 2Θ. Recall from one of my earlier posts in this thread that the matrix for a LP at angle Θ is R(Θ)LP(p,0)(R(-Θ), i.e.

CODE

( cos(Θ) -sin(Θ) ) ( 1   0 ) ( cos(-Θ) -sin(-Θ) )
(                ) (       ) (                  ) = LP(p,Θ)
( sin(Θ)  cos(Θ) ) ( 0   a ) ( sin(-Θ)  cos(-Θ) )

The x polarization component of the original unpolarized beam is
CODE

(1)
( ) = |X>
(0)

and the output that gets through the filters is |OUT_X> = LP(p,2Θ)*LP(Θ)*LP(p,0)|X>. The intensity of this is <OUT_X|OUT_X> = <X|LP'(p,0)*LP'(p,Θ)*LP'(p,2Θ)LP(p,2Θ)*LP(p,Θ)*LP(p,0)|X>, where ' means transpose of the matrix. Expanding this and remembering that LP'(p,0) = LP(p,0), R'(Θ) = R(-Θ) and R(Θ1)*R(Θ2) = R(Θ1+Θ2), you get <X|LP(p,0)*R'(-Θ)*LP(p,0)*R'(Θ)*R'(-2Θ)*LP(p,0)*R'(2Θ)*R(2Θ)*LP(p,0)*R(-2Θ)*R(Θ)*LP(p,0)*R(-Θ)*LP(p,0)|X> =<X|LP(p,0)*R'(-Θ)*LP(p,0)*R(Θ)*LP(p,0)*LP(p,0)*R(-Θ)*LP(p,0)*R(-Θ)*LP(p,0)|X>. Since the left and right halves of this expression are transposes of each other, you only need to calculate the right half, LP(p,0)*R(-Θ)*LP(p,0)*R(-Θ)*LP(p,0). Multiplying out the matrices gives the total filtering matrix F:
CODE

( c^2 - ps^2      p(p+1)cs )
(                          )  =  F
(p(p+1)cs   p^2(pc^2 - s^2 )

where c and s stand for cos(Θ) and sin(Θ) respectively.

Since |X> is the column vector (1,0), calculating <OUT_X|OUT_X> = <X|F'F|X> gives just the upper left entry of F'F, and since |Y> is the column vector (0,1), <OUT_Y|OUT_Y> is the lower right corner. The off-diagonal components only come into play if the original light x and y components are coherent with each other. In normal white light, this will not be the case, i.e. <X|Y> = 0. Therefore, the predicted total intensity of the output light is just [(c^2 -ps^2)^2 + (p(p+1)cs)^2] + [(p^2(pc^2 - s^2))^2 + (p(p+1)cs)^2] = (c^2 -ps^2)^2 + 2p^2((p+1)cs)^2 + p^4(pc^2 - s^2)^2.

At Θ=0, this gives just 1+p^6, at Θ=90 deg, it gives p^2 + p^4, and at Θ=45 deg, it gives 1/4 - 1/2*p + 3/4*p^2 + p^3 + 3/4*p^4 -1/2*p^5 + 1/4*p^6. Since P is expected to be small, this is very well approximated by dropping any terms in each expression which are smaller than the leading term by P^3 or more. This gives at Θ=0, just 1, at Θ=90 deg, p^2 + p^4, and at Θ=45 deg, 1/4 - 1/2*p + 3/4*p^2. Note that these are the sum of the outputs for separate X and Y polarized inputs. This means that the original input intensity was 2, not 1, because each component had intensity 1 by assumption. This doesn't affect relative intensity predictions, so you can still leave the Θ=0 output normalized to 1.

Next, I'll look at the much simpler 2 filter case, and then it will be possible to compare these formulas with your data. For 2 filters, you get |OUT_X> = LP(Θ)*LP(p,0)|X>, which as before gives <OUT_X|OUT_X> = <X|LP(p,0)*R'(-Θ)*LP(p,0)*LP(p,0)*R(-Θ)*LP(p,0)|X>. Again, you just compute the matrix product for the right half to get F:
CODE

( c        ps )
(             )  =  F
(-ps   p^2c^2 )

As before, the predicted intensity out is the sum of the diagonal entries of F'F, which is [c^2 + p^2s^2] + [p^2s^2 + p^4c^2] = c^2 + p^2*2s^2 + p^4*c^4. At Θ=0, this gives just 1.0, at Θ=90 deg, it gives 2p^2, and at Θ=45 deg, it gives 1/2 + 1/2*p^2.

Now, how well do these predictions fit the data? Suppose we assume that imperfections in the polarizers (i.e. the "p" in the formulas) account for the light leakage at 90 degrees. In that case, from the data in column 2 of experiment 1, 2p^2 = 11/346, so p^2 = .016. Therefore, the measurement of 11 lux is accounted for if your polarizers let through 1.6% of the contrary polarization. This is roughly the amount I would expect from photographic polarizers, since p is around 1% for the lower grade filters available from scientific supply catalogs, and phtographic filters are not intended as experimental filters.

So, supposing p=.016, what predictions do you get for the 3 filter case and for 45 deg? For 3 filters at 90 deg, the formula gives p^2 + p^4 = 0.1615, so the expected intensity is 346*0.1615 = 5.59 lux. This is roughly twice the observed amount. So does that mean that the explanation is inconsistent? Not necessarily, because I don't know if your luxmeter is zeroed properly. Since most meters have their best accuracy in the middle of their range, and your meter obviously goes up to at least 800 lux, it may not be very accurate at extremely low light levels. Having a resolution of 1 lux, only means that it can detect a change of 1 lux in the light level, not that the reading is correct in an absolute sense. The meter, for example may show a lux reading that is 2 or 3 lux away from the true value, but this is good enough for photography, as long as the meter reading increases by 1 lux whenever the light level does. In short, the meter may have a small constant offset.

Since the p^4 term is negligible, the predictions state basically that the 3 filter experiment at 90 deg should have half the intensity of the 2 filter experiment. Therefore, if you set (11+x) = 2(3+x), you get x=5 lux. In other words, if your lux meter is reading about 5 lux high, all is consistent. However, we don't know whether this is actually the case. One way to test for offset in your luxmeter is to use a smoked glass plate (or anything that sharply reduces the light intensity from 800 to about 10 lux) an another plate that reduces intensity by about 50%. Let's call them the 1% plate and the 50% plate. You would not want to use polarizers for this, just dark glass, to avoid confusing polarization effects with meter calibration. Then try this: measure the light 4 times: Once with no plates (1), then with 50% plate (2), then with 1% plate (3), then with both plates (4). If the ratio of intensities (1)/(2) is the same as (3)/(4), then your meter has no offset. If they are not equal, set [(1)+x)]/[(2)+x] = [(3)+x]/[(4)+x] and solve for x. This is your meter offset in lux.

Well, this is as far as I can carry the analysis without knowing the meter offset (if any).

More later.

--Stuart Anderson
mr_homm
@hexa, Nov.22 (hexa's third post of this date):

QUOTE
However, if you compare the relative percentage against what is predicted, you will notice that the error can be quite substantial.
Take a look at the variation between what you will observe against what is predicted by Malus at 45 degree. If you use two linear polarizers, the error is 2.31%. If you use 3 linear polarizers, the error climb to 10.34%. Imagine what you will get if you use 4 or 5 linear polarizers?
Next, take a look at angle θ=56.25 degree. With two polarizers, the error is 5.61%. With three polarizers, the error is 21.21%.
If we use angle θ=67.5 degree, the error for two polarizers is 15.69%. With three polarizers, the error climb to 85.71%.
Are these errors considered insignificant by your assessment?
This is where I hope a third party could also confirm the validity of my result.

In assessing whether the errors are significant, it is necessary to know the experimental uncertainty of the measurement. Especially, what is the uncertainty of the luxmeter? Most meters have a stated uncertainty guaranteed by the manufacturer, and it is usually as a fraction of the full scale reading. For example, if the full scale is 1000 lux (just a guess, I don't know the actual full scale of your meter), the uncertainty may be reported as 1% of full scale. This sounds very good (which is why manufacturers like to state it this way), but it translates into a +/- 10 lux uncertainty in absolute terms. Most importantly, this uncertainty is usually NOT proportional to the size of the meter reading. In other words, at a reading of 500 lux, the uncertainty is still +/- 10 lux, not +/- 5 lux. In that case, when the reading is 10 lux, the uncertainty is 100%, so the actual light intensity could be anywhere between 0 and 20 lux. That means that it is quite possible that NONE of the measured errors is significant, no matter how high the percentage looks.

In order to assess this, we need to know the uncertainty in your luxmeter. If the manufacturer does not provide it, then we have literally no way to know whether the errors are significant without calibrating the meter against a known standard light source, especially at low light levels. Constructing such a source is very hard, but perhaps there is a way around it in this case. With luck, the manufacturer will tell you the luxmeter uncertainty (and can be trusted). Failing that, since you don't need absolute measurements, only relative ones, you could do a more elaborate version of the calibration I described in my previous post.

Make or get several dark glass filters, and for each one alone, measure the fraction of light reduction with the meter. It should be a fairly small fraction, say in the 2X to 10X range. This way, you are using the luxmeter at fairly high lux values, where its % accuracy is very good. Since each filter passes a known CONSTANT fraction of the incident light (independent of intensity), you can find the predicted intensity for combinations of filters. Then by combining filters, you can find the intensity that the luxmeter SHOULD read and compare that to what it DOES read.

For instance, if you have light originally at 800 lux, and plate 1 reduces it to 400 lux (a factor of 2), but plate 2 reduces it to 200 lux (a factor of 4), then the combination of plates 1 and 2 should reduce it to 100 lux (a factor of 2*4=8). If the luxmeter doesn't say 100, then it is not calibrated well in that intensity range. If it says 105 lux, then you know that it is reading 5 lux high, so all readings in the vicinity of 100 lux should be reduced by about 5 lux to correct the meter calibration. Since the calibration is much better at higher intensities, you can always use the high range of the meter to correct the low range calibration.

QUOTE (->
 QUOTE However, if you compare the relative percentage against what is predicted, you will notice that the error can be quite substantial.Take a look at the variation between what you will observe against what is predicted by Malus at 45 degree. If you use two linear polarizers, the error is 2.31%. If you use 3 linear polarizers, the error climb to 10.34%. Imagine what you will get if you use 4 or 5 linear polarizers?Next, take a look at angle θ=56.25 degree. With two polarizers, the error is 5.61%. With three polarizers, the error is 21.21%.If we use angle θ=67.5 degree, the error for two polarizers is 15.69%. With three polarizers, the error climb to 85.71%.Are these errors considered insignificant by your assessment?This is where I hope a third party could also confirm the validity of my result.

In assessing whether the errors are significant, it is necessary to know the experimental uncertainty of the measurement. Especially, what is the uncertainty of the luxmeter? Most meters have a stated uncertainty guaranteed by the manufacturer, and it is usually as a fraction of the full scale reading. For example, if the full scale is 1000 lux (just a guess, I don't know the actual full scale of your meter), the uncertainty may be reported as 1% of full scale. This sounds very good (which is why manufacturers like to state it this way), but it translates into a +/- 10 lux uncertainty in absolute terms. Most importantly, this uncertainty is usually NOT proportional to the size of the meter reading. In other words, at a reading of 500 lux, the uncertainty is still +/- 10 lux, not +/- 5 lux. In that case, when the reading is 10 lux, the uncertainty is 100%, so the actual light intensity could be anywhere between 0 and 20 lux. That means that it is quite possible that NONE of the measured errors is significant, no matter how high the percentage looks.

In order to assess this, we need to know the uncertainty in your luxmeter. If the manufacturer does not provide it, then we have literally no way to know whether the errors are significant without calibrating the meter against a known standard light source, especially at low light levels. Constructing such a source is very hard, but perhaps there is a way around it in this case. With luck, the manufacturer will tell you the luxmeter uncertainty (and can be trusted). Failing that, since you don't need absolute measurements, only relative ones, you could do a more elaborate version of the calibration I described in my previous post.

Make or get several dark glass filters, and for each one alone, measure the fraction of light reduction with the meter. It should be a fairly small fraction, say in the 2X to 10X range. This way, you are using the luxmeter at fairly high lux values, where its % accuracy is very good. Since each filter passes a known CONSTANT fraction of the incident light (independent of intensity), you can find the predicted intensity for combinations of filters. Then by combining filters, you can find the intensity that the luxmeter SHOULD read and compare that to what it DOES read.

For instance, if you have light originally at 800 lux, and plate 1 reduces it to 400 lux (a factor of 2), but plate 2 reduces it to 200 lux (a factor of 4), then the combination of plates 1 and 2 should reduce it to 100 lux (a factor of 2*4=8). If the luxmeter doesn't say 100, then it is not calibrated well in that intensity range. If it says 105 lux, then you know that it is reading 5 lux high, so all readings in the vicinity of 100 lux should be reduced by about 5 lux to correct the meter calibration. Since the calibration is much better at higher intensities, you can always use the high range of the meter to correct the low range calibration.

The point which I was trying to make is that the distribution of the photon intensity against the angle θ is a BELL CURVE and not one that follows the cosine curve perfectly. We can amplify the difference by placing a third, a fourth and a fifth linear polarizer with each inclined at the same common angle θ to one another.

This is certainly true, but it is also true that imperfections in the polarizer (discussed in my previous post) will also be magnified, and as the light levels drop through several filters, calibration issues with the lux meter will become more serious. So it is not altogether clear that the experimental results will become more significant with more polarizers. I believe that this was mentioned by Confused2 also (credit where credit is due).

