Speed of light in a medium in different frames of reference Relativity states that speed of light in a vacuum is the same regardless of the observer. Does the same hold if the light is travelling through a medium?
 A: Assume that the light velocity in a medium resting in an inertial system $S$ is $u \lt c$. Then, to obtain the light velocity seen from an observer in a different inertial system $S'$ with relative velocity $v$, you have to use the velocity addition formula of Special Relativity $$u'=\frac {u+v}{1+u'v/c^2}$$ This shows that the velocity of light in a medium is not independent of the observer. It changes according to the SR velocity addition formula.
A: The answer is "no". Although Maxwell's equations and light-based Gedanken experiments had a lot to do with relativity's inception--the significance of $c$ is that it describes how time and space scale in Minkowski space (M4)--so it's really a parameter describing the shape of spacetime--and in fact everything moves through M4 with $u_{\mu}u^{\mu} = c^2 $, which means if you have a 3 velocity of $c$ in one frame--you have that in all frames--and the speed of light in a vacuum is $c$.
For a photon in a medium, it would appear as a particle with four velocity:
$$ u_{\mu} = \frac{c}{\sqrt{1-\frac{1}{n^2}}}(1, \frac 1 n \hat{\bf x}) $$
and transform accordingly.
A: Speed of light in medium are defined by:
$$  v = \frac{c}{n},   $$
where $c$ is the speed of light in vacuum and $ n $ is refractive index of medium.
