So there are multiple reasons given as to why does a photon (or any massless particle) have no rest frame (inertial, of course). I perfectly understand all the possible explanations one can give - it gives nonsensical results in terms of length contraction and time dilation, the standard argument where the energy momentum relation applied in such a frame gives $E^2=m^2+p^2=0$ implying 'no photon', etc.
But I am rather surprised to find very little mention of what I think should be the most obvious answer-The postulate of relativity. In all inertial frames, light (hence photons) must travel at $c$; so it is impossible to have an inertial frame where it is moving at anything other than $c$, let alone 'at rest'. So, no inertial rest frame for photons. This is the way I've understood it so far.
Is there a flaw in my reasoning? i.e. does the existence of a rest frame NOT violate the second postulate, but is wrong because of the other reasons mentioned above? (Hence nobody ever mentions it?) Or is it just too trivial to mention when there are more sophisticated arguments?
Answer
Given that the second postulate is what distinguishes Galiliean relativity from Einsteinian relativity, then the answer is yes.(*) An observer cannot move with the invariant speed because sie would necessarily have to see things in hir frame that moved with that speed be at rest, yet at the same time by the notion of invariance of the speed, in motion - a contradiction, which proves that no such reference frame can exist.
(*) Actually there are those that will claim that you can derive SR from only the first postulate, plus symmetry of space and time. This is, depending on how you interpret it and more accurately how you interpret math, something that may or may not be correct. You can get from the first postulate and the symmetry of space that the necessary transformation group on the space-time that gives the transformations relating reference frames can be one of three possible groups: the Euclidean group, the Poincare group, or the Galilean group. The Poincare group gives SR, it corresponds to taking the second postulate as well. The Galilean group gives Galilean relativity (the space-time background of Newtonian mechanics - note not "Newtonian mechanics" itself, that's a dynamical theory set therein; you can also set quantum mechanics in either foundation, indeed "undergrad QM" is just QM in Galilean background.) and approximates SR at low speeds. The Euclidean group was not the one that who/whatever decided the laws of nature used for our Universe used. (If you want, there are some very nice sci-fi novels by the Australian author Greg Egan called "Orthogonal" which explore the possibilities of a universe built using this case. It's very, very weird I'll tell you, but astonishingly, it manages to work out and could perhaps even support life. I've read it a bit; I'd recommend it a lot if you are into that kind of stuff.) Which one of these is actually the case is not determined from the first postulate alone.
The reason I say that "interpret math" is important is because technically when you derive this in the most "natural" way (again, interpretation interpretation) you get that the frame transformation group has a free parameter $K$, and which of the sets above you can get depends on the domain you allow for that parameter (which must be consistent enough for the logic to work out). If you allow your invariant speed $K$ to take values in the mathematical set $\bar{\mathbb{R}} \cup i\mathbb{R}$, that is, either imaginary or extended real values meaning you admit $\infty$ as an actual number, these three become unified into a single mathematical entity, and in the cases where the speed is not imaginary, _including $K = \infty$, the speed $K$ will have the property you mention. If $K$ is imaginary, every speed (since actually moving at imaginary speed doesn't make sense here because our spatial dimensions are strictly real-valued coordinates - I have no idea what happens if you try to extend them to be complex, but that would not be our universe or anything like it although it's a natural speculative possibility) including infinite speed will have a rest frame. So you could say that the most general solution to the first postulate in its full extent is a Poincare-like group with a free parameter $K$ which can range in this set. But we could apply constraints to $K$ then from considerations of "what we call mathematically meaningful" such that, starting from this formalism, those other groups would be weeded out.
However, you could also argue that the restrictions on choice of domain are essentially equivalent to assuming some form of the second postulate (you could say in a way Newtonian mechanics even assumes its own "second postulate" which is $K = \infty$. A weaker postulate that both the Newtonian and SR one is some statement to the effect that $K$ is extended real only. The fantastic postulate is $K$ is imaginary; I wonder how you'd formulate that in "physical" terms - I haven't read enough of Greg Egan, he probably knows :) Technically the SR postulate is stronger than "$K$ is real", it's actually $K = c$ where $c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}$ is taken from the natural speed in Maxwell's equations.). Thus I am a bit leery of saying "SR is derivable from the first postulate alone".
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