# The great Antiphon is stumped on a simple problem

• Antiphon
In summary, the conversation discusses the behavior of light passing through a thick piece of glass. It is mentioned that 4% of the light is reflected off the front surface, and of the remaining 96%, another 4% is reflected off the back surface. The question is raised about how long it takes for a single photon to pass through the glass, with three options presented for consideration. The concept of classical intensity and probability of photon detection is also discussed. There is a disagreement about the possibility of a single photon passing through the glass without interacting with the polarization dipoles. The conversation ends with a suggestion to restate the problem with fewer extraneous details.

#### Antiphon

Yes, I can be that full of myself sometimes.

Ok, I just got done posting a classical explanation of light reflection at a glass surface. Now I can't figure out how photons go through a window.

If you had a 186,282 mile thick piece of perfectly lossless glass and shot a single photon of visible light at it, then 4% of the time that photon would reflect off the front. No problem. Of the remaining 96% that got through the glass another 4% would reflect off the backside and not come out the back. Ok.

So I have a block of glass 186,282 miles thick and about 92% of the time, a light quantum will go through.

Question: how long does it take one of the quanta to go through? Here are the options:

(A) 1.52 seconds. The velocity of light in glass is reduced by the index of refraction.

(B) 1 second. The photon cannot possibly interact with the polarization moment of all that glass and come out the other side intact but simply delayed a little. That takes a steady wave train of photons interacting with the glass for many cycles.

(C) none of the above. It may not get the whole glass block oscillating but it sure isn't going to sail through without interacting. It's not a nutrino you know. It will come out eventually and who knows in what direction.

Let the quantum optical games begin.

I know next to nothing about QED, but what if you remove quantum mechanics from the problem for a moment and consider classical electrodynamics. Suppose you shot a short ( <1 us, say) burst of light at the glass. What would happen? I think the answer is that at first contact 4% would be reflected, then 1.52 seconds later most of the remaining light would exit the rear surface. But some would be reflected and 1.52 seconds later would hit the front surface, and so on: the light bounces back and forth within the glass with most of it leaking out each time it hits a wall. If you stand at the other end of the glass you will see bursts of light every 3.04 seconds, with each burst much less intense than the preceding.

Now turn down the intensity of the light down until you are emitting single quanta. In this limit, does the classical intensity correspond to the probability of detecting a photon? If that's true then the person standing on the other side of the wall can make a probability distribution of photon arrival time, which would look like the classical intensity plot: probably the photon will be detected at 1.52 seconds; with some small probability it will be detected at 4.56 seconds; with even smaller probability it will be detected at 7.60 seconds, etc.

I don't understand the question. The light will be attenuated in the glass and won't make it out. Glass is not that transparent.

I don't understand the question. The light will be attenuated in the glass and won't make it out. Glass is not that transparent.
Right.
Is it possible to re-state the question assuming a so low absorption coefficient that we have the technical possibility to detect a photon on the other side? (The theoretical possibility still exists even in the real case, it's just incredibly small).

There should be some restating of the problems. That would be helpful in understanding what is fundamental and what is a matter of degree.

Sorry, I intended the glass to be lossless, and there is no other light in the glass.

If you send a single quantum into the glass block, I would assert that it can't come out 1.52 seconds later because the quantum would have to have excited the whole glass block's polarization dipoles for the index of refraction to become 1.52. I don't think one quantum can do that.

I also don't think the quantum would pass through the block unscathed and come out 1 second later.

My best guess is that it gets randomly scattered by the unexited dipoles of the glass. But then how does any light ever get through?

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Right, but if the glass is lossless, I don't understand your complaint that it isn't lossless - "but it sure isn't going to sail through without interacting. It's not a nutrino [sic] you know. " It's as if you are arguing against your own premise.

It's not clear to me what the question is supposed to be.

Right, but if the glass is lossless, I don't understand your complaint that it isn't lossless - "but it sure isn't going to sail through without interacting. It's not a nutrino [sic] you know. " It's as if you are arguing against your own premise.

It's not clear to me what the question is supposed to be.
But it depends on what is intended with "interaction". If you mean absorption, then it doesn't match with his premise that the glass is lossless. But light "interacts" with glass, in a more general sense, even if it's not absorbed at all: the mere fact that its phase velocity changes inside the material, even if it's not known the microscopic mechanism, means that some kind of interaction has happened.

It takes some energy to get the dipoles in the glass oscillating. If they're not oscillating, then the photon doesn't see glass, it sees vacuum.