QUOTE
It is this Bell curve distribution of the photons passing through EACH linear polarizer that give rise to the cosine square observation by Malus. There is no intention on my part to prove that Malus Law is wrong.

I find this statement somewhat perplexing. Since Malus's law explicitly says that intensity of the light through two polarizers is proportional to cos(θ)^2, and your experiment is testing for deviations from this formula, proving Malus's law wrong is EXACTLY what your experiment is designed to do. If you agree that Malus's law is true, then there is nothing for your experiment to test, and you can go straight to constructing a theory that combines bell curve distributions to give Malus's Law.

But note that if this is true, then you have NO independent experimental verification of your hypothesis, because there is no way to measure the photon distribution coming through one polarizer without using a second polarizer. Since this measurement would agree with Malus's law, there would be no measurable effect that would distinguish your hypothesis from the conventional one. Experimentally, this would be a dead end for your hypothesis; therefore you MUST be looking for deviations from Malus's law sufficient to invalidate it.

QUOTE (->
 QUOTE It is this Bell curve distribution of the photons passing through EACH linear polarizer that give rise to the cosine square observation by Malus. There is no intention on my part to prove that Malus Law is wrong.

I find this statement somewhat perplexing. Since Malus's law explicitly says that intensity of the light through two polarizers is proportional to cos(θ)^2, and your experiment is testing for deviations from this formula, proving Malus's law wrong is EXACTLY what your experiment is designed to do. If you agree that Malus's law is true, then there is nothing for your experiment to test, and you can go straight to constructing a theory that combines bell curve distributions to give Malus's Law.

But note that if this is true, then you have NO independent experimental verification of your hypothesis, because there is no way to measure the photon distribution coming through one polarizer without using a second polarizer. Since this measurement would agree with Malus's law, there would be no measurable effect that would distinguish your hypothesis from the conventional one. Experimentally, this would be a dead end for your hypothesis; therefore you MUST be looking for deviations from Malus's law sufficient to invalidate it.

Apparently, QM uses Malus Experimental Result but makes no attempt to provide a more fundamental explanation on why the probability of light passing through two linear polarizer inclined at an angle θ is given as a square of the wave function, which in this case happen to be the cosine function and not any other trigonometrical function.

I responded to this assertion here. It seems to me that the fact that Malus's law can be derived mathematically from the basic postulates of QM together with just the observation that all the light gets through a second polarizer when it is aligned with the first one, and none gets through when it is perpendicular to the first one. Notice that from these two experimental points, QM is able to fill in the entire cos()^2 curve for all angles. So the proof of Malus's law represents mostly the structure of QM and only two angle observations. If we somehow knew in advance that the state space rotation angle was the same as the geometric one, then we wouldn't even need these two measurements, and QM would predict Malus's law directly from first principles. In fact, there probably IS such an independent way of proving that state θ = geometric θ, and I just didn't happen to learn it. It must depend on knowing that the photon is a spin 1 particle, because the angles are NOT equal for spin 1/2 particles.

As to the probability being the square of the wave function, this is a fundamental postulate of QM, and so it cannot be proven; rather it is that in terms of which other things are proven. It would be like proving Newton's third law directly from theory in classical physics; it is so basic that you CAN'T prove it, because there is nothing more basic to prove it in terms of. Every theory has fundamental postulates -- this is logically inescapable, so it is not especially a weakness of QM as opposed to any other theory.

It is clear that you are uncomfortable with the QM account of polarization, notwithstanding that it is logically and mathematically valid. There's nothing wrong with that; in fact, QM itself stands as an example of a new theory that looks COMPLETELY different at its basis from classical physics, and yet still manages to reproduce all the physical predictions of the older theory. This means that just because a theory has a coherent account of a particular phenomenon, it is not necessarily the ONLY coherent account. There may be another theory very different from QM which agrees with QM on the predictions where QM matches experiment and yet provides predictions in cases where QM makes no clear prediction, or perhaps makes different predictions in areas that have not yet been tested by experiment.

There is an old saying: He who lives by the sword, dies by the sword. QM has replaced classical physics by providing equally good or better explanations for phenomena, but on a completely new basis. If QM can do it to classical physics, it is certainly possible that some newer theory could do it to QM. But it will have to replace the WHOLE THING, because QM is very internally consistent, and can't be changed piecemeal and still retain that consistency.

@hexa, Nov.23

QUOTE
You may be correct to assume that the error could be amplified if we pass on to the next stage. But what is really important for us to note here is that the photons passing through A SINGLE Linear Polarizer obey the Gaussian Distribution or Bell curve which I had stated earlier. It does not matter whether it is exactly a cosine curve or not. Afterall, the cosine curve also belong to the Set of curves described by the Gaussian Distribution.

I'll accept (subject to investigation) the hypothesis that the photons that get through a LP, starting from unpolarized light, have a Gaussian distribution. However, as a mathematician, I must object strongly to your last statement that the cosine curve belongs to the set of curves described by the Gaussian distribution. This is absolutely false. The Gaussian distribution is 1/sqrt(pi*sigma)*exp(-(x-mu)^2/2sigma^2), which is asymptotic to zero as x goes to +/- infinity, is everywhere positive, has a total area of 1.0, never crosses the x axis, and is nonperiodic.. These properties are independent of sigma or mu, so they are shared by all Gaussian curves. A*cos(wx+phi) is not asymptotic to zero, is not everywhere positive, has an undefined total area, crosses the x axis infinitely many times, and is periodic. These properties are independent of A, w or phi, so they are shared by all cosine curves. These are very clearly not the same family of curves.

So I'm going to assume that you meant merely that the two curves have the same general shape (one hump, centered at the origin, provided you cut the cosine curve off at +/- 90 deg). It seems to me that what you're really saying is just that there are other graphs that look like a cosine, and if experiment shows that cosine is incorrect, it is reasonable to turn to these other curves to find a better fit to the data. However, from a mathematical standpoint, some choices are better than others. A true Gaussian would not be my first choice, because it is naturally infinitely wide (asymptotic to zero) and there are only 360 degrees in a circle, so it is necessary to chop it off. This raises the question, why chop it off in that particular way at that particular angle? which must be explained by your theory.

There are theories where functions are truncated in this way, so this is not unheard of. The interference pattern from two slits is an example, in that there are only finitely many bright lines, and the actual number of them can be calculated. However, the two slit theory provides a mathematically natural way to cut off the function, because a parameter keeps growing until an equation ceases to have a solution, and so the function, which is the solution to that equation, mathematically must cut off at that point.

@hexa, Nov.24

I'm not going to quote this one, because I'm not responding to anything point by point. In general just let me say that your explanation is admirably clear and I see exactly what you mean. Your exposition establishes that this is a prima facia reasonable hypothesis to explain linear polarization. To summarize my understanding (so you can check that I have it right), you are proposing that
1) every LP has a definite axis
2) every photon has a definite axis at angle θ
3) the angle between these axes is σ
4) the probability of a photon passing through the LP is a function p(σ).

The assumption that p(σ) is greatest when σ=0 seems to be coming from experiment (to make the hypothesis match observation) rather than being a basic part of the hypothesis. In other words, if there were another different function q(θ) that still caused the hypothesis to agree with experiment, then this other function would also be acceptable, unless it is eliminated by some further experiment.

This doesn't seem to me to be a proof of Malus's law. It does set up a hypothetical framework which can possibly account for the experimental results of linear polarizers, provided the function p(σ) is chosen properly. But how do you choose p(σ) from first principles without peeking at the experimental data first and adjusting it to fit? Of course, Malus just fit the cosine function to the data without knowing why, so as a starting hypothesis to explain observations, yours is as good as old Malus's. However, later on classical EM and then QM both provided more fundamental accounts based on unrelated experiments, that allowed them to derive the cosine behavior from the theory. This would constitute a proof of Malus's law, so in order to get to that stage, you need to show from your basic postulates exactly what p(σ) must be. I don't see any way of doing that, so I am assuming you have a trick up your sleeve.

In the meantime, your hypothesis is reasonable enough to bear analysis and further experimental testing. I still await some clarification about your deck of cards vs. box of marbles analogy.

I'll cut this post off here and get to work on my next one, so it won't get too long. BTW, I too am somewhat confused by the time lag, but I want to answer everything important in the discussion without skipping any points. I will be caught up very soon at this rate.

--Stuart Anderson
hexa
Hi Mr Homm,

I did not notice the gem ( http://forum.physorg.com/index.php?showtop...ndpost&p=115632 ) that you had shared earlier in our discussion.

QUOTE

BELOW IS A LONG RANT FULL OF MY PERSONAL OPINIONS:
Fourth, I tend to think about things from the opposite direction. [1] I think the state space IS the physical reality, and [2] the geometric space we perceive is a side-effect of the state space. Now this is very speculative, and it is just my opinion, but here it is: Really, [3]all that exists is particles in quantum states. [4]These states include many things, such as polarization, energy, etc. Among these things are position and momentum.[5] A point in space is just an eigenstate of position, and a precise mass and velocity is just an eigenstate of momentum. [6] These are related by the uncertainty relation, but for large objects, we don't notice it, because the uncertainty is too small for us to detect, and so we think that position and velocity can both be perfectly known.

In fact, [7]I think that the uncertainty principle is really a bad way of thinking about the situation, because it leads to questions about how nature enforces the uncertainty and the possibility of hidden variables. [8]The real situation (in my opinion) is that what we expect too much. [9]The universe contains only half as much information as we think it does, and [10] the reason that we think it contains more information is because we are spoiled by growing up in the luxury of a large scale, high energy part of the universe. [11] With large objects, there are many many copies of the position and momentum information, so when we measure position, we destroy one copy of the momentum information, but there are lots more copies, so we don't notice. Similarly, when we measure momentum, we destroy one copy of the position information and don't notice.

[1] Yes, I can agree to this.
[2] I tend to think that physical reality must be capable of being described in the geometric space. It must be capable of being described as a marble, a card, a spinning top, a string-- anything that we can comprehend within our physical world. This is intimately related to epistemology. There is the rationalist approach and there is also the empiricist approach. Both are needed to describe what constitute physical reality.
Beside shape, it must also be capable of being described by its size. Whether it is the smallest quantum entity or the largest galaxy, every physical entity has a distinct size. But I must qualify that there is One entity that will not be capable of being described as having a definite size. It is SPACE.
Next, physical objects must also have distinct mass. This will allow the quantum entity to manifest itself as momentum or energy. The property of Position is also dependent on where the mass is located at a particular instance. This is absolutely necessary if the Law of Conservation of Matter is to be observed in all instances.
Finally, the quantum entity must also have this intrinsic property called Charge. Charge possesses the innate ability to emit a FIELD. (It is the least understood and the most important topic in contemporary physics, if we ever want to unite all the forces in Nature. I will differ the discussion on this topic until much later). Combine mass and charge, this will then give rise to the quantum property which we call spin.
All these entities ought to be capable of being described within the geometric space if it has a PHYSICAL REALITY.
This must be distinguish from the Non-Physical Entity, but are equally real and relevant to our daily life. God, spirits and angels: things that one would attribute to the Next World. There are also expressions like joy, anger, sorrow, etc that cannot be physically quantified.
[3] Agree.
[4] I tend to believe that Nature is a lot simpler. I perceive that behind polarization, the quantum entity has a physical orientation that we can describe in geometric space. The Photon and Electron have axes in this geometric space. They differ primarily based on how they are constituted. I will describe a photon as a Deck of Cards based on it Polarization Property. For the electron, I will describe it as a marble or a ball based on how it behave in a Stern Gerlach Apparatus. Perhaps, both electrons and photons are made of something more fundamental than themselves. Perhaps the quarks that we understand now are also made of something more fundamental than themselves.
Similarly, consider the idea that energy is also a consequence of matter moving through this Geometric Space.
[5] and [6] consider the alternative proposition I discussed in [2].
[7] I will differ on this.
[8] I don’t see that there is anything wrong with this expectation. But what Nature does reveal at a particular instance is separate from our expectation.
[9] The APPARATUS that we could devise to measure mass, simply could not work the same way as we use it to measure the mass of charged particles that translate at less than the speed of light. This is where we may end up with missing information when we attempt to measure the mass of a Photon. The fault lies with the APPARATUS. This fault is not because of a lack of ingenuity or care on our part but rather a limitation impose by Nature.
[10] See [8] and [9].
[11] See [8] and [9].

You have also reiterate these opinion of yours in this other site ( http://forum.physorg.com/index.php?showtop...ndpost&p=121120 ):
QUOTE (->
 QUOTE BELOW IS A LONG RANT FULL OF MY PERSONAL OPINIONS:Fourth, I tend to think about things from the opposite direction. [1] I think the state space IS the physical reality, and [2] the geometric space we perceive is a side-effect of the state space. Now this is very speculative, and it is just my opinion, but here it is: Really, [3]all that exists is particles in quantum states. [4]These states include many things, such as polarization, energy, etc. Among these things are position and momentum.[5] A point in space is just an eigenstate of position, and a precise mass and velocity is just an eigenstate of momentum. [6] These are related by the uncertainty relation, but for large objects, we don't notice it, because the uncertainty is too small for us to detect, and so we think that position and velocity can both be perfectly known. In fact, [7]I think that the uncertainty principle is really a bad way of thinking about the situation, because it leads to questions about how nature enforces the uncertainty and the possibility of hidden variables. [8]The real situation (in my opinion) is that what we expect too much. [9]The universe contains only half as much information as we think it does, and [10] the reason that we think it contains more information is because we are spoiled by growing up in the luxury of a large scale, high energy part of the universe. [11] With large objects, there are many many copies of the position and momentum information, so when we measure position, we destroy one copy of the momentum information, but there are lots more copies, so we don't notice. Similarly, when we measure momentum, we destroy one copy of the position information and don't notice.

