Can Light's Speed be Considered Constant if it Can be Slowed Down?

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HELLO ALL, I'm new to the forum and this is my first post I've just recently switched from Bio-engeneering to physics and math for my undergrad. I have been reading a lot recently about the successes in slowing down light. I have just a basic question in relation to this. If we can slow light then how can its speed still be counted as a constant? This question also leads to another, that is how if light is not a constant can we still count photons as a massless particle? The gluon is still considered massless but it is only found in hadrons, but the photon it seems loses the property of a massless particle once is experiences time (I.E. slowing down from light speed) I thought this would cause a problem similar to the neutrinos having flavours? This has just been stumping me recently and all my professors are out of town at the moment. I would appreciate it if someone could clear it up for me. Thx
 
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What is constant is the speed of light in vacuum.
 
To avoid a lot of confusion later in the thread, I will mention now that what is commonly referred to as the speed of light, is distinct from the speed of individual photons. The speed of light, i.e. the phase velocity of light, does indeed vary depending on the medium through which it travels in accordance with Snell's law of refraction. However, individual photons always travel at C irrespective of the medium through which they travel.