The special theory of relativity says that the total energy of a particle is given by the following: E2
where E is the total energy, mo
is the rest mass, and p is the momentum. This equation has been verified by many, many experiments and as far as we know is correct. The fact that momentum carries energy is even true in classical E & M where electromagnetic fields are involved. Since photons have zero rest mass then their energy is simply E = pc. The fact that light carries momentum is also verified by experiment.
The other issue you raise, the fact that the apparent velocity of light is less in a dielectric medium, has to do with the interaction of light within the medium. The reason is that the light is continually being absorbed and then re-emitted in a coherent way by the atoms in the medium. The net result is that the effective re-radiated light has an apparent slower speed than c. There is a curious effect, the Cherenkov Effect, that happens when a relativistic charged particle travels though a dielectric medium. The electric fields get 'confused' by the fact the particle is traveling faster than c and so the medium compensates by emitting this Cherenkov radiation.
See: http://en.wikipedia.org/wiki/Cherenkov_radiation for some information.
(published on 12/29/2009)