Help me understand this. I have heard tell that they are now able to slow the forward progress of a photon traveling through an EBC to somewhere near 35mph. Is this actually the physical slowing down of the photon, or is it the slowing down of the absorption and emission process? If the photon is actually slowed down, does it gain mass? Or am I miss interpreting this all together. Thanks
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You are probably referring to Bose-Einstein condensates, commonly abbreviated BEC. If not, please comment and clarify your question.
The article you likely have heard of is Hau et al., Nature 397, 594-598 (1999): "Light speed reduction to 17 metres per second in an ultracold atomic gas," which translates to about 38 mph.
In fact, you will find that the Bose-Einstein condensate is actually secondary to your question. It just happens to provide the three states used for an effect called electromagnetically induced transparency (EIT). This effect takes place close to an absorption line.
Before continuing, allow me to rephrase your question even further:
What happens to light (or a photon) when it travels any slower than the vacuum speed of light?
See what I did there? The extent to which it was slowed is secondary,- the fact that it was slowed at all is the crucial bit. And it is slowed everywhere around us. And yes, the interaction between photons and matter is a constant absorption and re-emission and it is the very delay between the two of them which alters the group velocity (speed of light in a medium, Wikipedia). This is just as true for the cited EIT in a BEC.
Regarding your question about mass, I'd like to point you to another discussion on physics.SE (How can a photon have no mass and still travel at the speed of light?) which provides detailed and insightful descriptions. It is important to distinguish the rest mass (which always stays zero) from mass associated with their energy if confined though. However, dabbling with a concept of photon mass is likely to throw more fog than it clears.
Simply put, absorption & re-radiation and the statistics of these processes describe the speed of light in a medium.
