# How to relate photon's higher frequency to time dilation?

The usual explanation for photon's higher frequency in lower altitudes (higher gravity), when the photon is going downward towards a massive body, is that gravitational potential energy is converted into photon's energy which, by its turn, through $E=hf$ implies higher frequency. Because, since $c$ is constant, it doesn't make sense to turn that potential energy into kinetic energy.

That, I understand.

My question is, why is it affirmed that this implies that time runs slower in the lower altitude? I mean why is it such that this higher frequency is equivalent to slower running clocks?

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"Because, since c is constant, it doesn't make sense to turn that potential energy into kinetic energy." Why not? The energy of a photon is as you said: $E=hf$, which does not depend on its speed. If you are thinking of the classical formula $E=\frac{1}{2}mv^2$, clearly it doesn't apply to photons, since photons are massless and their speed is constant. The correct relativistic formula is $E^2 = (mc^2)^2 + (pc)^2$. Setting $m=0$ gives the correct energy for photons. – Michael Brown Jan 8 '13 at 1:51
I corrected attidude to altitude - if that's not what you meant, please roll back. – Nathaniel Jan 8 '13 at 2:09