[1] Yes, I can agree to this.
[2] I tend to think that physical reality must be capable of being described in the geometric space. It must be capable of being described as a marble, a card, a spinning top, a string-- anything that we can comprehend within our physical world. This is intimately related to epistemology. There is the rationalist approach and there is also the empiricist approach. Both are needed to describe what constitute physical reality.
Beside shape, it must also be capable of being described by its size. Whether it is the smallest quantum entity or the largest galaxy, every physical entity has a distinct size. But I must qualify that there is One entity that will not be capable of being described as having a definite size. It is SPACE.
Next, physical objects must also have distinct mass. This will allow the quantum entity to manifest itself as momentum or energy. The property of Position is also dependent on where the mass is located at a particular instance. This is absolutely necessary if the Law of Conservation of Matter is to be observed in all instances.
Finally, the quantum entity must also have this intrinsic property called Charge. Charge possesses the innate ability to emit a FIELD. (It is the least understood and the most important topic in contemporary physics, if we ever want to unite all the forces in Nature. I will differ the discussion on this topic until much later). Combine mass and charge, this will then give rise to the quantum property which we call spin.
All these entities ought to be capable of being described within the geometric space if it has a PHYSICAL REALITY.
This must be distinguish from the Non-Physical Entity, but are equally real and relevant to our daily life. God, spirits and angels: things that one would attribute to the Next World. There are also expressions like joy, anger, sorrow, etc that cannot be physically quantified.
[3] Agree.
[4] I tend to believe that Nature is a lot simpler. I perceive that behind polarization, the quantum entity has a physical orientation that we can describe in geometric space. The Photon and Electron have axes in this geometric space. They differ primarily based on how they are constituted. I will describe a photon as a Deck of Cards based on it Polarization Property. For the electron, I will describe it as a marble or a ball based on how it behave in a Stern Gerlach Apparatus. Perhaps, both electrons and photons are made of something more fundamental than themselves. Perhaps the quarks that we understand now are also made of something more fundamental than themselves.
Similarly, consider the idea that energy is also a consequence of matter moving through this Geometric Space.
[5] and [6] consider the alternative proposition I discussed in [2].
[7] I will differ on this.
[8] I don’t see that there is anything wrong with this expectation. But what Nature does reveal at a particular instance is separate from our expectation.
[9] The APPARATUS that we could devise to measure mass, simply could not work the same way as we use it to measure the mass of charged particles that translate at less than the speed of light. This is where we may end up with missing information when we attempt to measure the mass of a Photon. The fault lies with the APPARATUS. This fault is not because of a lack of ingenuity or care on our part but rather a limitation impose by Nature.
[10] See [8] and [9].
[11] See [8] and [9].

You have also reiterate these opinion of yours in this other site ( http://forum.physorg.com/index.php?showtop...ndpost&p=121120 ):

I see it this way: the uncertainty principle is just a very bad name for a fundamental fact, and the fact is that the universe contains exactly half the information that we classically expect it to contain. We are merely spoiled by living in the world of large objects, and so we expect to be able to "have our cake and eat it too." The universe is not "hiding" information from us; rather, we are falsely expecting to get information that is not really there.

Initially, I thought that as an educator of main stream science, one would only recite the official dogma permitted by the establishment. That is why I could not understand the profound message that you were trying to share with us. I only realized that you were also quite a radical after you have re-stated your position in this post ( http://forum.physorg.com/index.php?showtop...ndpost&p=143294 )
QUOTE

Surprisingly perhaps, I am less accepting of uncertainty than you are. I feel that the whole uncertainty idea represents a primitive interpretation of the theory, and is just a leftover from its early days. My position is that there is fundamentally no uncertainty. Instead, there are perfectly definite states AT ALL TIMES (which I think agrees with your position), but further, I think that these states are abstract (here is where I disagree with your position), and that uncertainty is basically an illusion created by our expectations. We expect to get separate answers for momentum and position for example, but for the particle, these are actually only ONE property. We expect to get two different answers to one question -- of course it doesn't work. In classical physics, there are so many particles in an object that we can ask the question twice in two different ways without disturbing the object much, so we can get the two answers we want, and we have gotten used to that, so we think it is our RIGHT now.

So basically, my position is that every particle is always in a perfectly definite state, but it might not be a state that we are comfortable with from our classical physics experience. Statements like "the particle doesn't have a definite position" are misguided attempts to express a more fundamental idea: position and momentum are points of view on a single underlying reality, just as are space and time, or energy and momentum. (BTW, I am not accusing you, hexa, of being misguided. It's the statements in popular accounts of QM (and in textbooks, even some of Feynman's) that I find misguided.

and you went further to state:

QUOTE (->
 QUOTE Surprisingly perhaps, I am less accepting of uncertainty than you are. I feel that the whole uncertainty idea represents a primitive interpretation of the theory, and is just a leftover from its early days. My position is that there is fundamentally no uncertainty. Instead, there are perfectly definite states AT ALL TIMES (which I think agrees with your position), but further, I think that these states are abstract (here is where I disagree with your position), and that uncertainty is basically an illusion created by our expectations. We expect to get separate answers for momentum and position for example, but for the particle, these are actually only ONE property. We expect to get two different answers to one question -- of course it doesn't work. In classical physics, there are so many particles in an object that we can ask the question twice in two different ways without disturbing the object much, so we can get the two answers we want, and we have gotten used to that, so we think it is our RIGHT now.So basically, my position is that every particle is always in a perfectly definite state, but it might not be a state that we are comfortable with from our classical physics experience. Statements like "the particle doesn't have a definite position" are misguided attempts to express a more fundamental idea: position and momentum are points of view on a single underlying reality, just as are space and time, or energy and momentum. (BTW, I am not accusing you, hexa, of being misguided. It's the statements in popular accounts of QM (and in textbooks, even some of Feynman's) that I find misguided.

and you went further to state:

However, that  doesn't mean that I think the answer to the question is to adopt the Copenhagen interpretation. In fact, as I said just above, I think there is continuity and a well defined state at every moment in time. The value of the Copenhagen interpretation, to me, is not that it answers these questions, but that it reminds us that we've never answered them properly in previous centuries.

Coming back to your post ( http://forum.physorg.com/index.php?showtop...ndpost&p=152518 )
QUOTE

QUOTE (->
 QUOTE I went on to HYPOTHESIZE that a photon is a “deck of cards” as opposed to a box of marbles. This proposition appears to be more suited to explain both Linear and Circular Polarization much better than QM. Most significantly, this proposition allows me to explain Malus Law fundamentally without having to resort to some abstract mathematical postulates It is pretty clear that you have some specific behavior in mind with the deck of cards vs box of marbles analogy, but I am not getting it. In exactly what way is a photon like a deck of cards or box of marbles? I'm sure I'm missing something obvious here.

The metaphor, a “Deck of Cards”, allows us to assign a physical axis that is normal to its plane. Contrast this if we were to describe a Photon as a Box of marbles. The axis that we can use to describe two marbles, three marbles or four marbles packed closely to one another will be very different from one another. This will mean that it is unlikely for photons of different energy to behave with any consistency when colliding with the atoms as it penetrate a medium, such as a linear polarizer. The consistency of how photons of varying energy, momentum, frequency or wavelength penetrate a Linear Polarizer allows me to infer that the Photon has the physical attribute of a Deck of Cards and not that of a Box of Marbles.
As a deck of cards, it also allows us to infer the most important discovery by Max Planck in the 20th century—the Quantization of Energy.

I have mentioned the difficulty in hypothesizing anything more complicated when I replied to Peter Robert:
QUOTE

Yes, I was also of this opinion when I first begin my search. But I come to realize the IMPOSSIBILITY of Nature to organize itself with the pervasive uniformity if we have too many components.

Hence, I see no harm in using such simple metaphor to describe Nature a bit more vividly.
Would you have preferred if I describe it as some abstract numbers and hope that you could accept these numbers as a representation of our Physical Reality.
Since we have the benefits of sight; unlike the 8 blind men trying to figure out how an elephant looks, I will continue to use macro metaphors as my preferred mode of communication and support it with the numbers thereafter. We should not mistake the horse from the cart.

I think I owe everyone an explanation on why I am looking at the topic of Circular Polarization of Light with such vivid details.
I will draw the parallel with Rutherford attempt when he bombarded the gold foil with alpha particles. He was not amused by the measurement of a few alpha particles in one direction or another. Nor was he contented to show that alpha particles traveling at great speed can recoil from the gold atoms making up the foil. His ultimate aim is to discover the STRUCTURE of the ATOM and all the bolts and nuts that goes into the making of a SINGLE ATOM.
This is where he found his teacher (J.J.Thomson) Raisin pudding Model of the atom unacceptable.

I hope to share an even more unexpected observation that I have made in predicting why STABLE ISOTOPES are found at one specific mass and not at any other mass.
But this observation will make less sense unless we can methodically establish a case of perceiving these quantum entities as having the physical attributes that I am attempting to establish in this discussion.

QUOTE (->
 QUOTE Yes, I was also of this opinion when I first begin my search. But I come to realize the IMPOSSIBILITY of Nature to organize itself with the pervasive uniformity if we have too many components.

Hence, I see no harm in using such simple metaphor to describe Nature a bit more vividly.
Would you have preferred if I describe it as some abstract numbers and hope that you could accept these numbers as a representation of our Physical Reality.
Since we have the benefits of sight; unlike the 8 blind men trying to figure out how an elephant looks, I will continue to use macro metaphors as my preferred mode of communication and support it with the numbers thereafter. We should not mistake the horse from the cart.

I think I owe everyone an explanation on why I am looking at the topic of Circular Polarization of Light with such vivid details.
I will draw the parallel with Rutherford attempt when he bombarded the gold foil with alpha particles. He was not amused by the measurement of a few alpha particles in one direction or another. Nor was he contented to show that alpha particles traveling at great speed can recoil from the gold atoms making up the foil. His ultimate aim is to discover the STRUCTURE of the ATOM and all the bolts and nuts that goes into the making of a SINGLE ATOM.
This is where he found his teacher (J.J.Thomson) Raisin pudding Model of the atom unacceptable.

I hope to share an even more unexpected observation that I have made in predicting why STABLE ISOTOPES are found at one specific mass and not at any other mass.
But this observation will make less sense unless we can methodically establish a case of perceiving these quantum entities as having the physical attributes that I am attempting to establish in this discussion.

1) That the photons passing through a Linear Polarizer obey the Gaussian Distribution about the polarizing axis of the linear polarizer?
2) That, it is plausible to assume that a photon in the unpolarized state has the probability to be found at any angle θ where 0 deg.<θ<360 deg ;
3) That, it is plausible to describe a PHOTON in the state vector lx> as a photon that has the probability to be found at any angle θ where 0 deg.<θ<45 deg; 135 deg.<θ<225 deg; 315 deg.<θ<360 deg;
4) That, it is plausible to describe a photon in the state vector ly> as a photon that has the probability to be found at any angle θ where 45deg.<θ<135 deg; 225 deg.<θ<315 deg

I hope you can appreciate why I am seeking some concurrence before I proceed to wave my hands on the next topic.

This is where I find tremendous comfort when you shared your profound thought.
It is reassuring that I am not alone who saw the Emperor (Copenhagen Interpretation based on the Uncertainty Principle) clothed in nothing but his birthday suit.

I will stop here.
I will address your comments in your latest post ( http://forum.physorg.com/index.php?showtop...ndpost&p=152809 ) in my next post. However, I would prefer to hear your comment on this other post ( http://forum.physorg.com/index.php?showtop...ndpost&p=145926 ) which is integral to the understanding of how Malus Law appears to be correct. I must qualify that Malus Law is only an approximation. The derivation in QM based on the application of the cosine function is also an approximation. Hence, I do not see the use of cosine function as an irrefutable proof of the validity of QM just as I do not see Ptolemic mathematics as proof that Earth is the center of the universe.

Cheers.
mr_homm
@Nick, Nov. 25:

@hexa, Nov. 25:

Here is my 2 cents worth on this Nick's question: The answer is that light DOES influence a compass. The compass needle will attempt to line up with ANY magnetic field; it doesn't care where it came from or whether it is from a beam of light or a bar magnet or the earth. The key here is the FREQUENCY of the light. The frequency of visible light is around 10^14 Hz, which means that the tugs on the compass needle are reversing roughly 100 trillion times per second. How is the compass needle going to respond to that? It just barely gets started turning one way, and then immediately the magnetic field reverses and pulls it back where it was. This means that the needle will only be able to do a VERY, VERY tiny vibration.

For example, if the magnetic field amplitude is 1 Tesla, the compass needle has a magnetic moment of 1Ampere*meter^2, then the field will exert a torque of at most 1 N*m. If the needle has a mass of 1 gram = .001 kg, and a length of 6 cm = .06m, then it has a moment of inertia 1/12*mL^2 = 5*10^-6 kg*m^2, which means that its angular acceleration will be torque/inertia = (1 N*m)/(5*10^-6) = 200,000 rad/sec^2. This sound huge, but over a time period of 10^-14 seconds, the velocity it reaches will be w = (2*10^5)*(10^-14) = 2*10^-9 radians/sec. Since it is starting from rest, the average velocity will be half this, i.e. 10^-9 rad/sec. During 10^-14 sec, it will therefore rotate by 10^-23 radians before reversing direction. This is an incredibly small rotation: the tip of the compass needle moves a distance that is roughly 1 billionth the diameter of an atomic nucleus.

