To clarify, is the speed limit of the universe the speed of light in a vacuum, or the speed of light in that particular medium, i.e. if the speed of light in a particular medium were only 17 m/s, would I be able to go faster than that speed?
Also, for the special relativity equations of time dilation, I was always taught to use c, as in the speed of light in a vacuum. But to me, it makes more sense to use cm the speed of light in that particular medium, since all the thought experiments (involving light clocks) seem to assume the speed of light in that medium is c, not cm.
Answer
The equations of relativity do not hold in a medium, which selects a preferred coordinate system (the one which rests in the medium). Can you go faster than the local speed of the quasi-particles formed by the photons and the polarized atoms of the medium? Of course. If you are charged you will be generating Cherenkov radiation, too. See http://en.wikipedia.org/wiki/Cherenkov_radiation.
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