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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