Measuring Time with Mirrors: Exploring Special Relativity

[43arcsec]

Special relativity is replete with examples of turning mirrors into clocks. Place two mirrors across from one another, bounce light between them, and measure the time.

But as I thought about this, when a photon hits the mirror, it is absorbed by an electron which moves to a higher energy state, and then released as the electron moves back to the lower state, and this must take time. So the time it takes light to move to a mirror and back is the twice the distance to the mirror divided by c PLUS the time for absorption and re-emission.

I've never seen that adjustment anywhere, which tells me I am either thinking about this wrong, or places like Ligos are actually making this type of adjustment when they bounce light back and forth between mirrors to measure gravity waves. Can anyone add some insight into what I'm missing?

 

[DaveC426913]

I've never seen that adjustment anywhere, which tells me I am either thinking about this wrong,

The examples are thought experiments. They use ideal mechanisms, designed to highlight the principles without getting mired in the mechanical complications.
LIGO is an engineering feat - which means they must take into account all real-world effects.

 

[Vanadium 50]

Can anyone add some insight into what I'm missing?

There is not absorbtion and reemission. If that were the case, mirrors would only work at certain frequencies.

 

[43arcsec]

There is not absorbtion and reemission. If that were the case, mirrors would only work at certain frequencies.

Hmmm, I don't believe mirrors reflect all frequencies, here's a Physics Forum link discussing that. Seems like that would be evidence that there is absorption.

 

[43arcsec]

The examples are thought experiments. They use ideal mechanisms, designed to highlight the principles without getting mired in the mechanical complications.
LIGO is an engineering feat - which means they must take into account all real-world effects.

So are you saying the absorption and re-emission is a real world effect?

 

[Cthugha]

Hmmm, I don't believe mirrors reflect all frequencies, here's a Physics Forum link discussing that. Seems like that would be evidence that there is absorption.

No. As has been pointed out already, in that case mirrors would only work at certain single discrete frequencies, not at wavelength bands.

Roughly speaking, what happens in mirror reflection is that plasmon-polariton-like modes become excited at the surface of the mirror, these are hybrid particles consisting of a superposition of a collective electron oscillation and the light field. However, there is no absorption and reemission as this would randomize the phase of the light field. If this sounds too complicated, the classical picture is not too far off: The light field forces the electrons to perform an oscillatory motion, which in turn makes them emit light as acclerated charges radiate light. The superposition of the incoming light field and the emitted light field is the reflected light field. There is no reemission delay as you imagine it (because this is a coherent process and therefore no absorption and reemission), but there is a well-known phase shift in reflection.

 

[DaveC426913]

So are you saying the absorption and re-emission is a real world effect?

No, I'm concentrating on the difference between the relativity examples you mention and the engineering project you mention.

I got the impression that was the crux of your question.

 

[Vanadium 50]

Seems like that would be evidence that there is absorption.

Note that even that link does not show reflection only at certain frequencies. Your thinking about how a mirror works is not correct.

 

[43arcsec]

No. As has been pointed out already, in that case mirrors would only work at certain single discrete frequencies, not at wavelength bands.

Roughly speaking, what happens in mirror reflection is that plasmon-polariton-like modes become excited at the surface of the mirror, these are hybrid particles consisting of a superposition of a collective electron oscillation and the light field. However, there is no absorption and reemission as this would randomize the phase of the light field. If this sounds too complicated, the classical picture is not too far off: The light field forces the electrons to perform an oscillatory motion, which in turn makes them emit light as acclerated charges radiate light. The superposition of the incoming light field and the emitted light field is the reflected light field. There is no reemission delay as you imagine it (because this is a coherent process and therefore no absorption and reemission), but there is a well-known phase shift in reflection.

Ok, while I'm not sure what plasmon-polariton-like modes" are, but after reading up here I think I might have stumbled on to something: electrons can be absorbed and re-emitted, but they can also be scattered (Compton scattering). Is it correct to say that in a mirror the incident photons interact with the conduction band electrons in the metal via Compton Scattering, which allows the reflected photons to keep their phase?

 

[Cthugha]

Is it correct to say that in a mirror the incident photons interact with the conduction band electrons in the metal via Compton Scattering, which allows the reflected photons to keep their phase?

No, that would be even worse. In Compton scattering the scattered photon loses energy if it is scattered at some angle, so you would get a different wavelength of the reflected light. There is no explanation of reflection using single electrons. You need plasmon-like excitations, which simply means coherent oscillations of the whole electron gas.