And this is with VERY generous values for the magnetic field and magnetic moment. A normal compass needle will have a magnetic moment some hundreds of times smaller than the one I assumed, and as for the light beam.... Well, a 1 Tesla magnetic field has an energy density B^2/(2*mu_0) = (10^7)/2pi, and therefore a beam power of twice this energy density (because E field contributes an equal share) multiplied by the speed of light. This is 10^15/pi = roughly 3*10^14 Watts per m^2. Since full sunlight above the earth's atmosphere delivers about 1300 W/m^2, so this light is about 2*10^11 times brighter than the sun. This is approximately the brightness of an average quasar, equivalent to the entire light output of every star in our galaxy. So with ordinary levels of light, the motion of the compass needle will be far, far smaller even than the tiny number I calculated in the previous paragraph. So you probably won't notice it with the naked eye.

On the other hand, there is nothing special about visible light. The entire electromagnetic spectrum appears to be basically the same, all the way down to the electromagnetic waves emitted by power lines at 60Hz (in the US, other places use 50 or 70Hz depending on where you go). If you had a slow wave, at say 1 Hz, then the angle of the compass swing would be 10^28 times greater than what I quoted above. With a field of .001 Tesla (which is quite easy to produce by running large currents through wires and holding the compass close up to them), and with a magnetic moment of .01 Ampere*m^2, the compass would swing by 1 full radian. This would be quite easy to observe.

So the answer is that the EM wave DOES affect the compass, but the higher the frequency, the less it affects it. At low frequencies, it is easy to observe, but at visible light frequencies, you don't have even a prayer of seeing it.

@Maltida, Nov.26

Yes, I am sorry to be so late with my responses. It confuses me, too, but I don't want to skip anything important. And I should mention, the irony of my responding 2 weeks later to your post asking me to try to stay current has not escaped me!

I should be able to catch up rapidly now. Glad you are enjoying the discussion.

More later.

--Stuart Anderson
"THEY"
Trying to get caught up on this thread here... two quick questions.

Mr Homm - I know you are short on time, but I sent you a pm on equipment for "sharing" for the experiment, did you receive it?

Hexa - I have not had time to keep up with this thread well, but I did notice your post to me regarding "prospect sheets". I did a quick google and couldn't find them for sale? I guess I need to get going on this project if it is going to happen...
hexa
Hi Mr Homm,

Thanks for helping Nick and me with the answer.
I hope you could provide me the reference to the said experiment.

I am just curious as to what we would observe if we were to conduct the following experiments:

1. Place a red laser gun before a cylindrical vacuum chamber.
2. Locate the position of the laser beam at say 1000 m (more if possible) away from the laser gun by using a screen and mark the position of the laser.
3. Next, place a pair of magnets (5 tesla or more) orthogonally to the vacuum chamber and the laser beam; and then locate the position of the laser beam on the screen.
4. Rotate the axis of the magnets on the orthogonal plane and then measure the position of the laser beam on the screen at various angles.
5. Replace the pair of magnets by placing two electrodes with a potential difference of say 100,000 V (more if it is available).
6. Rotate the axis of the electrodes on the orthogonal plane and then measure the position of the laser beam on the screen at various angles.
7. Fill the chamber wth air and repeat step 2 to step 6.
8. Replace the red laser gun with a green laser. Repeat step 2 to step 7.

I wonder whether there is anyone out there who happen to have these apparatus to conduct the aforesaid experiments to verify whether Light is affected by electric or magnetic field.

Do suggest any improvement or modification that you would add to test whether Light is affected by the influence of electric or magnetidc field.

Cheers.

Hi They,

It is perspex or acrylic sheet. Not PROSPECT sheet.
Many household items are made of such materials.
Some fish tanks use perspex sheet instead of glass.
All you need is to look for one that is transparent.
The effect that I hope your daughter would be able to see is the variation in stress pattern as you apply a stress to these objects. They are very colorful and spectacular when viewed though these circular polarizers.
I hope the clarification helps.

Cheers.

mr_homm
Answering current posts this time, then back to catch-up.

@THEY:
My main email computer has been down for a while (which has made it even harder to respond to posts). I did get the pm you sent me via physorg, but since I didn't get the email notification, I didn't see them right away. I only noticed a few days ago that I had messages. Sorry about that! I'll respond to them by the physorg pm system. Hope all is well with you and THEY2.

@hexa:

Glad to help. There is no particular experiment I can point you to, but it has been common knowledge for many years, among workers in electric power generation plants, that compasses would go absolutely crazy if you walked around the plant with them. Sometimes vibrating, or spinning and changing direction randomly (that happens when the amplitude of vibration exceeds pi radians -- once the needle has swung more than half way around, the field just keeps it going around the same direction instead of vibrating). They are essentially little electric motors running off the energy in the electromagnetic waves that leak from the power lines. This is the same effect that Tesla used to light up bulbs with no external connections. So this isn't so much a formal experiment as just the everyday experiences of power plant workers.

As to the laser deflection experiment, current theory (both QM and classical EM) predict no deflection whatsoever in all the cases with vacuum, red or green light, electric or magnetic field, doesn't matter. With air, there may possibly be a slight effect, but because nearly all the molecules of air are N2 or O2 or CO2, which are all electrically and magnetically NONPOLAR, there would be no net effect on these molecules by either the electric or magnetic fields, so they won't align with the field or develop a concentration gradient or anything.

On the other hand, humid air vs dry air MAY make a difference, because water vapor is an electrically polar molecule. I don't remember whether it has a magnetic moment or not. There may be a secondary effect if the electric field is not completely uniform: If E is stronger near the electrode plates and somewhat weaker in the middle of the vacuum chamber, then the water molecules will be slightly attracted to the poles because they will have a lower potential energy there. This means that at thermal equilibrium, the air will be slightly drier in the middle than at the sides. Since humid air has a somewhat different refractive index than dry air, the vacuum chamber will become a lens. (A lens doesn't need to bulge to work. It could simply have a refractive index gradient and achieve the same effect.) It wouldn't really matter whether the lens was converging or diverging, because if its focal length was much less than a mile, it would end up by defocussing the laser beam. So rather than moving to one side, the spot on the target might spread out so much that it disappears.

Other than the water vapor test, I can't think of anything to add to this experiment. It seems pretty well designed to me, and should be a sensitive test of light deflection. One thing I would be careful about is that the electric or magnetic fields may affect the operation of the laser itself, and you might get beam deflections due to some hard-to analyze effect inside the laser. You could test this by moving the laser source farther from the magnets, and see if the effect diminishes. If so, it is an effect happening inside the laser; if not, it is an effect happening to the light beam itself as it passes through the fields. I don't have the equipment to try this myself, unfortunately.

And now, back to catching up with older topics.

--Stuart Anderson
"THEY"
QUOTE (hexa+Dec 12 2006, 04:44 PM)

It is perspex or acrylic sheet. Not PROSPECT sheet.

cute typo! Actually what I MEANT to type was "perspect" and that was what I googled. It was typed that way in that post to me pages ago.

ANYWAY! My typos aside, I did google it right today, and found out what it is. Here in USA it is called lucite, I believe this is the same product.

Sounds like her experiment will get bigger and bigger... Will be educational no matter where it goes. Will the perspex/lucite only work with the lenses, or will it do anything to the lasers also?

Sorry, I shouldn't take this thread so off track.... maybe in future I should ask questions directly (pm) when they are on the 12 year old experiment instead of the laser/filter setup?
hexa
Hi Mr Homm,

QUOTE

As to the laser deflection experiment, current theory (both QM and classical EM) predict no deflection whatsoever in all the cases with vacuum, red or green light, electric or magnetic field, doesn't matter.

I was mistaken when you said that magnetic compass would respond to the presence of light.
I though you were saying that light can be deflected by the presence of electric or magnetic field.
If light could be deflected by electric or magnetic field, then I am very surprised that we did not rely on this property to devise an APPARATUS to measure the mass of photons.
Since I do not have the budget to conduct such an experiment, I will take your clarification that light is not affected by electric or magnetic field as correct.

Coming back to your earlier comment:
QUOTE (->
 QUOTE As to the laser deflection experiment, current theory (both QM and classical EM) predict no deflection whatsoever in all the cases with vacuum, red or green light, electric or magnetic field, doesn't matter.

I was mistaken when you said that magnetic compass would respond to the presence of light.
I though you were saying that light can be deflected by the presence of electric or magnetic field.
If light could be deflected by electric or magnetic field, then I am very surprised that we did not rely on this property to devise an APPARATUS to measure the mass of photons.
Since I do not have the budget to conduct such an experiment, I will take your clarification that light is not affected by electric or magnetic field as correct.

Coming back to your earlier comment:

QUOTE

It is this Bell curve distribution of the photons passing through EACH linear polarizer that give rise to the cosine square observation by Malus. There is no intention on my part to prove that Malus Law is wrong.

I find this statement somewhat perplexing. Since Malus's law explicitly says that intensity of the light through two polarizers is proportional to cos(θ)^2, and your experiment is testing for deviations from this formula, proving Malus's law wrong is EXACTLY what your experiment is designed to do. If you agree that Malus's law is true, then there is nothing for your experiment to test, and you can go straight to constructing a theory that combines bell curve distributions to give Malus's Law.

But note that if this is true, then you have NO independent experimental verification of your hypothesis, because there is no way to measure the photon distribution coming through one polarizer without using a second polarizer. Since this measurement would agree with Malus's law, there would be no measurable effect that would distinguish your hypothesis from the conventional one. Experimentally, this would be a dead end for your hypothesis; therefore you MUST be looking for deviations from Malus's law sufficient to invalidate it.

The way I have put it is perhaps base on my cultural upbringing.
Generally, we prefer not to say someone is wrong. We say that we have a differing opinion.
More often than not, one can only claim so much based on the evidence that one possesses.
I do not think you are asserting what President Bush is saying: “You are with us or you are against us”.
I think our objective in Science should be based on improving the understanding of Nature. Whoever is right is secondary. What I hope with your help and the others like Confused2, Zephir, Montec, Peter Robert, They, Maltida, Nick, Dr. Brettmann, Schneibster, MrMysteryScience, etc, is to see whether it is possible to comprehend Nature using visually simple and logical metaphor that even a child could understand. I am glad that “They” and her daughter are enthusiastic to learn more about this topic on Circular Polarization of Light by investing some money to see the effect with their own eyes.

Malus had the vision based on the data that was available to him then. Cosine square does appear to fit admirably to the set of data that was available to him. Since he made no further postulate where he can be faulted, I see no necessity to challenge his observation. Similarly, I see no need to fault QM on its prediction as it does not pretend that there is something more fundamental. QM is only interested in the probability. The wave function is just a postulate along with the use of the cosine function. What it claim in Linear Polarization of Light is that through the use of Quantum Mechanics one could predict the probability of the intensity. Again, empirical data appears to support this proposition except for its prediction on the topic of Circular Polarization of Light. This is where I find a substantial discrepancy between what is predicted and what is observed.
However, if we were to put the data under the microscope, there is some slight discrepancy even for Linear Polarization.

Let us take a look at these data. The data that I have obtained were as follows:

QUOTE (->
 QUOTE It is this Bell curve distribution of the photons passing through EACH linear polarizer that give rise to the cosine square observation by Malus. There is no intention on my part to prove that Malus Law is wrong.

I find this statement somewhat perplexing. Since Malus's law explicitly says that intensity of the light through two polarizers is proportional to cos(θ)^2, and your experiment is testing for deviations from this formula, proving Malus's law wrong is EXACTLY what your experiment is designed to do. If you agree that Malus's law is true, then there is nothing for your experiment to test, and you can go straight to constructing a theory that combines bell curve distributions to give Malus's Law.

But note that if this is true, then you have NO independent experimental verification of your hypothesis, because there is no way to measure the photon distribution coming through one polarizer without using a second polarizer. Since this measurement would agree with Malus's law, there would be no measurable effect that would distinguish your hypothesis from the conventional one. Experimentally, this would be a dead end for your hypothesis; therefore you MUST be looking for deviations from Malus's law sufficient to invalidate it.

The way I have put it is perhaps base on my cultural upbringing.
Generally, we prefer not to say someone is wrong. We say that we have a differing opinion.
More often than not, one can only claim so much based on the evidence that one possesses.
I do not think you are asserting what President Bush is saying: “You are with us or you are against us”.
I think our objective in Science should be based on improving the understanding of Nature. Whoever is right is secondary. What I hope with your help and the others like Confused2, Zephir, Montec, Peter Robert, They, Maltida, Nick, Dr. Brettmann, Schneibster, MrMysteryScience, etc, is to see whether it is possible to comprehend Nature using visually simple and logical metaphor that even a child could understand. I am glad that “They” and her daughter are enthusiastic to learn more about this topic on Circular Polarization of Light by investing some money to see the effect with their own eyes.

