Also posted this in the SR and GR forum, but wasn't sure which was more appropriate. Hi, I'm a non-physics student trying to use primarily Einstein's original 1905 essay to write a paper on the philosophical questions that E=mc^2 brings up. However, I've hit a snag which I can't seem to get past. 1. The problem statement, all variables and given/known data Einstein essentially uses what he's proven about the Doppler shift to show that a moving body emits a more intense light flash than does a stationary one. Since the internal energy of the body remains the same, he asserts that the increased energy of light must have come from the kinetic energy of the body-- and since KE=1/2mv^2, and v didn't change, therefore m changed. That is, 1) E(bef)=IE1 E(aft)=IE2 2) E'(bef)=IE1+KE1 E'(aft)=IE2+KE2 Subtracting 1) from 2) yields: E'(bef-aft)-E(bef-aft)=ΔKE My question: how can we be sure that the internal energy of the body does not change when the body moves? I suppose we could say that, "by definition, 'internal energy' means 'that energy which does not change in motion.'" But then we'd be questioning the equation for KE energy above-- we'd be saying that kinetic energy is 1/2mv^2 PLUS some other energy which doesn't necessarily relate to the mass, but increases with increased velocity. We could, I suppose, assert that the equation above is an approximation for very low velocities, but this runs us into trouble. Why? Well, because the Doppler shift only occurs at very high velocities! So while KE=1/mv^2 could be said to be an approximation of kinetic energy for low velocities, so could A'/A=1 be an approximation for the doppler shift of intensity at low velocity. If we want to say that KE only deviates from the classical equation by a negligible amount, we have to say that the light's energy only deviates a negligible amount as well. 2. Relevant equations Attached. 3. The attempt at a solution Attached. Thanks!!