 

[43arcsec]

OK, so photons are not absorbed by electrons and re-emitted, as evidenced by no loss in phase. They do however interact in some complicated way, resulting in a photon being reflected elastically with the same phase so we still see the same image. So let me focus on the interaction. It is my understanding that photons ALWAYS move at c, even in materials, even though I commonly read that the speed of light in a material can be less than c. The distinction is that the electromagnetic wave, a collection of photons, does go less than c in a vacuum, but not the individual photons. The photons remain at c, but because of the interactions, they are not always photons as they pass through the material, but instead interact to form virtual particles that have mass, slowing them down. If so, then these interactions take time, and so the interaction of the photon with the mirror would take time. And if that were the case, the SR Einsteinian clocks, as well as Ligos, should have to account for this. Do I have this right?

 

[Vanadium 50]

It is my understanding that photons ALWAYS move at c, even in materials, even though I commonly read that the speed of light in a material can be less than c. The distinction is that the electromagnetic wave, a collection of photons, does go less than c in a vacuum, but not the individual photons. The photons remain at c, but because of the interactions, they are not always photons as they pass through the material, but instead interact to form virtual particles that have mass, slowing them down.

That is not your understanding, but rather your misunderstanding. See https://www.physicsforums.com/insights/do-photons-move-slower-in-a-solid-medium/

 

[43arcsec]

Thanks Vandium50. I read the link, finding this:

"So the lattice does not absorb this photon and it is re-emitted but with a very slight delay. This, naively, is the origin of the apparent slowdown of the light speed in the material. "

Which doesn't seem too far off from my misunderstanding. If I correct my statement by eliminating the "interaction to form virtual particles that have mass" and replace it with "interaction with the phonons of the material," in essence it is the same result: The interactions slow down the photon in the aggregate. I see nothing in that link that refutes the idea that between "it is re-emiited" and "interacting" the photon can still be traveling at c. But the bigger point is if the photon and the mirror surface interact similar to a photon traveling through a medium, then I'm still thinking there is a slowdown at the mirror which would need to be accounted for.

 

[Cthugha]

Thanks Vandium50. I read the link, finding this:

"So the lattice does not absorb this photon and it is re-emitted but with a very slight delay. This, naively, is the origin of the apparent slowdown of the light speed in the material. "

Which doesn't seem too far off from my misunderstanding. If I correct my statement by eliminating the "interaction to form virtual particles that have mass" and replace it with "interaction with the phonons of the material," in essence it is the same result: The interactions slow down the photon in the aggregate. I see nothing in that link that refutes the idea that between "it is re-emiited" and "interacting" the photon can still be traveling at c. But the bigger point is if the photon and the mirror surface interact similar to a photon traveling through a medium, then I'm still thinking there is a slowdown at the mirror which would need to be accounted for.

Photons are simply not eigenstates of the electromagnetic field inside a material. You need to consider the collective response of the material to the incoming field. These contributions cannot be divided.

With respect to the time delay upon reflection: Have you heard about reflected light undergoing a phase shift? This phase shift IS the whole delay occurring in the process of reflection and it is routinely accounted for in any interferometric application.

 

[Nugatory]

then I'm still thinking there is a slowdown at the mirror which would need to be accounted for.

We don't care what the round trip time for a photon is, we care what the round trip time for successive wave crests in the light wave is. These might be the same if the wave crest were a bunch of photons moving through space the way a river is a bunch of water molecules moving through space... but it's not. In fact, for this problem you would be better off forgetting that you ever heard the word "photon". That saves you having to deal with some really hairy quantum electrodynamics that complicates the problem while adding no new physical insight. Instead, just use ordinary classical optics, calculate an upper bound on the possible error introduced by using this approximation, and consider whether that error is enough to invalidate the analysis.

It would be a good exercise to calculate an upper bound for yourself:
- reflection happens in a layer only a few atoms thick, so the hypothetical delay there will be in order of magnitude terms the time that light takes to traverse a distance of a few atomic diameters.
- slowdown from the light moving through the glass face in front of the mirrors reflective surface can be approximated by knowing the thickness of the glass and the speed of light in glass.
- For the thought experiments in which we imagine light clocks, we don't care about the exact value of the round trip, we care about the ratio of the round trip times under different conditions.

 

[43arcsec]

So summing up, a photon heads towards a mirror, at the mirror, something complicated yet instantaneous happens, resulting in a photon seemingly being reflected with the same energy in the opposite direction with 0 delay. How's that?