The Universe of Discourse

Mon, 16 Jan 2006

The nature of transparency

It's with some trepidation that I'm starting this section of my blog, because I really don't understand physics very well. Most of it, I suspect, will be about how little I understand. But I'm going to give it a whirl.

Sometime this summer it occurred to me that the phenomenon of transparency is more more complex than one might initially think, and more so than most people realize. I went around asking people with more physics education than I had if they could explain to me why things like glass and water are transparent, and it seemed to me that not only did they not understand it any better than I did, but they didn't realize that they didn't understand it.

A common response, for example, was that media like glass and water are transparent because the light passes through them unimpeded. This is clearly wrong. We can see that it's wrong because both glass and water have a tendency to refract incident light. Unimpeded photons always travel in straight lines. If light is refracted by a medium, it is because the photons couple with electrons in the medium, are absorbed, and then new photons are emitted later, going in a different direction. So the photons are being absorbed; they are not passing through the water unimpeded. (Similarly, light passes more slowly though glass and water than it does through vacuum, because of the time taken up by the interactions between the photons and the electrons. If the photons were unimpeded by electromagnetic effects, they would pass through with speed c.)

Sometimes the physics students tell me that some of the photons interact, but the rest pass through unimpeded. This is not the case either. If some of the photons were unimpeded when passing through water or glass, then you would see two images of the other side: one refracted, and one not. But you don't; you see only one image. (Some photons are reflected completely, so you do see two images: a reflected one, and a transmitted one. But if photons were refracted internally as well as being transmitted unimpeded, there would be two transmitted images.) This demonstrates that all the photons are interacting with the medium.

The no-interference explanation is correct for a vacuum, of course. Vacuum is transparent because the photons pass through it with no interaction. So there are actually two separate phenomena that both go by the name of "transparency". The way in which vacuum is transparent is physically different from the way in which glass is transparent. I don't know which of these phenomena is responsible for the transparency of air.

Now, here is the thing that was really puzzling me about glass and water. For transparency, you need the photons to come out of the medium going in the same direction as they went in. If photons are scattered in all different directions, you get a translucent or opaque medium. Transparency is only achieved when the photons that come out have the same velocity and frequency as those going in, or at least when the outgoing velocity depends in some simple fashion on the incoming velocity, as with a lens.

Since the photon that comes out of glass is going in the exact same direction as the photon that went in, something very interesting is happening inside the glass. The photon reaches the glass and is immediately absorbed by an electron. Sometime later, the electron emits a new photon. The new photon is travelling in exactly the same direction as the old photon. The new photon is absorbed by the next electron, which later emits another photon, again travelling in the exact same direction. This process repeats billions of times until the final photon is ejected on the other side of the glass, still in the exact same direction, and goes on its way.

Even a tiny amount of random scattering of the photons would disrupt the transparency completely. So, I thought, I would expect to find transparency in media that have a very rigid crystalline structure, so that the electromagnetic interactions would be exactly the same at each step. But in fact we find transparency not in crystalline substances, such as metals, but rather in amorphous ones, like glass and water! This was the big puzzle for me. How can it be that the photon always comes out in the same direction that it went in, even though it was wandering about inside of glass or water, which have random internal structures?

Nobody has been able to give me a convincing explanation of this. After much pondering, I have decided that it is probably due to conservation of relativistic momentum. Because of quantum constraints, the electron can only emit a new photon of the same energy as the incoming photon. Because the electron is bound in an atom, its own momentum cannot change, so conservation of momentum requires that the outgoing photon have the same velocity as the incoming one.

I would like to have this confirmed by someone who really understands physics. So far, though, I haven't met anyone like that! I'm thinking that I should start attending physics colloquia at the University of Pennsylvania and see if I can buttonhole a couple of solid-state physics professors. Even if I don't buttonhole anyone, going to the colloquia might be useful and interesting. I should write a blog post about why it's easier to learn stuff from a colloquium than from a book.

[ Update 20231128: Jez Humble posted (in 2007) [an answer to this]( If I understand it correctly, the answer is, in fact, because of the conservation of momentum as I guessed above. See the next-to-last paragraph of M. Humble's explanation. ]

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