1. Yes. The basic equation relating energy (E), momentum (p), rest mass (m0
) and the speed of light (c) is E2
. When m0
=0, you just get E=pc. Now we also have p*sqrt(1-v2
v, where v is the velocity. So that means that when m0
) = 0. When p isn't zero, we must have v=c.
2. It's not that light is taking a longer route. To the extent that there are gaps between the wave-functions of the atoms (partially the case), you can think of the speed in the gaps as being just plain c. The slowing down is, as you say, a larger-scale average effect that shows up when you include the parts of the wave that are scattered by the material.
3. To the best of my knowledge, the mechanism by which mass couples to spacetime geometry is not yet understood. That's what the string theorists are trying to do.
4. This one will require some help from somebody who understands the Higgs field. We'll update at some point. Meanwhile, you can have a look at http://en.wikipedia.org/wiki/Higgs_boson
5. There are probably more direct ways, but here's an old example. The angular momentum of the electrons in say a piece of iron can be measured by taking a magnetized block and heating it up. When the magnetism melts, the spin angular momentum transfers to the ordinary mechanical angular momentum of the block. Einstein was in on the first version of that experiment. The angular momenta of electromagnetic waves can be then measured by letting them be absorbed by electrons in a spin resonance experiment, flipping the direction of a known number of electron spins. Translating from the total wave momentum to the photon pieces just requires knowing how many photons there are, obtained from simply accounting for the energy. The angular momentum is always either plus or minus in the direction of the wave propagation.
(published on 07/06/2011)