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. 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. My question: how can we assert 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, because the Doppler shift only occurs at very high velocities! That is, 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. My paper, unfortunately, depends on the validity of the original Einstein argument--NOT as a generalized or perfectly logical proof, but as an instance of science's empiricism telling us we're wrong about something that we didn't realize we could be wrong about ("mass" not being a constant which is synonymous with "stuff"). Is the Einstein argument an appropriate approximation which points us to the more general conclusion, which we can grant has not yet been proven? Or is it not even that? Thanks!! EDIT: Does it have something to do with the Taylor theorem expansion?