The reason I am asking is because higher energy would cause greater gravitational time dilation. Therefore I would expect, from the perspective of a radio wave, a gamma ray having more energy would appear slower than its lower energy radio wave counterpart.
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3There is no photon rest frame, so the question is effectively meaningless. – Kyle Kanos Aug 08 '15 at 14:09
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The fundamental postulate of special relativity is that the speed of light is a universal constant. No matter what you do, no matter what you consider, the speed of light will be $c$. So, what is the speed of the photon as seen from its own perspective? I would not say your question is meaningless. Your hypothesis is simply in contradiction with special relativity and therefore is beyond the scope of accepted physical theories. – vosov Aug 08 '15 at 14:31