special relativity - Is the Speed of Light an universal spacetime constant, the velocity of electromagnetic waves, or of photons?

This question has been touched tangentially by What's a better phrase than "speed of light" for the universal spacetime speed constant? and Could light travel more slowly than the "universal speed limit"? Could this imply quantization of spacetime? but I do not think they reach the core of my question.

When I read that many other theories, e.g. the Standard Model, have been constructed to be Lorentz invariant it appears that electromagnetism has some of preponderant role in the universe compared to other theories. I suspect that the answer is that this is not the case, and that the space-time Speed of Light (with upper-case) is really more of a universal constant that is not necessarily related to the speed of the electromagnetic waves or of photons.

There are many other related questions:

1. would it really be devastating for relativity that we find out in the future that photons have a tiny mass and move slower than ... uhh... the speed of light?


2. which "c" is applicable in different situations? I mean, possibly the space-time constant should be used in $E=mc^2\gamma$, it would be the velocity of gravitational waves, etc..., but in other situations such as the Bohr radius or Compton wavelength I am not sure.

Well, any answer will be appreciated. Please tell me if you know any reference to bibliography that address this issue.

Answer

it appears that electromagnetism has some of preponderant role in the universe compared to other theories

This is not true. It played an important historic role, but is in no way theoretically "unique" because the photon travels at speed c. Indeed, the gluon also travels at speed c. If photons were found to be slightly massive, it would change a lot of things, but it wouldn't change relativity. At this point we have a well constructed theory where all and only massless particles travel at speed c. In other words, the photon is only historically central to relativity, not conceptually.

the space-time Speed of Light (with upper-case) is really more of a universal constant that is not necessarily related to the speed of the electromagnetic waves or of photons.

You've pretty much answered your own question, because this is exactly right. Historically, questions regarding inertial reference frames and electromagnetism led to the development of special relativity. Within relativity, an important speed constant appears. If indeed the photon is massless, then this speed should be the same as the speed of light. Even if the photon were to turn out to be massive, this in no way obligates us to rewrite our theory. It just means that the historical tool we used to build relativity wasn't exactly what we thought it was, but was close enough for the early development of the theory. Our current theoretical understanding of Minkowski space (the space-time geometry described by special relativity) is not one that depends on electromagnetism, in fact it's the other way around : in our current understanding of electromagnetism, we use our understanding of Minkowski space to conclude that massless particles like photons should move at the speed of light.