Why is it that the amount of energy of mass has anything to do with the cosmic "speed limit?" Why did God choose that number (c squared
it is not certain if it is actually c and not some other special case whose one predominant approximation is with c. Einstein chose it and it was Rudolf Hertz and Maxwell who first realzied the significance of c constant; God is either too busy to care, or to nonexistant to effect any change.
Blame God for our ignorance?
That's a prize.
All I have to say is why is the speed of light involved with apparently disparate things like the amount of energy contained in mass? Why should the speed limit squared be the energy? What would make God choose that?
8th June 2014 - 10:04 PM
You asked where the c^2 came from. Here is the best answer I know:
World's Quickest Derivation of E = mc2
Adapted from a derivation posted on the internet by John D. Norton
Department of History and Philosophy of Science, University of Pittsburgh
This derivation assumes we are adding force, momentum, energy to a mass traveling so close to the speed of light, the difference is negligible.
Consider a body of mass m moving at a velocity very close to c. A constant force F acts on the body in the same direction as its motion for a duration set at unit time interval delta T (=1), and as a result, the force increases both the energy and momentum of the body. The force cannot increase its speed because it is already c, so all of the increase of momentum = mass x velocity of the body manifests here mathematically as an increase in mass. This thought experiment dispenses with any references to center of mass for Isaac Newton's benefit.
Note the choice of unit time in this derivation (as opposed to unit c, popular among classical physicists including Einstein himself).
We want to show that in unit time interval delta T, the energy E gained due to the action of the Force applied is equal to mc2, where m is the mass gained by the relativistic projectile, and c is the speed of light. For this example, E = delta E, and m = delta m.
We have two relations involving Energy, Force, and Momentum over the unit time interval delta T (=1):
The first relation is about the change in energy in unit time interval delta T, (or 'work' in classical physics):
delta E = E = Force x (distance through which force acts) = Force x (c x delta T), or
E = Force x c (1-1)
The second relation is about the change in momentum P in unit time interval delta T (or 'impulse' in classical physics):
delta P = (delta m) x c = m x c = (Force) x (delta T), or
m x c = Force (1-2)
delta E = E = Force x c = (m x c) x c
In other words (QED):
E = mc2 (0-0)
We now see that c2 = c x c derives from relating energy to distance and momentum to time in the same expression.