Assume you are in a medium where the speed of light has been slowed down to 15 mph. Can you then go faster than light in that medium, or do the effects of outpacing the speed of light only apply to the speed of light in a vacuum? If the entire universe were made of a medium that limited light to 15 mph (even though the speed was still 186,000 mps in a vacuum) would traveling at 16mph produce no real effects?
Light is slowed down in some media not because it actully moving more slowly, but because it is being absorbed and re-emitted. It’s still traveling at “c” most of the time, because most of the medium is still a vacuum.
So the answer to your questions is yes and no, respectively. It’s only the speed of light in a vacuum that determines the effects of relativity.
It’s possible for particles, and seems to be a semi-regular occurance in situations like particle accelerators and nuclear reactors. Google “Cherenkov Radiation” for some details. From what I understand, the mass increase / time dilation effects in relativity is related to the constant c, which is fixed (duh, it’s a constant 
) at all points of the universe. c happens to also be identical to the speed of light in a vacuum (because photons always go as fast as possible), but doesn’t necessarily have any bearing on the observed speed of light in whatever medium you happen to be inhabiting.
As for whether it’s possible for a massive object like a person to speed through a medium faster than photons and what they’d see…I dunno.
In retrospect obviously you can travel faster than light in a non-vacuum because light has been slowed down to zero in labs. However what if the entire universe were made of a material that is a non-vacuum that limited light speed to a certain slow speed?
Oh, and if the entire universe were made up of a medium, it would still be mostly empty space unless you postulated some type of medium other than matter. So your second question belies a misunderstanding of what constitutes a medium, I think. And if you postulate some type of medium that isn’t matter, then all bets are off because you’re not talking about this universe anymore.
Well goddammit
Ok here’s a real nitipick-- please forgive.
In most cases the photon isn’t truly absorbed because the atoms in the medium don’t happen to have any allowed transitions at that specific energy. However the energy / time uncertainty principle does allow the atom / photon to form what is called a dressed state or virtual energy state.
Since the photon has not been really absorbed it doesn’t change state and therefore, among other things, maintains the same propagation direction.
Part of the confusion is the continuing misuse of c.
Try it this way: C is Einstein’s constant, the speed of light in a theoretical absolute vacuum. This is the figure that is used in all calculations of relativity effects.
But c is the actual speed of a “lightwave” in a medium, always lower than C. In most astronomical determinations c can be set equal to C with little loss of precision. In some media, however, certain energetic particles can travel v where c < v < C.
I agree that “you” could never travel at v, since no complicated bits of matter have ever been observed to do so, to my knowledge.
You should take a look at John Stith’s Redshift Rendezvous, a fascinating hard sf book set in a starship with a dense core that warps gravity and c. Each layer of the ship has a different figure for c and the relativistic effects for each are minutely portrayed. [Link goes to an ebook, since that has reviews and stuff. A hardback edition, much cheaper used, can be found by searching.]
I always believed that called “c” the “Speed of Light” has caused much more confusion than any other term in science.
“C” should be referred to in popular media as “The ultimate speed limit of the universe now and forever”. It just so happens that light travels near that speed much or most of the time but it has nothing to do with the property itself.
Your implication that c arbitrarily being identical to speed of light in a vacuum absolutely not true. There is a fundamental, if not completely understood, connection between the speed of light and the plenum through which it moves; this relationship forms the premise of special relativity. That light travels slower in a medium is a result of interactions between the medium and the photon travelling though it doesn’t change the fact that an individual “free” photon always moves at c.
And while c is a constant speed for light and unattainable limit for massy particles in free space, there are conditions under which that “constant” may be increased, either apparently or absolutely, though we assume that causality (i.e. the notion that actions occur in a time-like manner, such that we can’t observe an event and then go backwards and become the cause of it) holds on molecular scales and above.
Stranger
You are forgiven. Isn’t QM fun?
c is the Lorentz-invariant speed. We could talk about c and relativity even in a universe where there was no light. Now, it so happens that one of the consequences of Special Relativity is that any particle with 0 mass must travel through vacuum at exactly c. And we’re reasonably sure that photons are massless (or at least, if they do have a mass, it’s incredibly tiny), so it so happens that because of that, photons travel at c (or at least, really, really close to it). But the fact that photons are massless is essentially independant from the fact that there is one and only one speed which is Lorentz-invariant. For comparison, until recently, it was generally accepted that neutrinos were massless, and that they would therefore travel at c, but it is now known that they actually have a nonzero (though small) mass, and therefore do not travel at c. If we knew about neutrinos before we knew about light, we might have named c “the speed of neutrinos”, but we’d have been mistaken.