Why does a Feynman diagram simulate the Coulomb field?

In this blog we have touched this question many times. If we let high-speed electrons collide head-on, then their scattering can be calculated in two ways:

1.   from the Coulomb electric field, using classical physics, or

2.   from the simple Feynman diagram, by integrating the "probability amplitude".

https://en.wikipedia.org/wiki/M%C3%B8ller_scattering

It is easy to calculate that the Coulomb model and the Feynman model approximately agree about the scattering probabilities. But why do they agree?

Also, what is the "virtual photon" γ which the electrons exchange?

In the Feynman diagram, the photon is a Fourier component of Green's function which describes the impulse response of the electromagnetic field. What does it mean that the other electron "absorbs" that component?

The rubber foam model

In our previous blog post we introduced the rubber foam model as an analogue of the Coulomb field.

  

         ○○○○○○○○○○○

        ○○●○○○○○●○○○      ○ = rubber foam

         ○○○○○○○○○○○       ● = electron

Electrons move inside rubber foam. They have to clear enough space for themselves so that they can fit in. They use hammers to hit the foam, so that the foam is squuezed enough and the electron fits in the empty space. The hammers constantly knock the foam around the electron. This creates the required pressure.

If two electrons come close to each other, they have to squeeze the foam more. Let us assume that the foam resists squeezing superlinearly. Then the electrons have problems squeezing the foam between them. The electrons feel a repulsion.

In this model, the "virtual phonon" is easily understood: the first electron hits the foam and the other electron's hammer feels the impulse. The first electron emitted a virtual phonon, and the other one absorbed it.

Virtual phonons are the analogue of virtual photons.

***  WORK IN PROGRESS  ***