As far as I understand, “a photon in a medium” is a quasiparticle. Actual photons always travel at the speed of light, and the “photon” that travels through glass at a lower speed is the sum of an incredibly complicated process that cancels out perfectly into something that can be described as one or several particles if you squint a little because the energy of the electromagnetic field excitation can’t be absorbed by the transparent material and because of preservation of momentum.
The model of the photon “passing by atoms and plucking them” is a lie to children, an attempt to describe a quantum phenomenon in classically comprehensible terms. As such, what “the momentum of the quasiparticle” is depends on what you consider to be part of the quasiparticle, or which parts of the quasiparticle(s) you measure when doing an experiment.
Specifically, for the mirror-in-a-liquid, when light hits the liquid it is refracted. That refraction makes the angle of the path of the light more steep, which means the mirror has to reflect momentum that is entering at a more steep angle, and so the momentum the mirror measured is multiplied by the refractive index. At the quasiparticle level, when hitting the liquid interface, the light interacts with the quasiparticle phonon [sic] field of the liquid, exchanging momentum to redirect the quasiparticle light, and the mirror has to reflect both the quasiparticle light and the phonon field, resulting in the phonons being included with “the momentum of the light”.
However, for the light-through-a-glass-fiber, you are measuring the momentum of the phonons as part of the not-light, because the phonons are part of the medium, so part of the glass fiber getting nudged by the light beam.
I’m not sure how this works out in rigorous calculation, but this is my intuition pump for a [1]-ish answer.
I think you might have muddled the numbering? It looks like you have written an argument in favor of either [2] or [3] (which both hold that the momentum of the full polariton is larger than the momentum of the photonic part alone—in the cartoon of the original post whether or not the momentum “in the water” is included), then committed to [1] instead at the end. This may be my fault, as the order I numbered the arguments in the summary at the end of the post didn’t match the order they were introduced, and [2] was the first introduced. (In hindsight this was probably a bad way to structure the post, sorry about that!)
″ “passing by atoms and plucking them” is a lie to children ”—I personally dislike this kind of language. There is nothing wrong with having mental images that help you understand what is going on. If/when those images need to be discarded then I don’t think belittling them or the people who use them is helpful. In this case the “plucking” image shows that at any one time some of the excitation is in the material, which is the same thing you conclude.
[In this case I think the image is acceptably rigorous anyway, but lets not litigate that because which mental images are and are not compatible with a quantum process is a never ending rabbit hole.]
Thank you very much for reading and for your thoughts. If I am correct about the numbering muddle it is good to see more fellow [2/3]’ers.
As far as I understand, “a photon in a medium” is a quasiparticle. Actual photons always travel at the speed of light, and the “photon” that travels through glass at a lower speed is the sum of an incredibly complicated process that cancels out perfectly into something that can be described as one or several particles if you squint a little because the energy of the electromagnetic field excitation can’t be absorbed by the transparent material and because of preservation of momentum.
The model of the photon “passing by atoms and plucking them” is a lie to children, an attempt to describe a quantum phenomenon in classically comprehensible terms. As such, what “the momentum of the quasiparticle” is depends on what you consider to be part of the quasiparticle, or which parts of the quasiparticle(s) you measure when doing an experiment.
Specifically, for the mirror-in-a-liquid, when light hits the liquid it is refracted. That refraction makes the angle of the path of the light more steep, which means the mirror has to reflect momentum that is entering at a more steep angle, and so the momentum the mirror measured is multiplied by the refractive index. At the quasiparticle level, when hitting the liquid interface, the light interacts with the quasiparticle phonon [sic] field of the liquid, exchanging momentum to redirect the quasiparticle light, and the mirror has to reflect both the quasiparticle light and the phonon field, resulting in the phonons being included with “the momentum of the light”.
However, for the light-through-a-glass-fiber, you are measuring the momentum of the phonons as part of the not-light, because the phonons are part of the medium, so part of the glass fiber getting nudged by the light beam.
I’m not sure how this works out in rigorous calculation, but this is my intuition pump for a [1]-ish answer.
Yes, you are certainly right it is a quasiparticle. People often use the word polariton to name it (eg https://www.sciencedirect.com/science/article/pii/S2666032620300363#bib1 ).
I think you might have muddled the numbering? It looks like you have written an argument in favor of either [2] or [3] (which both hold that the momentum of the full polariton is larger than the momentum of the photonic part alone—in the cartoon of the original post whether or not the momentum “in the water” is included), then committed to [1] instead at the end. This may be my fault, as the order I numbered the arguments in the summary at the end of the post didn’t match the order they were introduced, and [2] was the first introduced. (In hindsight this was probably a bad way to structure the post, sorry about that!)
″ “passing by atoms and plucking them” is a lie to children ”—I personally dislike this kind of language. There is nothing wrong with having mental images that help you understand what is going on. If/when those images need to be discarded then I don’t think belittling them or the people who use them is helpful. In this case the “plucking” image shows that at any one time some of the excitation is in the material, which is the same thing you conclude.
[In this case I think the image is acceptably rigorous anyway, but lets not litigate that because which mental images are and are not compatible with a quantum process is a never ending rabbit hole.]
Thank you very much for reading and for your thoughts. If I am correct about the numbering muddle it is good to see more fellow [2/3]’ers.