Time dilation, increase in mass, Lorentz contraction calcs all involve velocity of light in vacuum. But in optical media light slows down. So what of relativity calcs in media? Do we ever need to adjust the speed of light?
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No, because in a dielectric medium light isn't light, and that's why its speed isn't $c$.
The speed of light in a dielectric medium remains unchanged. You'll find lots of questions discussing exactly what goes on with light in a medium, but basically the EM field of the light interacts with electrons in the medium to form an entangled system that has an effective mass greater than zero and hence travels slower than light. In highly interacting systems like BECs we get a distinct quasiparticle called a polariton, though in usual dielectrics like glass and water the coupling isn't strong enough to make the quasiparticle a useful description.
Though undergraduate descriptions of special relativity focus on the constant speed of light, special relativity is really a geometric theory. It is a consequence of the geometry of flat spacetime, and the constant speed of light is a result of this geometry. The geometry of spacetime is the same inside a dielectric medium as it is outside it.
answered Jul 5, 2017 at 15:27
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$\begingroup$ Thanks for an intriguing thought. " ...in a dielectric medium light isn't light ..." Never would have expected such an answer. So experiments where they claim to 'stop' light, then restart it, are these the polaritons you speak of? If I recall they used a BEC to accomplish that. I didn't see it in the wiki leak you provided. So then Special Relativity, indeed just a 'stepping stone' for Einstein towards a much bigger picture of reality. $\endgroup$ Commented Jul 5, 2017 at 16:55
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$\begingroup$ Yes, slowing light in a BEC is this kind of physics. I'm not sure what your last sentence means though, since the slowing of light is nothing to do with relativity. $\endgroup$ Commented Jul 6, 2017 at 4:35
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$\begingroup$ My last comment just stepping back to a different thought, regarding Einstein. Thanks $\endgroup$ Commented Jul 6, 2017 at 14:42
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$\begingroup$ So... I didn't quite get it: in material media then, can one put an observer to travel along with light there?(16 y.o. Einstein's famous thought experience). Would this observer always see static E and B fields then? This looks bad, since he'd know his state of motion... $\endgroup$ Commented Dec 29, 2021 at 19:33
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1$\begingroup$ @daydreamer Remember that we are in some medium. The observer could use their observations of the E and B fields to determine their speed relative to the medium, but only relative to the medium not an absolute speed. Though of course they could just look at medium around them to get the same information. This is very different from travelling in a vacuum where by definition there is nothing you can look at to determine your speed. $\endgroup$ Commented Dec 30, 2021 at 5:31