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It is a well known result of the special theory of relativity that the photon has no rest mass, because for a particle to attain the speed of light, it must have zero rest-mass. I will not dig into this more, but the interested reader can see these questions for more information:

How can a photon have no mass and still travel at the speed of light?

Why can't photons have a mass

Also, this Wikipedia link:

http://en.wikipedia.org/wiki/Photon#Experimental_checks_on_photon_mass

Now my question is what about a photon in non-empty space? It is well known that light in non-empty spaces travel slightly slower than its speed in empty space. But that means that the photon cannot have zero rest mass, as every mass-less particle should always attain the speed of light (see the links above)! How can this be explained?

Let us assume for the moment that the answer to this question is that the the photon does indeed have an extremely small mass in non-empty spaces. But let's direct a ray of light towards a box of glass which is completely empty. Now before it reaches the empty space inside the box, it has velocity c - $\epsilon$, where $\epsilon$ is some small positive real number. Once it enters the empty space, it should raise to the the exact speed of light. However, it is a result of special relativity that any particle with a non-zero mass, however small it is, cannot attain the speed of light.

Couldn't this mean that the photon does indeed have a mass, but a very very small one, and that it is actually moving in a speed less than the universal maximum limit of speed?!

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Possibly related question: here –  twistor59 Jan 6 '12 at 21:52
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Actually, no, something different is going on. In materials, the reason light travels slower than $c$ is because the photons occasionally hit atoms and are absorbed, then re-emitted. So the average velocity with which they propagate is less than the speed of light. However, between interactions with the atoms, the photon does travel at speed $c$. (N.B. this is a simplification of the real quantum-mechanical picture, though it yields the same results) There is no evidence to suggest that the photon has a mass.

The exception would be in superconductors, where the photon does acquire some sort of effective mass, but I'm not completely familiar with the details of that process.

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:Thinking of photon propagation in a transparent medium: is it really the case that a significant part of the propagation is due to real absorption and re-emission processes? If so, wouldn't the re-emission have to be at a transition level frequency ? I can see that computing the in-medium propagator using virtual absorption and re-emission processes would give you a shift in the pole of the propagator which would make the photon behave as if it had an effective mass whilst in the medium wouldn't it ? –  twistor59 Jan 7 '12 at 8:56
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