Malus had the vision based on the data that was available to him then. Cosine square does appear to fit admirably to the set of data that was available to him. Since he made no further postulate where he can be faulted, I see no necessity to challenge his observation. Similarly, I see no need to fault QM on its prediction as it does not pretend that there is something more fundamental. QM is only interested in the probability. The wave function is just a postulate along with the use of the cosine function. What it claim in Linear Polarization of Light is that through the use of Quantum Mechanics one could predict the probability of the intensity. Again, empirical data appears to support this proposition except for its prediction on the topic of Circular Polarization of Light. This is where I find a substantial discrepancy between what is predicted and what is observed.
However, if we were to put the data under the microscope, there is some slight discrepancy even for Linear Polarization.

Let us take a look at these data. The data that I have obtained were as follows:

Experiment 1
Angle θ (measured in degree) against Intensity of light (measured in lux) versus the values predicted by Malus Law for two linear polarizers:
Column 1      Column 2        Column 3        Column 4     Column 5
1) 00.00 deg.   346 lux. ;        346 lux.;           0 lux.;        0.00%
2) 11.25 deg.   335 lux. ;        333 lux.;           2 lux.;        0.60%
3) 22.50 deg.   302 lux. ;        295 lux.;           7 lux.;        2.37%
4) 33.75 deg.   244 lux. ;        239 lux.;           5 lux.;        2.09%
5) 45.00 deg.   177 lux. ;        173 lux.;           4 lux.;        2.31%
6) 56.25 deg.   113 lux. ;        107 lux.;           6 lux.;        5.61%
7) 67.50 deg.    59 lux. ;           51 lux.;          8 lux.;       15.69%
8) 78.75 deg.    23 lux. ;           13 lux.;         10 lux.;      76.92%
9) 90.00 deg.    11 lux. ;            0 lux.;          11 lux.;       Infinity
Notes:
Column 2 = Reading obtained from luxmeter
Column 3= Computation using Malus Law based on the same measured initial intensity of 346 lux.
Column 4 = difference between Column 2 and Column 3.
Column 5 = difference between Column 2 and Column 3 in percentage

And

QUOTE

Experiment 2
Angle θ (measured in degree) against Intensity of light (measured in lux) versus the values predicted by Malus Law for three linear polarizers; the angle θ is the same between any two adjacent linear polarizers:

Column 1      Column 6        Column 7        Column 8     Column 9
1) 00.00 deg.     346 lux. ;      346 lux.;            0 lux.;       0.00%
2) 11.25 deg.     328 lux. ;      320 lux.;            8 lux.;       2.50%
3) 22.50 deg.     267 lux. ;      252 lux.;          15 lux.;       5.95%
4) 33.75 deg.     177 lux. ;      165 lux.;          12 lux.;       7.27%
5) 45.00 deg.       96 lux. ;        87 lux.;           9 lux.;      10.34%
6) 56.25 deg.       40 lux. ;        33 lux.;           7 lux.;      21.21%
7) 67.50 deg.       13 lux. ;         7 lux.;            6 lux.;      85.71%
8) 78.75 deg.         4 lux. ;         1 lux.;            3 lux;     300.00%
9) 90.00 deg.         3 lux. ;         0 lux.;            3 lux;        Infinity

Notes:
Column 6 = Reading obtained from luxmeter
Column 7 = Computation using Malus Law based on the same measured initial intensity of 346 lux.
Column 8 = difference between Column 6 and Column 7.
Column 9 = difference between Column 6 and Column 7 in percentage

From the data that I have obtained from Experiment 1 and Experiment 2, you will notice in Column 5 and Column 9 that the discrepancy compared with Malus Law increases with the increase in angle θ. You are right to think that the discrepancy is due to instrument error. I am sure if we were to use 10 different sets of instruments, we will get 10 different sets of readings. Some may have smaller discrepancy while others may have greater discrepancy compared to what Malus or QM had predicted.
To me this is not important. What I hope to establish is that as photons pass through a Linear Polarizer, they obey the Gaussian Distribution. If a Linear Polarizer is placed before a source of unpolarized light with its polarizing axis placed along the x-axis, then only 50% gets through the linear polarizer. The distribution of the photons will be contained within the range of +45 deg. and –45 deg. from the polarizing axis. At 45 deg. we can assume the intensity as zero. This allow us to normalise the curve. I must qualify that there is no means available to us to determine that at this angle the intensity is zero since light does not respond to the influence of electric or magnetic field.
Alternatively, we can place the polarizing axis at 90 deg. In this instance, all the photons that could not get through under the previous arrangement will get through the linear polarizer placed at this angle. The distribution will be contained within the angle +45 deg. and –45 deg. but measured from 90 deg. instead of the angle 0 deg. In both cases the intensity distribution are normalized. The intensity in both states will add to 100 percent (theoretically).
This can be demonstrated that if the photons in the lx> vector state were to pass through another x-polarizer, theoretically all the photons will pass through polarizer unimpeded whether we are using the Gaussian distribution or cosine square law.

I hope I have allay your concern on using less than premium grade apparatus to demonstrate Gaussian Distribution. But for you to fully comprehend the implication of Malus Law, QM or my proposition, it is important for you to understand the principle behind it based on the analysis of the hypothetical example of children running through the series of doors on two sliding walls ( http://forum.physorg.com/index.php?showtop...ndpost&p=145926 ). We need to INFER more from the data based purely on the numbers of children getting through when one wall is shifted relative to the other.
The Principle that I used to analyse the children running through the doors is applied to Inferring the Data passing through two or three polarizers which I have done for the Experiments shown above.

Cheers.

Hi They,

I hope you will be able to get all that you need for your daughter.
Hope she enjoy playing with these apparatus and get to love Science.

Cheers.
mr_homm
@hexa, Nov. 28:

I'll respond to your numbered comments point by point, at least for those where I have a comment to make:

2: Supposing that, as you say, a photon has a size and shape, then why is it that size and shape? These qualities seem to necessarily point to a deeper structure which explains the size and shape. By this logic, a photon cannot be a fundamental particle. If there ARE fundamental particles at all, then the concepts of size and shape would seem to me NOT to apply to them. How can a thing have a size, unless you can at least conceptually consider portions of it? Similarly, what is shape other than the relation of the positions of some sub-parts to others? These are philosophical critiques of the concepts of size and shape, of course, but I find them convincing. A truly fundamental particle must have neither size nor shape, because these qualities automatically imply that the particle has parts. So either there are no fundamental particles at all, just parts within parts forever, or there are fundamental particles, but they have no size or shape.

When you say "...“FIELD” that does not fit into the same definition of a physical entity that obey the Law of Conservation" I do not quite know what you mean. All the fields I am familiar with DO obey the law of conservation. As an amusing side note: in quantum field theory, the fields emit particles, not the other way around.

For all the rest of your comments on the gradual historical revelation of smaller and smaller structures, this seems quite reasonable to me and pretty much in line with what I think. Right at the end, though, where you mention the fine structure constant: I don't thing QM predicts this number. As far as I recall, it is one of the adjustable parameters in the Standard Model, because I always hear it being discussed in anthropic principle arguments as one of the parameters that must be fine tuned in order for life to exist. If it were predicted from first principles by QM, then it wouldn't be adjustable at all. On the other hand, QM has correctly predicted the gyromagnetic ratio of the electron to around 11 decimal places, so perhaps this is what you were thinking of. It doesn't matter to the force of your argument, since either example would prove your point equally well.

3&4: Discussed in 2.

5: When you say "Next, consider the fact that if we were to move the same mass in this blob of matter to the speed of light c. Does it not then becomes Energy, given by Einstein’s hallmark equation?" I would respond: no, I don't see why that would happen. E = mc^2 says that mass is already equivalent to energy, or that energy has mass; take your pick. If the blob of mass were accelerated to the speed of light, the equations of relativity predict that its measured mass would diverge to infinity. In that case, you might say that its original mass (the mass measured when it was at rest), was only an infinitesimal fraction of its measured mass. However, this doesn't mean that its original mass went away and became energy, only that a very large ADDITIONAL amount of energy had been added. The original mass was in no way reduced.

In fact, this can be used as an argument that the mass of a photon must be zero. Since the energy of the "rest mass" forms only an infinitesimal fraction of the total energy when the speed = c, then either the total energy is infinite and the rest mass is finite, or the total energy is finite and the rest mass is zero. Since a photon cannot possibly have infinite energy, then if the Special Theory of Relativity is true, the rest mass of a photon MUST be zero. So if its not zero, then we will have to discard Special Relativity, and of course that will force us to discard General Relativity as well.

As to your remark that all measurements ultimately reduce to displacements and all measuring devices ultimately convert other quantities into displacements, I had also been struck by this observation. Displacement does indeed seem to have a privileged place in our experimental procedures.

You are also of course correct in saying that one cannot use electric or magnetic fields to measure the mass of a photon, but I do not see what traveling at the speed of light has to do with it, or how it prevents such a measurement from being carried out. Perhaps this is one of the things you would like to defer; if so, I'll just have to wait. However, since gravity DOES deflect photons, it is clearly possible for some fields to deflect them, even though they travel at the speed of light, so light speed can't cause immunity to ALL types of fields, only to some of them. I look forward to seeing where this difference comes from. Of course, since gravity causes all different masses to deflect by the same amount, the gravitational deflection cannot be used to measure the photon's mass.

QUOTE
To extend Relativity to imply that Two different photons (carrying different energy and momentum) has the same “zero mass” will cause us to run foul of the Law of Conservation of Matter. This Law essentially means that we cannot create something from nothing and neither can we cause something to vanish into nothingness.

I would really like an explanation of this one. I have looked at it for a long time, and I just cannot see any way to get a contradiction out of this. Having two different photons with different momentum and energy but zero rest mass doesn't seem to me to be creating anything or destroying anything, it's just two photons existing.

Also, there are several indirect proofs that the photon's mass must be zero. For one, consider the ratio of kinetic energy to momentum. Nonrelativistically, E=p^2/(2m), so that E depends QUADRATICALLY, not linearly, on momentum. Relativistically, E^2 = (mc^2) + p^2*c^2. This is again a nonlinear equation. Therefore, energy is NOT proportional to momentum, and the mismatch of proportion allows you to infer the mass. Suppose you consider several light beams, in a range of frequencies. The photoelectric effect lets you determine the energy of the individual photons in each beam, and it is observed to be EXACTLY proportional to the frequency. On the other hand, if you use the same beams, at equal intensities, to push on black targets inside vacuum chambers, you can measure the rates of momentum transfer, and they are EXACTLY the same at equal intensities for all frequencies.

Since rate of momentum transfer = momentum per photon * number of photons/sec in the beam, and intensity = energy per photon * number of photons/sec in the beam, it follows that E is EXACTLY proportional to p. Putting this into the relativistic energy formula, it follows that the photon mass must be EXACTLY proportional to p as well, since only this will make the equation turn into a linear one.

On the other hand, we know that photons can be Doppler shifted to a new frequency just by using a moving observer. This cannot make any change in the inherent properties of the photon, because you haven't actually done anything to the photon, you've just moved the observer. Even if photons have different masses, the rest mass of one individual photon could not change after the photon was emitted, because rest mass is a relativistically invariant property. Therefore, after Doppler shifting, the rest mass of the photon must be the same as it was when the photon was first emitted.

Now you have a direct contradiction: If a photon were emitted with mass m and frequency f, then Doppler shifted to a frequency 2f, its rest mass MUST become 2m to be proportional to the momentum, but it must also remain m because it is an inherent property of this particular photon. Therefore, m = 2m, which is a contradiction unless m=0.

BTW, the Law of Conservation of Matter isn't really accepted as such any more since 1905. It has been split into two laws: conservation of mass_energy and conservation of particle number. Since mass and energy are interconvertible in relativity, they cannot possibly be separately conserved. Only the total mc^2 + E is conserved. The law of particle number conservation is more like the old-style conservation of matter idea. Although particles can be created and destroyed, the total number remains constant because they can only be created or destroyed in particle-antiparticle pairs, and antiparticles count as -1 particle.

QUOTE (->
 QUOTE To extend Relativity to imply that Two different photons (carrying different energy and momentum) has the same “zero mass” will cause us to run foul of the Law of Conservation of Matter. This Law essentially means that we cannot create something from nothing and neither can we cause something to vanish into nothingness.

I would really like an explanation of this one. I have looked at it for a long time, and I just cannot see any way to get a contradiction out of this. Having two different photons with different momentum and energy but zero rest mass doesn't seem to me to be creating anything or destroying anything, it's just two photons existing.

Also, there are several indirect proofs that the photon's mass must be zero. For one, consider the ratio of kinetic energy to momentum. Nonrelativistically, E=p^2/(2m), so that E depends QUADRATICALLY, not linearly, on momentum. Relativistically, E^2 = (mc^2) + p^2*c^2. This is again a nonlinear equation. Therefore, energy is NOT proportional to momentum, and the mismatch of proportion allows you to infer the mass. Suppose you consider several light beams, in a range of frequencies. The photoelectric effect lets you determine the energy of the individual photons in each beam, and it is observed to be EXACTLY proportional to the frequency. On the other hand, if you use the same beams, at equal intensities, to push on black targets inside vacuum chambers, you can measure the rates of momentum transfer, and they are EXACTLY the same at equal intensities for all frequencies.

Since rate of momentum transfer = momentum per photon * number of photons/sec in the beam, and intensity = energy per photon * number of photons/sec in the beam, it follows that E is EXACTLY proportional to p. Putting this into the relativistic energy formula, it follows that the photon mass must be EXACTLY proportional to p as well, since only this will make the equation turn into a linear one.

