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Originally Posted by absael
Yes, this is what I'm getting at - photons always travel at c. But if you measure the travel time of light through the medium, it will be less than c, because of the delay caused by all those atoms absorbing and re-emitting the photons. The photon that you measured exiting the medium is not the same one that entered on the upstream end.
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Your picture is correct, but note we have no way to test if it is the "same photon" or not. In pure refraction, the emergent photon has the same frequency, and a definite phase and angle, relative to the incident photon, so in many ways that sure sounds like "the same photon". But one does not have to think of it as the same photon. Words like this are just the stories we tell ourselves-- what matters is what we can actually test.
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Assuming this is correct, I don't understand why it's said that the speed of light varies depending on the medium. In the post that I'm referring to, the poster seemed to be saying that the photons were actually traveling at a slower speed - I believe that is incorrect, and this is why I want to be sure that I understand exactly what is happening.
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It's really semantics. If you think of speed as an average speed, then the photon really is slowed down (if you think of it as the same photon). But the mathematics that models what the photon does when it is not interacting with atoms would come out c. This is very related to the quantum mechanical "principle of superposition", which says that what ends up happening involves adding up (and tracking interferences) between all the things that could happen. So which is the "reality", what actually happens (a slow photon) or all the possibilities you are adding (normal photons)?
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Now, to further complicate matters, I'll add that I was under the impression that a transparent material passes light because it (ideally) contains no atoms with electrons having energy levels matching those of photons of the wavelength at which the material is transparent, so no photons are absorbed. If this is the case, would light travel more slowly through a perfectly transparent medium?
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Glass is pretty darn transparent, but it may depend on what you mean by "perfectly" transparent. There is a theorem (Kramers-Kronig, IIRC) that connects absorption and dispersion, but if all frequencies were slowed by the same amount, I believe you could have zero absorption in principle, though of course never in practice. Transparency does not require there be no interaction, it requires that the atoms preserve some phase attributes of the photon, as if the atom just "held on" to the photon a certain time, then let it go.