I can follow the point of this proof intuitively (I never realized that E=mc^2 was derived from special relativity…I thought it was a consequence of general relativity), but I don’t accept it mathematically because of where he replaces KE with 1/2 m*V^2. Certainly there’s a relativistic definition of kinetic energy, otherwise you could accelerate to the speed of light using finite energy, or you would need to introduce the concept of relativistic mass, which he didn’t do. While I haven’t derived it myself, I think there was a shortcut taken here that is misleading.
There’s also the hand-wavy bit where he tells us what the relativistic doppler shift amounts to. I suspect this may have just been backed out from the expected result.
I can follow the point of this proof intuitively (I never realized that E=mc^2 was derived from special relativity…I thought it was a consequence of general relativity), but I don’t accept it mathematically because of where he replaces KE with 1/2 m*V^2. Certainly there’s a relativistic definition of kinetic energy, otherwise you could accelerate to the speed of light using finite energy, or you would need to introduce the concept of relativistic mass, which he didn’t do. While I haven’t derived it myself, I think there was a shortcut taken here that is misleading.
There’s also the hand-wavy bit where he tells us what the relativistic doppler shift amounts to. I suspect this may have just been backed out from the expected result.