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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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marked as duplicate by ACuriousMind, Kyle Kanos, Brandon Enright, John Rennie, Danu Aug 15 '14 at 10:00

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ possible duplicate of Do all massless particles (e.g. photon, graviton, gluon) necessarily have the same speed $c$? $\endgroup$ – ACuriousMind Aug 15 '14 at 0:01
  • $\begingroup$ 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. $\endgroup$ – user1247 Aug 15 '14 at 0:19
  • $\begingroup$ You can check the following topic for the answer you want to get: physics.stackexchange.com/q/76492 . $\endgroup$ – Andrew McAddams Aug 15 '14 at 0:24
  • $\begingroup$ 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. $\endgroup$ – ACuriousMind Aug 15 '14 at 0:35
  • $\begingroup$ @LubosMotl argued in a blog post that a quantum theory with two metrics (hence two light cones) can't be physically consistent. $\endgroup$ – benrg Aug 15 '14 at 0:37