# What is the mass of a photon in non-empty spaces?

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?!

• Possibly related question: here Jan 6, 2012 at 21:52

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.