On the other hand, we know that photons can be Doppler shifted to a new frequency just by using a moving observer. This cannot make any change in the inherent properties of the photon, because you haven't actually done anything to the photon, you've just moved the observer. Even if photons have different masses, the rest mass of one individual photon could not change after the photon was emitted, because rest mass is a relativistically invariant property. Therefore, after Doppler shifting, the rest mass of the photon must be the same as it was when the photon was first emitted.

Now you have a direct contradiction: If a photon were emitted with mass m and frequency f, then Doppler shifted to a frequency 2f, its rest mass MUST become 2m to be proportional to the momentum, but it must also remain m because it is an inherent property of this particular photon. Therefore, m = 2m, which is a contradiction unless m=0.

BTW, the Law of Conservation of Matter isn't really accepted as such any more since 1905. It has been split into two laws: conservation of mass_energy and conservation of particle number. Since mass and energy are interconvertible in relativity, they cannot possibly be separately conserved. Only the total mc^2 + E is conserved. The law of particle number conservation is more like the old-style conservation of matter idea. Although particles can be created and destroyed, the total number remains constant because they can only be created or destroyed in particle-antiparticle pairs, and antiparticles count as -1 particle.

1) That the photons passing through a Linear Polarizer obey the Gaussian Distribution about the polarizing axis of the linear polarizer?
2) That, it is plausible to assume that a photon in the unpolarized state has the probability to be found at any angle θ where 0 deg.<θ<360 deg ;
3) That, it is plausible to describe a PHOTON in the state vector lx> as a photon that has the probability to be found at any angle θ where 0 deg.<θ<45 deg; 135 deg.<θ<225 deg; 315 deg.<θ<360 deg;
4) That, it is plausible to describe a photon in the state vector ly> as a photon that has the probability to be found at any angle θ where 45deg.<θ<135 deg; 225 deg.<θ<315 deg.

None of these is plausible WITHIN current QM, but since you are setting out to change it, that is an irrelevant consideration. As a starting point for investigation, all four are sufficiently plausible to be used to try to set up an explanation for polarization. Therefore, I will accept them pro tem and see where they lead us.

More later.

--Stuart Anderson
mr_homm
@hexa, Dec. 2:

QUOTE
I hope you will pardon me if I had used words and terms that may not be entirely comfortable to you.

That has not been a problem for me, so do not worry about it. If there is something that I feel I must dispute, then I will simply dispute it, with no hard feelings. That is part of the dialectical process of science (when it works as it is supposed to): theoretical point/counterpoint with periodic input of experimental data from investigations inspired by the theory.

@hexa, Dec. 3:
QUOTE (->
 QUOTE I hope you will pardon me if I had used words and terms that may not be entirely comfortable to you.

That has not been a problem for me, so do not worry about it. If there is something that I feel I must dispute, then I will simply dispute it, with no hard feelings. That is part of the dialectical process of science (when it works as it is supposed to): theoretical point/counterpoint with periodic input of experimental data from investigations inspired by the theory.

@hexa, Dec. 3:
I thoroughly enjoy your analysis that you put forth in the thread on Superposition and Electromagnetism. I hope to expand on the discussion a little later.

I'm game for such a discussion, and am looking forward to it.

QUOTE
Yes, I fully agree that as astute as the logician, one should simply sit on the fence. It is the safest choice. Unfortunately, life is about making choices. Science would not have progressed if nobody makes any decision to turn right or left. Life are full of cross-roads and T-junctions. Life would be a COMPLETE STANDSTILL if nobody makes any decision when they come to a cross-road or T-junction.

Well, this depends entirely on one's attitude. I agree that fence-sitting leads to inaction in the world of human affairs, but I think that science proceeds best by a kind of dynamic fence-sitting. If the logician just shrugs and says, "well, we can't see the other side" then nothing will happen. But what if the logician says, "the answer must be determined by experiment; therefore we must investigate both possibilities and see which is true"? In that case, the fact that the logician has refused to accept the obvious leads to MORE investigation, not less.

So my point of view on this is that if the logician just says "the sheep is white" then no investigation will ensue, and the assumption will pass unquestioned, but if he refuses to make that assumption, then instead of fence-sitting, he is pointing out to everyone that there IS an assumption here, and that we do not actually know the answer yet. This can only lead to further investigation, which is much better for the progress of science. Since scientific investigation is conducted by more than one person, science can turn BOTH right and left at the crossroad, instead of neither, once a crossroad is noticed. Unquestioned assumptions are ALWAYS the enemy of progress, because if the crossroad is not noticed, then only one branch (the one assumed to be true) will be investigated, while the truth may lie on the other branch.

The history of the wave/particle debate on the nature of light could support either of our points of view. I see this history as showing that an awareness of the fact that we do not absolutely know the nature of light drove forward the investigations on both sides of the debate. If everyone just assumed that it was a particle (or a wave) without checking, there would have been no debate, no investigation, and no progress. One of the nice things about the way scientific investigation works is that it harnesses natural human contentiousness in the service of experiment.

QUOTE (->
 QUOTE Yes, I fully agree that as astute as the logician, one should simply sit on the fence. It is the safest choice. Unfortunately, life is about making choices. Science would not have progressed if nobody makes any decision to turn right or left. Life are full of cross-roads and T-junctions. Life would be a COMPLETE STANDSTILL if nobody makes any decision when they come to a cross-road or T-junction.

Well, this depends entirely on one's attitude. I agree that fence-sitting leads to inaction in the world of human affairs, but I think that science proceeds best by a kind of dynamic fence-sitting. If the logician just shrugs and says, "well, we can't see the other side" then nothing will happen. But what if the logician says, "the answer must be determined by experiment; therefore we must investigate both possibilities and see which is true"? In that case, the fact that the logician has refused to accept the obvious leads to MORE investigation, not less.

So my point of view on this is that if the logician just says "the sheep is white" then no investigation will ensue, and the assumption will pass unquestioned, but if he refuses to make that assumption, then instead of fence-sitting, he is pointing out to everyone that there IS an assumption here, and that we do not actually know the answer yet. This can only lead to further investigation, which is much better for the progress of science. Since scientific investigation is conducted by more than one person, science can turn BOTH right and left at the crossroad, instead of neither, once a crossroad is noticed. Unquestioned assumptions are ALWAYS the enemy of progress, because if the crossroad is not noticed, then only one branch (the one assumed to be true) will be investigated, while the truth may lie on the other branch.

The history of the wave/particle debate on the nature of light could support either of our points of view. I see this history as showing that an awareness of the fact that we do not absolutely know the nature of light drove forward the investigations on both sides of the debate. If everyone just assumed that it was a particle (or a wave) without checking, there would have been no debate, no investigation, and no progress. One of the nice things about the way scientific investigation works is that it harnesses natural human contentiousness in the service of experiment.

his is where QM came into the picture by providing the mathematics to allow prediction to be made based on the ASSUMPTION that these Quantum entities also has this wave properties

A general philosophical comment about this: in philosophy, there is the so-called "fallacy of reification," which the mistake of assuming that something abstract or conceptual has a real existence and can be treated like a real thing. The discussion about particles and waves (I mean in general, not yours specifically) suffers from this fallacy. Particles and waves are not real things. The words "particle" and "wave" refer to BEHAVIORS which we observe, and therefore they are CATEGORIES, not things. We categorize something as a particle if we observe it to have the properties to which the word "particle" refers, and similarly for a wave.

There is no inherent logical reason why these categories cannot overlap, but in our classical experience they are not observed to do so. This leads very quickly to the mistake of reifying these categories and regarding them as things. Then when experiments show that light simultaneously manifests properties characteristic of the category "wave" and also properties characteristic of the category "particle" people become confused. The only logically correct response to these experimental results is to remind ourselves that the words "wave" and "particle" are just shorthand for sets of observed properties. So saying that it is both a particle and a wave is not an assumption, it is a tautology, because it is really just an abbreviation for saying that it is observed to have the properties that we categorize as wave properties and also the properties that we categorize as particle properties. But this is just exactly the same thing as saying that it DOES show a speckle pattern and it DOES show interference fringes. In other words, the statement that it is both a wave and a particle means nothing more or less than that the experiments show what the experiments show, which IS a tautology and therefore logically true.

To me, this says that the wave/particle duality debate is philosophically barren and physically a dead end, because it plays around with categories rather than trying to get down to the basic properties of the photon which lead to its exhibiting wave and particle properties. So in conclusion, I agree with you that there ought to be a deeper level of understanding than this.

QUOTE
I do look forward to your comment, even if you do not agree to the above propositions.

I have commented on these in my previous post. By the way, I am undertaking a mathematical analysis of the consistency of these assumptions, but we should not hold back the discussion waiting for that to be complete. I'll post it when it is ready, but I wanted to give you advance notice that it is coming soon.

@Peter Robert, Dec. 4:

I am interested in all the same questions as you are. Thanks for stating them so clearly. However, I am not particularly uneasy about any of this, because if it is false, then QM is right and we're on the right track already, and if it is true, then we will have learned something that puts us on the right track.

On the topic of measurement, yes, measurement is a thornier issue than is usually recognized. Of course if several experimental physicists get the same results using DIFFERENT measurement techniques, then we can treat the results as fairly reliable. However, sometimes experiments are replicated using the SAME technique as the original experiment, and here we have a real problem. This is because very high precision experiments are nearly always very INDIRECT, which means that the interpretation of the results strongly depends on the theory behind the experiment's indirect measurement. This in turn means that a large part of the prevailing theory must be accepted in order to interpret the results of the experiment. Otherwise, there is no connection between what is directly observed (spot of light moving, pointer dial pointing, computer readout, the displacements hexa has mentioned, etc.) and the quantity the experiment was actually intended to measure.

Therefore, there is always a remote but logically nonzero possibility that the whole theory is just a self-fulfilling prophecy, i.e. that the theory suggests how to do the measurements and how to interpret them, but in such a way that the experiments must confirm the theory even if the theory is not actually true. When experiments measure the same quantity by DIFFERENT indirect methods, this is not such a problem, because it is very unlikely that different approaches to measurement would yield the same result if the theory is not actually true (at least to a good enough approximation to correctly predict the measured value).

However, this does not keep me up at night worrying, because most of the major predictions have been cross-checked by independent methods of measurement.

@Confused2, Dec. 5:

It seems to me that hexa has chosen the Gaussian distribution precisely because it does not give perfect cancellation at 90 degrees. After all, this is what his experiments are showing. I am more worried at this moment about the mathematical arbitrariness of cutting off an inherently infinitely wide bell curve at a specific location. As for the cancellation at 90 degrees, this is a matter for further experiment to decide. If non-cancellation survives all experimental tests, then the bell curve may also survive as a hypothesis. However, if refinements of the experiment lead to ever decreasing light intensities at 90 degrees, this would argue that the actual answer is zero, and that we are approaching that via better and better experiments. In that case, the Gaussian is eliminated as a hypothesis.

Once again, I am out of time for now. I will take up hexa's experimental results in my next post.

--Stuart Anderson
hexa
Hi Mr Homm,

I think we are making good progress.
We now seem to be able to agree in more areas than we first begin.
I like your tautology description of the particle wave duality explanation. And I also concur with you that there ought to be a deeper level of understanding.
It was important to have some pro tem agreement, even though we see the same thing using entirely different lenses. As you said, from the lens of QM, those 4 assertions of photons having an orientation θ and Gaussian distribution are incongruous. At the least, I would know whether I had correctly described my proposition using ordinary logic and common sense.
Let me take up the point you made on “fallacy of reification”.
I will like to draw you to Feynman Lectures on Physics Vol.II, Chapter 1. He drew the lines of Electric and Magnetic Field based on the Superposition Principle and conclude that the electric field lines of E and magnetic field lines B are:
QUOTE

only a crude way of describing a field, and it is very difficult to give the correct, quantitative laws directly in terms of field lines. Also, the ideas of the field lines do not contain the deepest principle of electrodynamics, which is the superposition principle.

and he went on to advocate that:
QUOTE (->
 QUOTE only a crude way of describing a field, and it is very difficult to give the correct, quantitative laws directly in terms of field lines. Also, the ideas of the field lines do not contain the deepest principle of electrodynamics, which is the superposition principle.

and he went on to advocate that:

The best way is to use abstract field idea. That it is abstract is unfortunate, but necessary.

and cited McCullough case as a misfortune to Science when the main stream scientific community then rejected his proposition in 1843.
He concluded the chapter by giving Maxwell the accolade for his works in stating the laws of electrodynamics.

Generally, I can agree with Feynman on the need to simplify our REPRESENTATION of Nature using simple and elegant vectors, without which we can NEVER understand Nature. This is because there are far far too much information for us to process in any meaningful way when dealing with all the big numbers. For example, the entire mass of the sun can be represented mathematically by a SINGLE point. Without such simplification and representation Newton will never be able to describe the Laws of Motion with such elegance and beauty.
Similarly, the trillions of atoms with one extra electron contain in a single marble can also be represented by a single point as 1e.
This has serve us well—very well indeed for us to make devices without having to worry about what is happening to the other trillions of charged particles contained in the marble when what matters for our device to work is just the Single electron.

However, I would like to ask some very naïve questions:
QUOTE

1. What if the Lines drawn to represent E and B using the Superposition Principle is too detached from the Physical entity it seek to represent?
2. The E field is drawn as originating from the charge. Is B field a correct representation of the magnetic field when we could not draw any physical lines that link directly to the charge? Is circulation a correct physical representation of the magnetic field?
3. Could we be throwing away far too much information when we simplify the problem using vector algebra--such that we end up with insufficient information for us to understand Nature more fundamentally?
4. Is there something more fundamental than electrons, quarks and photons that will allow us to understand more fundamentally why there is Planck constant, h and the speed of light c as our universal constant?

