In a dispersive media light's velocity can change substantially. Imagine we can slow it down to near 0 what the wave would look like?
Frequency of light does not seem to change even at v=0 (at least 20m/s is observable), E=pc, and p=h/lambda, E=h*frequency. There is a duality, but that this mean the wave properties should disappear and the particle should have zero mass with E energy conserved ? Is there any symmetry that "protecting" the masslessness of the photon in a sense why is it so special that we tend to say that EM electromagnetic energy of charged particle Eem=mc^2 and we calculate its classical radius, but we can not say same for photon ? I am looking for the popular understanding, not deep theory.
And a question for vacuum : how the light from the big bang was able to "cool down" or change its frequency to 3K nowadays. And how the space was curved at that point and changed so that we are able to detect it now. Meaning if the big bang happened at one point and the speed of light is the limit how we can detect something that is way ahead of us. The light seems delayed billion of light years ?