Are photon rest frames distinguishable from other inertial frames?

Question

The principle of relativity suggests that all inertial frames are indistinguishable. But if I consider the rest frame of a photon (i.e. an IRF traveling at speed $c$ w.r.t. me), then won't it be distinguishable from my rest frame? And both are IRFs.

For example, time is not well-defined for the photon rest frame. I've heard that time stands still for a photon.

Isn't that a special property of photon rest frames, and therefore something that can be used to fundamentally distinguish it from regular IRFs (like mine)?

Answer 1

A photon doesn't have a rest frame.

Answer 2

Inertial frames in special relativity are limited to sub-light-speed. The concept only applies, and only makes sense, for frames that could in principle be the rest frames of things like rods and clocks.

So light signals simply do not have a rest frame.

The relative speed between a photon and any inertial frame is $c$.

Answer 3

In special relativity we can move between inertial frames with the Lorentz transformations. However, there does not exist an inertial frame that corresponds to a photon. If you look at the Lorentz factor that appears in the Lorentz transformations: $$\lim_{v\rightarrow c}\frac{1}{\sqrt{1-v^2/c^2}}=\frac{1}{\sqrt{1-c^2/c^2}}=\frac{1}{\sqrt{1-1}}=\frac{1}{0}=\infty.$$ This quantity diverges to infinity if we try and move into a frame travelling at the speed of light.