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Does it make sense to say, "The speed of light varies?" Some may say right off the bat yes, it changes as a wave passes through a different medium. However, I'd like to say no, because when I hear someone say the speed of light, I always think of the constant C (unless the medium is specified to not be a vacuum, but then it isn't C anymore), not the speed of a particular wave. To me, it makes more sense to say something like, "The speed of a particular wave varies." What is the correct way to state this in the professional world? And in general, when professional physicists say "the speed of light," are they referring to the constant or the actual speed of the wave?

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It sounds like you're asking whether, when physicists say "the speed of light," are they referring to the actual propagation velocity of a light wave or the universal constant? If so, that's specific enough to physics that I think it's okay here. (My guideline: asking "what does X mean" goes on English; asking "what does X mean to physicists" goes here.) – David Zaslavsky♦ Sep 19 '11 at 20:03
Yes, that's exactly what I'm asking! – MGZero Sep 19 '11 at 20:03
OK, cool. I edited your question a bit to (hopefully) clarify it. Feel free to edit it further or revert if you think it's necessary. – David Zaslavsky♦ Sep 19 '11 at 20:19

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I would generally say that most physicists mean "speed of light in a vacuum" when they say "speed of light," and therefore would say that the "speed of light is constant." If it is in a field that often deals with light propagation in materials (optics, condensed matter), people are usually pretty careful to say "speed of light in a vacuum" when they mean it.

Generally whenever some says "the speed of light is a constant," most physicists will assume they mean speed of light in a vacuum.

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I find the well defined case of "speed of light in a vacuum" to be somewhat boring (no offense to the discovery, measurement, and accuracy of this value). In practice, very few environments are in a vacuum, so its important to consider how the speed of light differs from this ideal case, and why does the speed of light change in non-vacuum environments? How does the speed of light change in a material as a function of the wavelength--are we looking at a true speed chagne, or are we measuring the change in phase and extrapolating this to a change in speed? Are delays in speed due to interactions with EM potentials due to electrons and protons in matter, or are they due to transient absorption/emission events? If you can explain this, does this help to explain why neutrinos would travel faster than light through matter?

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That's a question not an answer. The simple (but slightly wrong) way to think about the slower speed in material is: light is absorbed by an atom (not quite), a fraction of second it emits another photon in the same direction which travels at 'c' to the next atom where is is absorbed, and emits ... and so on. Neutrinos aren't absorbed and re-emitted and so go straight through the material – Martin Beckett Jan 16 '12 at 16:45

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