Rest frame of a photon

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I've read that in relativity the concept of the rest frame of a photon doesn't make sense. Why is that?

A rest frame of some object is a reference frame in which the object's velocity is zero. One of the key axioms of special relativity is that light moves at c in all reference frames. The rest frame of a photon would require the photon to be at rest (velocity=0) and moving at c (velocity=299792458 m/s). That of course is contradictory. In other words, the concept doesn't make sense.

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One thing to add to this is a brief comment that while it is not possible to have a reference frame (tetrad) where light is at rest, it is possible to have a non-inertial coordinate system where some light rays have constant coordinates. Light cone coordinates are one such example. This is one place where it is important to understand the subtle distinction between reference frames (tetrads) and coordinate systems.
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