I guess I'm saying that I don't think a quantum can go through a piece of glass unless a lot of light is also going through, but I don't think that's correct either.

I think it would be valuable to go back to the beginning, and try to clearly state the problem with as few extraneous things (light-year thick glass) as possible.

I think it would be valuable to go back to the beginning, and try to clearly state the problem with as few extraneous things (light-year thick glass) as possible.

Ok. When light goes through glass, it excites a volume polarization current which oscillates at the frequency of the light and causes a progressive phase shift through the material resulting in a retardation effect. The group velocity of the light wave slows down by the index of refraction and therefore the light goes more slowly through glass than air by a factor of 1.52.

Now if you have a classical wave with an abrupt beginning that encounters glass that has been dark, then the frontmost part of the wave makes it through the glass at close to c. There are small oscillations that build up in time, and then the main part of the light makes it through delayed by a factor of 1.52. The initial part of the wave had not yet been retarded by the polarization-induced phase shift and so it sailed through the glass at c. The part of the wave coming behind it expended energy in getting the dipoles going (even if the glass is lossless, you have to give the dipole some energy or the index of refraction would stay 1.0). Finally, the main part of the wave arrives, the amplitude goes up, and we say "the light is going through but slower by a factor of 1.52".

My question is this; when you send a single quantum of light through dark glass, how does it manage to excite all the dipoles and get the index of refraction up to 1.52?

Perhaps it doesn't and the first quantum you send into dark glass is one of those that are getting the dipoles excited. If so, the first N photons should have a very low probability of coming through at all.

Yet I know optical experiments are routinely done where a single photon is sent through an array of lenses, beamsplitters etc. and nobody ever worries about this.

How does it work? How does a single quantum come through dark glass slowed down by 1.52? or does it?

I wouldn't try and think about it that way, as it mixes up classical, quantum, microscopic and macroscopic pictures all together. This strategy makes it very difficult to get a consistent picture, as the approximations and assumptions are different in each viewpoint.

Your question seems to be "what is the speed of a single photon in a medium". The way I would solve that is to figure out what the ground state is in that medium, and then to quantize excitations in the EM field of fixed E and p. Those are photons.

Nobody will be surprised that the velocity of these photons is c/n, and that I can understand what happens when a photon enters or exits the media by looking at the interface and matching up coefficients. So you can figure out reflection and transmission in this view.

Now, you're probably unhappy by treating the material as continuous as opposed to made of atoms. But in a volume of one wavelength cubed, you have something like a hundred billion atoms. So not only is a view where the medium is continuous a good approximation, treating it as single particles is computationally intractable.

I wouldn't try and think about it that way, as it mixes up classical, quantum, microscopic and macroscopic pictures all together. This strategy makes it very difficult to get a consistent picture, as the approximations and assumptions are different in each viewpoint.

Your question seems to be "what is the speed of a single photon in a medium". The way I would solve that is to figure out what the ground state is in that medium, and then to quantize excitations in the EM field of fixed E and p. Those are photons.

Nobody will be surprised that the velocity of these photons is c/n, and that I can understand what happens when a photon enters or exits the media by looking at the interface and matching up coefficients. So you can figure out reflection and transmission in this view.

Now, you're probably unhappy by treating the material as continuous as opposed to made of atoms. But in a volume of one wavelength cubed, you have something like a hundred billion atoms. So not only is a view where the medium is continuous a good approximation, treating it as single particles is computationally intractable.

This is good advice. I'm going consider this in one dimension and see if I can crack it. Thanks.

since the Photon is in the visible range it won't have enough energy to excite an electron in the lattice from the HOMO to the LUMO and any interaction could be approximated by Compton scattering so the Answer would be C. This is my hypothesis

Antiphon said:
Sorry, I intended the glass to be lossless, and there is no other light in the glass.

If you send a single quantum into the glass block, I would assert that it can't come out 1.52 seconds later because the quantum would have to have excited the whole glass block's polarization dipoles for the index of refraction to become 1.52. I don't think one quantum can do that.

I also don't think the quantum would pass through the block unscathed and come out 1 second later.

My best guess is that it gets randomly scattered by the unexited dipoles of the glass. But then how does any light ever get through?

Vanadium 50 has it right! You are confusing quantum mechanics with classical physics. Quantum mechanics is only about probabilities. It does not tell us what the photon is doing in the glass. It does not predict whether the photon will be reflected or transmitted. It only tells us the probability for reflection and the probability for transmission. We have no idea what the photon is doing in the glass. Of course, classical physics doesn't tell us either, since the photon is not a classical object.