I saw a post here in which the poster seemed to be saying that the speed of light is less when traveling through matter. I have also seen numerous Internet sites that seem to say this. My understanding is that the speed of light is constant, but that it propagates through matter at different rates as atoms absorb and re-emit photons. This seems to me to be an important distinction. Which is correct?

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The speed of light is constant in a particular medium. So yes, the speed of light is different in different media. But it will always be the same speed in the same medium. So the speed of light in water (at 1 atmosphere, 20 deg Celsius) , for example, will always be the same in any water in the same environment.

However, light has a maximum speed, the speed of light in a vacuum. Nothing travels faster than this upper limit.

They've conducted experiments with exotic materials and gasses in which they've slowed down the speed of light in that medium to several miles per hour!

Rob

And yes, the "speed in a medium" depends on how you treat the medium. If you treat it as one continuous thing, then you can get a slower speed. If you treat it as a discrete bunch of atoms, then there is a sense to which the speed is c in the vacuum "between atoms", but the combined effect of all the atoms slows the net progress of the signal.

Source

Not considering the subatomic speeds, the speed of light is not constant in any given non-vacuum medium. Different frequencies have different speeds which is the basis/cause of refraction of light into a spectrum.
Somehow I can't find a direct quote stating this. But it is implied in index of refraction being a factor of incident frequency and also being a factor of speed of light in the particular medium.

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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.

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.

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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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.
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)?
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.

Correct me here if I'm wrong but it takes a very special nuclei to absorb and readmit a photon and when doing so the readmitted photon goes off in a different direction. So light going through a medium can't be thought of absorption and readmitting a new photon in the quantum sense of a photon transferring energy to excite an electron to a higher orbit then having that photon get readmitted. I also think electron/positron pair production can be ruled out due to the levels of energy required by them.

I'd like a better mental model of what is going on when a photon passes throught different mediums too.

There are various ways of describing the QM interaction between the photon wavefunction and the electron shells of the atoms in the transparent medium.
One way, which tells the story as if we could actually find a specific photon interacting with a specific atom at a specific moment, makes sense of the above quite nicely. I've offered it a few time on BAUT. Here's a snippet from a previous post:Grant Hutchison

Very informative and intelligent analysis.

Glad to see there is a direct quotation to non-constant speed of light in transparent materials after all (including a quantum explanation). Even though the BAUT forum seems to be the sole source available on the internetwork.

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And note that the effect is not inherently quantum mechanical-- the index of refraction of materials can be understood classically, the primary requirement is an understanding of complex numbers (and most of those advances came with quantum mechanics!). The classical description is related to the response you get from a harmonic oscillator if you drive it at a frequency away from its resonance frequency-- the amplitude of the response is less the farther from the resonance you are. There is also a phase shift that comes from the interaction, so the amplitude of the response controls how much out-of-phase interference you have to add in when you do the "superposition" of all the things the light is doing. The higher the amplitude of the interfering terms, the more the light is slowed.

Quantum mechanically, you can frame the amplitude of the response in terms of the probability that the photon will interact with that atom. So I'm not sure where the uncertainty principle per se comes into play (in some sense it is hiding behind all quantum phenomena, that is true), because I wouldn't necessarily characterize the issue as how long the atom holds the photon, because the phase shift far from resonance is always pi/2, and a fixed phase shift will act like a fixed "residence time". Instead, what changes with frequency is the amplitude, or likelihood, that the atom will be involved in slowing the photon's progress. I'd like to understand the connection between these two descriptions of the frequency dependence.

a1call Here's your changing refractive index over the spectrum graph. pete

see:http://upload.wikimedia.org/wikipedi...sion-curve.png

oddly enough, my teaching observation this year was on refraction...the principal had never understood rainbows, and was quite pleased

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I don't believe that photons interact with the nucleus; I think they only interact with the electrons around the nucleus.

Rob

That's quite true, though Wayne could counter that the behavior of the electrons is in turn controlled by the nucleus (essentially, its charge and the fact that it has a relatively high mass). If you build the nuclei, the electrons will come!

Synchronicity.
I had to look up the origin of the quotation "If you build it, he will come" just last night, when I encountered it for the first time in Edwards and Westling's book The Space Elevator.

Grant Hutchison

Do you recall the movie in which that concept featured?
And I saw Field of Dreams before even coming to Iowa, a minor synchronicity/coincidence, but I can do much better: you probably don't think of Iowa as the music capital of the world. Nevertheless, several years before I knew I would ever live in Iowa, and long before I or any of my friends could name a single musician from Iowa, a friend of mine made a cassette tape for me with some favorite singer-songwriter tunes. My two favorites were "Poet Game" by Greg Brown, and "Over my Shoulder" by Dave Moore. Years later I moved to a city of about 50,000 people in Iowa. Guess where both Greg Brown and Dave Moore lived? At one point, I lived a block away from Greg Brown.

Magnolia is certainly one.

Grant Hutchison

I had in mind an older one-- Repo Man. A classic ode to synchronicity, and the general impossibility of reason, worthy of Catch 22.

Few, if any elements are transparent in solid form, but quite a few solid compounds are transparent, so perhaps we should say the light is absorbed by a molecule (silicon dioxide instead of an atom) To keep images intact, the light needs to be emitted out the opposite side of the molecule, with the same yaw, pitch and elevation. Or so it seems to me. The re-emission delay is about one picosecond, varying with the molecule and the photons wave length, and the path length = Not too believable: Is there an alternate theory on the transparency of solids? Neil

I prefer to think of the photons as being 'locked' into a certain quantum state instead of saying it's absorbed and re-emitted.

Photons & the Speed of Light
See post #9 by Grant.

That's how I like to imagine the photon behaving. The whole emission and reemission in the same direction doesn't jive with me. It's just too classical.

I wanted to edit the above post to say Grant gave my favorite answer by quoting himself in post #8. However, due to the link to another thread, it's held for moderator approval.

Why just solids? Why not liquids and gases?

In any case...sulfur crystals are a transparent brownish yellow, white phosphorus is reasonably translucent, nitrogen is a colorless clear solid, oxygen is a pale blue clear solid, I suspect the solid noble gases will be clear, and of course there's a form of carbon that's very well known for its excellent optical properties. In any case, being an element does not mean a substance consists of lone atoms, and being opaque in visible light doesn't mean something isn't transparent in other wavelengths or vice versa, so I think you're heading down the wrong path here.

The speed of light is constant in a vacuum, but transits matter in the process you described. The actual speed of light in the matter (any dielectric) remains c between the atoms, but the constant absorption and re-radiation introduces delays at the atoms. The net effective velocity is therefore less than c, and it equal to the refractive index times c, where the refractive index is the square root of the relative permitivity of the material divided by the relative permeability.

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