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The "speed of light" is not just the speed of electromagnetic radiation, but of any massless particle. Therefore must not there be an expression for $c$ that is not in terms of $\mu_0$ and $\epsilon_0$ (and more generally not in terms of electromagnetic quantities such as charge and the fine structure constant)? If not, then what prevents some massless $U(1)^\prime$ field from having $\mu_0^\prime$ and $\epsilon_0^\prime$ that result in a $c^\prime\neq c$?

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user1247
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    possible duplicate of Do all massless particles (e.g. photon, graviton, gluon) necessarily have the same speed $c$? – ACuriousMind Aug 15 '14 at 00:01
  • Thanks, that is basically the same question, although I'm annoyed at the answers being so qualitative (and I think the top-voted one mentioning virtual particles is terrible). The "Is there a no-go theorem"? question wasn't addressed very directly. Maybe if I leave this up it will have some better luck. – user1247 Aug 15 '14 at 00:19
  • You can check the following topic for the answer you want to get: http://physics.stackexchange.com/q/76492/ . – Andrew McAddams Aug 15 '14 at 00:24
  • There are some other questions about this if you search for "massless particle" and "speed of light", I chose the one as duplicate I thought might best suited for this, but the answer you seek is probably in there somewhere. I've found no answer that would fully satisfy me either, I have to admit. Might be worth it to offer a bounty with "The current answers do not contain enough detail" or somesuch on one of the old ones, though, instead of asking it anew, but I'm not really sure. – ACuriousMind Aug 15 '14 at 00:35
  • @LubosMotl argued in a blog post that a quantum theory with two metrics (hence two light cones) can't be physically consistent. – benrg Aug 15 '14 at 00:37
  • The expression is c = 1, i.e. the appearence of c in equations is an artifact of the fact that classical mechanics is a scaling limit of special relativity with c playing the role of the scaling parameter that is sent to infinity. Expressed in SI units, c is a measure of how slow we are compared to our size. – Count Iblis Aug 15 '14 at 01:16
  • @Andrew McAddams, thanks. The question itself is trying to do what I was getting at, but unfortunately is tautological (the 'c' in the E-relation could just as well be c-prime in my question). On the other hand I really like Ben Crowell's answer. That's a good no-go argument, although it still leaves me feeling somewhat empty, that there must be a derivation of or expression for c itself that is not tautologically dependent on electromagnetism specifically as an example of a massless field. – user1247 Aug 15 '14 at 04:28
  • We know the speed of gravitons? When has that been measured? – CuriousOne Aug 16 '14 at 01:36

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