I’ll level with you. I know how to use QED to compute the cross section of a scattering reaction. But I do not remember, or perhaps never knew, what the QED theoretic description of classical wave mechanical phenomena like diffraction, reflection, refraction, and dispersion look like.
Well… actually of those phenomena, I think diffraction is fine. A single waveform will exhibit diffraction. It doesn’t entail any interactions. A single photon can still exhibit a diffraction pattern. It doesn’t mean that the photon has changed directions or circled around or in any way accelerated. The only reason you might think so is that you’re thinking of photons as billiard ball type classical particles, but of course they are not, they are quantum particles with spread out wavefunctions.
Dispersion I guess is just scattering combined with absorption re-emission (and as we discussed, even scattering is itself a form of absorption & re-emission). But as for reflection and refraction? Those are the phenomena that Entropius was pointing to elsewhere in this thread. I remember how those look in terms of solutions to Maxwell’s equations and boundary conditions, but that’s classical wave mechanics. I do not remember how to translate that into the language of QED.
QED is a fundamental theory, so I assume that a description exists, and of course because I know what QED looks like, so I am certain that it will still be true that in this description, photons will be absorbed & emitted by charged particles, but photons will not interact with photons. However beyond that I cannot say much. How do we describe reflection of light in a mirror as photons scattering off electrons? I don’t know exactly.
One thing I can say is that generally classical states are modeled in quantum mechanics as coherent states, which are eigenstates of the annihilation operator. They look something like exp(N)|0> where N is the number operator, which means that they are states with a superposition of 0 photons, 1 photons, 2 photons, etc. They don’t have a well defined number of particles. So maybe if you want a QED theoretic description of reflection, you can have it, but you won’t be able to talk about specific numbers of photons. But again, I don’t know the details of this.
I wonder whether this concept of classical waveforms as coherent states with a superposition of all numbers of particles will help at all with this philosophical debate about whether two photons are the same particle or not, or about whether you can have a universe with only 3 photons