Ball throwing model and some questions about QED

[sf1001]

I read recently in my old ugrad 2012 solid state physics textbook, in its discussion of the attractive force between electrons in cooper pairs (in superconductors), that the attractive force between cooper pairs is explained mostly by the exchange of phonons (a quasiparticle associated with the displacement of atoms (and resulting increase in energy) in a crystal lattice. It explained that the exchange between mutually attracted particles could be thought of as two people exchanging helium filled balloons on Earth's surface; implying (I think) that this attractive force between the electrons in cooper pairs is only possible because of the interactions of the phonons with either the crystal lattice itself, or maybe other phonons.

I'm only familiar with the non-relativistic Schrödinger equation, which only includes a scalar potential; I figured the equations governing photons would also have a vector potential, which would not be independent of the photon's wave function, thus making the wave equations for photons nonlinear. When trying to look up info. about this, I came across a Wikipedia article that said that wave equations for photons in QED are nonlinear in a vacuum, and that this allows photons to interact with themselves and other photons.

I read in my ugrad intro. to electrodynamics textbook that "(classical) electrodynamics extends with unique simplicity to (quantum mechanics and quantum field theory)". However, in classical electrodynamics, I think that if a sinusoidal planar electromagnetic wave began to travel through a region with an electric or magnetic field that did not vary with time, the wave pattern would be unaffected except for the addition of a constant to B(t) and E(t) when the wave travels through the region with the time-independent fields. I would guess that A: this slightly contradicts the behavior of E&M fields that one might expect from QED.

I read in my intro. modern physics textbook that in general, energy, matter, etc. can be thought of as existing in waves or fields when propagating, and as particles when interacting. This would suggest that classical electrodynamics could mostly explain how E&M fields behave in a vacuum, but this would contradict point A (from last paragraph). In my modern optics ugrad class, I generally got the impression that the behavior of E&M fields was assumed to be fully consistent with Maxwell's equations (which contradicts A), but the deviations of atomic matter from the Lorentz force Law could be explained (almost fully) by QED. My modern physics textbook also mentioned that, according to some theories in particle physics and cosmology, all particles could be thought of as quasiparticles.

In QED models of two oppositely charged particles exchanging photons resulting in an attractive force, is this attraction best explained via the photons interacting with themselves and other photons, or the photons' interaction with some type of structure in the vacuum of space, which might be suggested by some theories in particle physics and cosmology that regard all particles as quasiparticles?

 

[Simon Bridge]

In QED models of two oppositely charged particles exchanging photons resulting in an attractive force, is this attraction best explained via the photons interacting with themselves and other photons, or the photons' interaction with some type of structure in the vacuum of space, which might be suggested by some theories in particle physics and cosmology that regard all particles as fictitious?

None of the above.
The virtual photons that mediate the EM interaction are thought of as interacting with the charged particles.
The attraction/repulsion effect comes from symmetries in the photon wavefunction.

I don't know that "fictitious" is a helpful word to use to describe virtual particles.