I will address each of these questions separately a little later. It must be answered if we hope to comprehend Nature more fundamentally.

Let me attempt to provide you with some answer to some of your questions. Unfortunately, to provide you all the answers in this post ( http://forum.physorg.com/index.php?showtop...ndpost&p=154144 ) will require me to cover everything from QM to Einstein’s Relativity. That will be too ambitious. We could make greater progress along the way if we could agree to some obvious proposition that I have made so far including the observation on Circular Polarization of Light. It is important that we have some pro tem agreement even if we are looking through different lenses. Ordinary logic and common sense is not so abstract that we have difficulty in determining what is reasonable and what is not.

QUOTE (->
 QUOTE 1. What if the Lines drawn to represent E and B using the Superposition Principle is too detached from the Physical entity it seek to represent?2. The E field is drawn as originating from the charge. Is B field a correct representation of the magnetic field when we could not draw any physical lines that link directly to the charge? Is circulation a correct physical representation of the magnetic field?3. Could we be throwing away far too much information when we simplify the problem using vector algebra--such that we end up with insufficient information for us to understand Nature more fundamentally?4. Is there something more fundamental than electrons, quarks and photons that will allow us to understand more fundamentally why there is Planck constant, h and the speed of light c as our universal constant?

I will address each of these questions separately a little later. It must be answered if we hope to comprehend Nature more fundamentally.

Let me attempt to provide you with some answer to some of your questions. Unfortunately, to provide you all the answers in this post ( http://forum.physorg.com/index.php?showtop...ndpost&p=154144 ) will require me to cover everything from QM to Einstein’s Relativity. That will be too ambitious. We could make greater progress along the way if we could agree to some obvious proposition that I have made so far including the observation on Circular Polarization of Light. It is important that we have some pro tem agreement even if we are looking through different lenses. Ordinary logic and common sense is not so abstract that we have difficulty in determining what is reasonable and what is not.

Quote Mr Homm:
Supposing that, as you say, a photon has a size and shape, then why is it that size and shape? [1]These qualities seem to necessarily point to a deeper structure which explains the size and shape. [2]By this logic, a photon cannot be a fundamental particle. [3] If there ARE fundamental particles at all, then the concepts of size and shape would seem to me NOT to apply to them. [4] How can a thing have a size, unless you can at least conceptually consider portions of it? [5]Similarly, what is shape other than the relation of the positions of some sub-parts to others? [6]These are philosophical critiques of the concepts of size and shape, of course, but I find them convincing. [7]A truly fundamental particle must have neither size nor shape, because these qualities automatically imply that the particle has parts. [8]So either there are no fundamental particles at all, just parts within parts forever, [9]or there are fundamental particles, but they have no size or shape.

[1]Yes, I agree with your inference.
[2] Yes. Photons in general cannot be the most fundamental particle. How do we reconcile that the entire range of electromagnetic radiation span from the weakest radiowave {with the smallest amount of energy contain in each packet given by E(radiowave)=hf(1)} to the most powerful gamma radiation {with energy contain in each packet given by E(gamma)= hf(10E24)}? Do you see the advantage in describing a photon as a deck of cards? If we are going to describe a photon as a deck of cards, would it not make any sense that the photon containing just ONE card will then be the most fundamental particle in Nature?
[3] Based on the explanation in [2] do you still maintain this supposition?
[4] Was it not too long ago when the philosopher critique had pronounced that it is inconceivable to perceived the size or shape of an atom?
[5] Yes. I see some difficulty to name the exact shape. But that should not deter us from making an attempt to guess the shape. It is necessary for us to construct a Model before throwing in the numbers to describe this animal. Without which we will be buried by the “fallacy of mathematics” rather than the “fallacy of reification”.
[6] No major objection to this statement.
[7] Philosophically we could perpetually choose to entrap ourselves in this philosophical maze without ever finding an answer. Alternatively, we could accept the limit of what we can know at a particular point in time and develop our knowledge that will advance our overall well being. Irrespective of how we view Nature, whether in smaller parts or not, I think the Law of Conservation of Matter cannot be violated. Chemistry would not have been possible without this Law. I will try to answer this question in greater details below.
[8] You could be right in making this assumption?
[9] Why do we need to deny that the fundamental particle of matter has a shape and size if we think it exist? To deny that there is such a physical reality, is to deny ourselves the most important tool available in the development of epistemology.
Why do we deny the benefits of sight to describe how an elephant looks and instead rely only on our senses of touch (similar to relying on some abstract numbers)?
Historically, did we benefit from the time when Democritus first made the conjecture of the ATOM some 2500 years ago even though it may not be entirely correct based on what we now know?
If so, do we need to worry what is beyond Planck Length when we have difficulty based on QM to even conjure an image on how all these elementary particles look within this range? In fact, we are told that it is NAIVE and WRONG to even expect that there is such a Physical Reality.

I think it is fundamentally wrong to deny the Law of Conservation of Matter. To do so, we subject ourselves to the Ridiculous possibility that we can create something from nothing and cause something to vanish into nothingness. All experiments appear to support this Immutable Law of Nature including those you said does not.
This is because based on the paradigm of QM and Relativity, we are told how to interprete our observation which you have elegantly discuss this in your last post. This is what that has led us to conclude that the Law of Conservation of Matter is violated. But did we pause to ask ourselves whether such interpretation is correct to begin with???

Consider the ALTERNATIVE proposition that when we annihilate an electron with a positron to obtain energy in the form of photons. All that has happen is that the same fundamental building blocks that go into the construction of the electron and positron is now traveling at the speed c. The Law of Conservation of Matter is observed.
Conversely, a gamma photon can also materialize into an electron and positron pair. We can create only so many electron and positron pairs and no more from a single gamma photon. It must observe the Law of Conservation of Matter.

I will pause here before I pick a quarrel with Einstein.
I would much prefer if we can clear up the topic on Circular Polarization followed by the Double slits experiment before opening up the topic on Relativity.
Anyway, if it is absolutely necessary to discuss some aspect of Relativity before we can fully comprehend what we are discussing on the earlier topic, please do not feel inhibited by this desire of mine which I thought would be clearer to everyone following this thread.

Cheers.
Al Khwarizmi - step-by-step
QUOTE
Ridiculous possibility that we can create something from nothing and cause something to vanish into nothingness

But is this not the definition of a virtual particle pair?
hexa
Hi Al Khwarizmi - step-by-step,

Are photons virtual particles by your definition?
Are electrons deem to be virtual particles as well?
Or Are you referring to the electric and magnetic field as virtual photons?
Please elaborate what you mean by virtual particles.

Cheers.

Al Khwarizmi - step-by-step
Hi, Hexa

My not-to-be-taken-too-seriously definitions are these:
1) photons are real dynamic entities with measurable properties;
virtual photons and their counterparticles (photons) are self-annihilating surreal versions of the same dynamic entity.
2) electrons are real dynamic entities with measurable properties;
virtual electrons and their counterparticles (positrons) are self-annihilating surreal versions of the same dynamic entity.

3) Yes - I am referring to the electro~magnetic fields in terms that are virtually particulate, thus (i) Hawking radiation, and (ii)
QUOTE
One has two parallel metal plates, a short distance apart. The plates act like mirrors for the virtual particles and anti particles. This means that the region between the plates, is a bit like an organ pipe, and will only admit light waves of certain resonant frequencies. The result is that there are slightly fewer vacuum fluctuations, or virtual particles, between the plates, than outside them, where vacuum fluctuations can have any wavelength. The reduction in the number of virtual particles between the plates means that they don't hit the plates so often, and thus don't exert as much pressure on the plates, as the virtual particles outside. There is thus a slight force pushing the plates together. This force has been measured experimentally.
-ref
<-- uncertainty principled
mr_homm

Apologies for the delay. I had intended to catch up with the current discussion this weekend, but I have had no internet connection at my house. I will now try to get caught up, so that discussion can take place in real time.

@hexa, Dec. 6:

Your description of your experimental set up is clear, and your data are nice and clean and easy to interpret. The only question I have about it is the light source. White or laser, and if laser, what wavelength? I'll proceed on to your inferences:

QUOTE

1. Column 3 shows the result that when both the LP1 and LP2 are aligned at 0 degree, the lux meter will register the highest intensity. Conversely, when LP2(θ) =90 degree, the intensity will be minimum at 3 lux. compared to 178 lux. when LP2(θ) = 0 degree.
Result:
1.1 Malus Law/Classical Optics = Observed;
1.2 QM = Observed;
1.3 My proposition = Observed.

I agree.

QUOTE (->
 QUOTE 1. Column 3 shows the result that when both the LP1 and LP2 are aligned at 0 degree, the lux meter will register the highest intensity. Conversely, when LP2(θ) =90 degree, the intensity will be minimum at 3 lux. compared to 178 lux. when LP2(θ) = 0 degree.Result:1.1 Malus Law/Classical Optics = Observed;1.2 QM = Observed;1.3 My proposition = Observed.

I agree.

2. Column 4 shows that there is a minimum intensity of 81 lux. at LP3(θ) = 45 degree and a maximum of 104 lux. at LP3(θ) = 135 degree.
This observation is consistent with the hypothesis that I am making with regards to linear polarizer and circular polarizer.
Unfortunately, this is where QM or classical optics will not be able to make the same prediction consistent with this observation.
Result:
2.1 Malus Law/Classical Optics = Not Observed;
2.2 QM = Not Observed;
2.3 My proposition = Observed

At first I thought that this might be explained by the QWP having a delay that is not exactly 1/4 wave. However, mathematical analysis of this case shows that the max and min intensities should then be at 0 and 90 degrees, rather than 45 and 135 degrees. So that explanation is ruled out for column 4. However, I note in your data that the max and min do not appear to be at exactly 45 and 135 degrees, but somewhere between 45 and 56.25, and between 135 and 146.25. This suggests that the QWP component of your photographic circular polarizer is misaligned at an angle of about 50 degrees from the axis of the linear polarizer component.

On this assumption, the max and min values represent the E field components along the fast and slow axes of the QWP. If the angle of the QWP is around 50 degrees, these components will be proportional to cos(50) and cos(140), so the ratio of amplitudes will be cos(140)/cos(50) = sin(50)cos(50) = tan(50), so the ratio of the intensities should be (tan(50)^2 = 1.42. Since the actual minimum is going to fall between your data points, it should be a little less than 81, say about 80. Likewise, your actual max must be about 105 or so. 105/80 = 1.3125. So a 5 degree misalignment is more than enough to explain your data. In fact, if I start from the actual ratio 1.3125 and work backwards, arctan(sqrt(1.3125)) = 48.88 degrees, a 3.88 degree misalignment. Since you're also seeing the max and min values a few degrees above their expected locations, this explanation seems very consistent to me. Besides, the makers of the photographic circular polarizers do not care how accurately the QWP is positioned because as long as it is close to 45 degrees, the photographers will be satisfied.

A more detailed calculation (details available upon request, but they're not important for the main point) shows that if the QWP is misaligned to an angle pi/4 + d then the expected intensity of the transmitted beam is I(θ) = I_0(1-2dsin(2θ)), where I_0 is the intensity at θ=0. This curve shows a minimum at θ = 45 degrees and a maximum at 135 degrees. (This is only a first order approximation to the intensity curve, so the actual max and min are not guaranteed to be exactly at 135 and 45 degrees.) Looking at the amplitude of the deviation from rotation invariance gives (1-2dsin(90))/(1-2dsin(270)) = 80/105, so d = 25/370 = .0675675 radians = 3.87 degrees, which agrees extremely well with the cruder estimate above. I personally find this evidence and its consistency strong enough to make me question the orientation of the QWP in your photographic circular polarizer.

QUOTE

3. Column 5 shows that there is no significant variation in intensity when the LP3(θ) of the second circular polarizer is rotated relative to the linear polarizer of the first circular polarizer.
Result:
3.1 Malus Law/Classical Optics = Not Observed;
3.2 QM = Not Observed;
3.3 My proposition = Observed

This is exactly what QM and Classical Optics predict, so their laws ARE observed in this case.

QUOTE (->
 QUOTE 3. Column 5 shows that there is no significant variation in intensity when the LP3(θ) of the second circular polarizer is rotated relative to the linear polarizer of the first circular polarizer.Result:3.1 Malus Law/Classical Optics = Not Observed;3.2 QM = Not Observed;3.3 My proposition = Observed

This is exactly what QM and Classical Optics predict, so their laws ARE observed in this case.

4. Column 6 shows that there is a minimum intensity of 75 lux. at LP3(θ) = 45 degree and a maximum of 95 lux. at LP3(θ) = 135 degree.
This observation is consistent with the hypothesis that I am making with regards to linear polarizer and circular polarizer.
Unfortunately, this is where QM or classical optics again will not be able to make the same prediction consistent with this observation.
Result:
4.1 Malus Law/Classical Optics = Not Observed;
4.2 QM = Not Observed;
4.3 My proposition = Observed

Since the QWP component of the photographic circular polarizer {LP(3) + QWP(3)} passes light of all polarizations, the expected effect on column 6 as compared to column 4 is that there should be an overall intensity reduction due to the extra (angle independent) absorption of the QWP. This means that the expected output of column 6 is smaller than that of column 4 by a constant factor. I have checked the ratios, and they appear to be around 1.09:1 and are pretty nearly constant. This means that the variations of intensity with θ in column 6 can be traced back to those in column 4, and the same explanation will work here as well, namely, that the QWP is turned about 3.88 degrees away from its proper 45 degree position.

QUOTE

Questions:
1. Are these result due to the artefacts of photographic circular polarizers that render the entire experiment invalid?
2. If acceptable, is there an explanation of the observation based on QM or classical optics?

1: Although I would not go so far as to say that the experiments are invalid, it does seem that there are relatively straightforward explanations for your observations within QM or Classical EM (given above in my responses to (5) and (7). This means that your results are not wrong, but are insufficient to distinguish between your hypothesis's predictions and those of QM/Classical EM. Unfortunately, this leaves your hypothesis (in the words of movie producer Samuel Goldwyn) "a definite maybe."

As to your response to Peter Robert, let's discuss this later, since it seems to be out of place at the current level of presentation of your hypothesis. I cannot resist one question, though:
QUOTE (->
 QUOTE Questions:1. Are these result due to the artefacts of photographic circular polarizers that render the entire experiment invalid?2. If acceptable, is there an explanation of the observation based on QM or classical optics?

1: Although I would not go so far as to say that the experiments are invalid, it does seem that there are relatively straightforward explanations for your observations within QM or Classical EM (given above in my responses to (5) and (7). This means that your results are not wrong, but are insufficient to distinguish between your hypothesis's predictions and those of QM/Classical EM. Unfortunately, this leaves your hypothesis (in the words of movie producer Samuel Goldwyn) "a definite maybe."

As to your response to Peter Robert, let's discuss this later, since it seems to be out of place at the current level of presentation of your hypothesis. I cannot resist one question, though:
Hence, one photon can be distinguished from another photon (with different energy and momentum) by the number of cards that goes into the construction of a packet of photon.

If the number of cards is finite, there must be a smallest possible photon energy, represented by a single card. Now suppose you are stationary relative to a light source, and you are observing single-card photons from it. Now you start traveling away from the source, so that the light is Doppler shifted to a lower momentum (even if you treat it as a particle, not a wave, the momentum should appear smaller because of the relative motion of your reference frame). The question is, what would you see?

@hexa, Dec. 7:

QUOTE
Look at Column 4 of my latest post. The minimum and maximum intensity are located at 45 deg. and –45 deg.(135 deg.) respectively relative to the linear polarizer (at 0 deg.) that make up the Circular polarizer.
In the absence of a QWP, the intensity of light will be distributed in accordance with the readings as shown in Column 3.
Note the following comparison:
At 0 deg, : Column 3 = 178 lux. ; Column 4 = 96 lux.
45 deg, : Column 3 = 88 lux. ; Column 4 = 81 lux. (Minimum)
90 deg, : Column 3 = 3 lux. ; Column 4 = 89 lux.
135 deg, : Column 3 = 89 lux. ; Column 4 =104 lux. (Maximum)

This is where I infer that a QWP has two molecular axes based on the analysis of intensity passing through the Linear polarizer that act as an analyzer.

OK, I can agree with this. When I said earlier that a QWP had only one axis, I was speaking of the 3 dimensional crystal. The optical properties of the crystal as a whole are consistent with the crystal having a single axis, such that light polarized along this axis sees an extraordinary refractive index, but light polarized perpendicular to this axis sees the ordinary refractive index. For example, if the optic axis is along x, then light with E field along z will see the extraordinary refractive index, and light with E field anywhere in the yz plane will see the ordinary one. Since there are many axis (anything in the yz plane) that will give the ordinary refractive index and only one that gives the extraordinary refractive index, it makes sense to say that optical calcite (considered 3 dimensionally) has only 1 special axis.

On the other hand, a QWP is a calcite crystal cut so that the extraordinary axis is parallel to the surface. If the surface is the xy plane and light propagates along z for instance, then the only part of the yz plane that the E field can align with is the y axis itself, since E is transverse to the propagation. This means that from a 2 dimensional point of view, there is only one direction where the refractive index is the ordinary one, and one direction where it is the extraordinary one, so neither direction is more special than the other. This makes the situation much more symmetrical, and so it is now possible to speak of an ordinary axis and an extraordinary axis, or alternatively, a "fast axis" and a "slow axis." So from this point of view it appears that there are are two axes in a QWP, even though optical calcite only has one optic axis.

QUOTE (->
 QUOTE Look at Column 4 of my latest post. The minimum and maximum intensity are located at 45 deg. and –45 deg.(135 deg.) respectively relative to the linear polarizer (at 0 deg.) that make up the Circular polarizer.In the absence of a QWP, the intensity of light will be distributed in accordance with the readings as shown in Column 3.Note the following comparison:At 0 deg, : Column 3 = 178 lux. ; Column 4 = 96 lux.45 deg, : Column 3 = 88 lux. ; Column 4 = 81 lux. (Minimum)90 deg, : Column 3 = 3 lux. ; Column 4 = 89 lux.135 deg, : Column 3 = 89 lux. ; Column 4 =104 lux. (Maximum)This is where I infer that a QWP has two molecular axes based on the analysis of intensity passing through the Linear polarizer that act as an analyzer.

OK, I can agree with this. When I said earlier that a QWP had only one axis, I was speaking of the 3 dimensional crystal. The optical properties of the crystal as a whole are consistent with the crystal having a single axis, such that light polarized along this axis sees an extraordinary refractive index, but light polarized perpendicular to this axis sees the ordinary refractive index. For example, if the optic axis is along x, then light with E field along z will see the extraordinary refractive index, and light with E field anywhere in the yz plane will see the ordinary one. Since there are many axis (anything in the yz plane) that will give the ordinary refractive index and only one that gives the extraordinary refractive index, it makes sense to say that optical calcite (considered 3 dimensionally) has only 1 special axis.

On the other hand, a QWP is a calcite crystal cut so that the extraordinary axis is parallel to the surface. If the surface is the xy plane and light propagates along z for instance, then the only part of the yz plane that the E field can align with is the y axis itself, since E is transverse to the propagation. This means that from a 2 dimensional point of view, there is only one direction where the refractive index is the ordinary one, and one direction where it is the extraordinary one, so neither direction is more special than the other. This makes the situation much more symmetrical, and so it is now possible to speak of an ordinary axis and an extraordinary axis, or alternatively, a "fast axis" and a "slow axis." So from this point of view it appears that there are are two axes in a QWP, even though optical calcite only has one optic axis.

Let me address your concern on the type of filters used, and how this may affect the readings that we can make using a photographic grade rather than the scientific grade filters. I am under no illusion that there will be some deviation between these two grades of equipments.
I am less concern with the absolute intensity that I may be able to observe but more on the general behavior of how a Linear or Circular Polarizer would behave. You may have noticed that without any filter, the lux. meter register a reading of 850 lux. The presence of a linear or circular polarizer reduces the intensity to less than half at 296 lux. and 265 lux. respectively.
Further, I am also not concern because the readings in Column 4 is less than half the intensity of the light that passes through a Single Circular Polarizer.

I am not concerned especially about the light intensity reduction either. This is to be expected with uncoated optics, since there will be significant reflection, and also, the LPs will most likely absorb some of the polarized component that aligns with their axes, simply because no material is perfectly transparent. The important features of your experiments are the RELATIVE light intensities as functions of θ, which are not affected by the overall intensity reduction of your filters.

QUOTE
Similarly, I have also taken the precaution to distinguish the result based on a white light source or a monochromatic source. The variation using a monochromatic source will be more pronounced compared to a source using white light.
You are correct to state that different color light APPEARS to pass through the polarizers at different speed and hence the relative intensity will vary differently at one angle for one monochromatic light compared to another angle. But this does not negate the observation that the intensity will fluctuate around the two axes found in the QWP.

QUOTE (->
 QUOTE Similarly, I have also taken the precaution to distinguish the result based on a white light source or a monochromatic source. The variation using a monochromatic source will be more pronounced compared to a source using white light.You are correct to state that different color light APPEARS to pass through the polarizers at different speed and hence the relative intensity will vary differently at one angle for one monochromatic light compared to another angle. But this does not negate the observation that the intensity will fluctuate around the two axes found in the QWP.

For your information, the readings of the experiments that I have last posted is based on White Light.

Thanks, that is important information.

QUOTE
With these results, I will like to know how you would infer from these observations.

Is it reasonable to make these ASSUMPTIONS that I have stated in my earlier post?
I hope you are not faulting it because the experiments are not conducted using the premium grade apparatus.

I have commented on the observations themselves earlier in this post. The ASSUMPTIONS are prima facia reasonable as a starting point for analysis, as I have mentioned. Because of the severe time lag in my replies, I think you didn't receive that statement from me until after you posted this.

I am not faulting your hypothesis because of the quality of your equipment. It is possible to get very good experimental results with only moderately precise equipment, but you must work very hard to eliminate every conceivable source of error and to check the calibration of your equipment, in order to get conclusive results. From the results you have posted thus far, I see nothing that strongly contradicts QM or Classical EM. Both of these theories, together with yours, CAN agree with these results. The agreement of QM and Classical EM depend upon explanations in terms of artifacts generated by your equipment, so to distinguish between them and your theory, you next need to determine whether there are or are not sufficient equipment artifacts to explain the discrepancy from standard theory. It's not an issue of bad equipment invalidating your results, so much as a case of the quality of your equipment necessitating a LOT more work for you to validate your results.

I must stop here for now. I'll take up your next post very soon.

--Stuart Anderson
hexa
Hi Al Khwarizmi - step-by-step,

QUOTE

My not-to-be-taken-too-seriously definitions are these:
1) photons are real dynamic entities with measurable properties;
virtual photons and their counterparticles (photons) are self-annihilating surreal versions of the same dynamic entity.
2) electrons are real dynamic entities with measurable properties;
virtual electrons and their counterparticles (positrons) are self-annihilating surreal versions of the same dynamic entity.
3) Yes - I am referring to the electro~magnetic fields in terms that are virtually particulate, thus (i) Hawking radiation, and (ii)
QUOTE (->
 QUOTE My not-to-be-taken-too-seriously definitions are these:1) photons are real dynamic entities with measurable properties;virtual photons and their counterparticles (photons) are self-annihilating surreal versions of the same dynamic entity. 2) electrons are real dynamic entities with measurable properties; virtual electrons and their counterparticles (positrons) are self-annihilating surreal versions of the same dynamic entity. 3) Yes - I am referring to the electro~magnetic fields in terms that are virtually particulate, thus (i) Hawking radiation, and (ii) One has two parallel metal plates, a short distance apart. The plates act like mirrors for the virtual particles and anti particles. This means that the region between the plates, is a bit like an organ pipe, and will only admit light waves of certain resonant frequencies. The result is that there are slightly fewer vacuum fluctuations, or virtual particles, between the plates, than outside them, where vacuum fluctuations can have any wavelength. The reduction in the number of virtual particles between the plates means that they don't hit the plates so often, and thus don't exert as much pressure on the plates, as the virtual particles outside. There is thus a slight force pushing the plates together. This force has been measured experimentally.-ref <-- uncertainty principled

Thanks for the reference.
I have taken a look at the site and could not resist noticing the usage of the term "virtual photon".
I thought the conventional definition of virtual photon refers to the electric and and magnetic FIELDS. Some prefer to call FIELDS as the Charge Carrier since a Positive charge will emit a positive Coulomb Field that we can distinguish from the negative Coulomb Field that a Negative charge emits.

Let me take a passage from the site provided by you:

QUOTE

[1]In quantum physics the empty space isn't empty at all. [2]In it there are always particles flashing into existence and disappear again. [3]They always come in pairs; [4]one particle and one anti-particle, like an electron and a positron, or a photon (a particle of light) and another photon with opposite spin and impulse. [5]These particles are called "virtual particles". [6]They only exist for a very short time

[1] Generally I can agree to this only because empty space is always filled with FIELDS. But FIELDS as I have stated earlier is a physical entity that APPEARS not to obey the Law of Conservation. The reason I use the word APPEARS is because FUNDAMENTALLY Everything including the positive and negative fields that are emitted by all the charged particles in the Universe must also be Conserved. I don't think there is any free lunch. It is created and emitted from the charge indefinitely. Since, it carries no MATTERS, a substantial amount can be concentrated on ONE point in space. This is unlike a PHOTON or an electron or a positron. They are MATTERS. It is VERY IMPORTANT that we distinguish one from the other. I will discuss more of this later.
[2] No. That is NOT POSSIBLE when you are dealing with FIELD alone. What is observed could be some NEUTRAL REAL particles that are not detected by our Standard APPARATUS. They are subsequently detected as a positive and negative PAIRS if they are subsequently separated through collision with other particles or decay over their natural life cycle as in radioactive decay. It dosn't flash into existence. It is not detected earlier because of the limitation of our APPARATUS.
[3] See [2]
[4] See [2]
[5] NO. They are NOT VIRTUAL PARTICLES. They are not measured by our Standard APPARATUS. A more accurate term is NEUTRAL COMPOSITE PARTICLES.
[6] They can be constituted from gamma PHOTON and separated as positron and electron pair. Thereafter they can have their separate existence indefinitely. I think you are referring to the subsequent annihilation after the positron and electron pair has been constituted. Hence, I don't think this Statement is always true.

For us to understand the problem surrounding the Uncertainty Principle, it is necessary for us to understand the Double-slits Experiment (using electrons and photons) Inside out.
Hence, I would appreciate that we differ discussing this topic until a little later.

Cheers.