Coulomb law and photons

Question

When we consider process like

$e^- e^- \to e^- e^-$

in QED, we see that from exchanges of one photon (tree-level diagrams) one can obtain Coulomb's law, while loop-diagrams give quantum corrections to this law. I know that virtual particles, which appear in loop-diagrams, are not observable. But real particles can be observed.

So, I wonder, are such photons that contribute to classical Coulomb's law (tree-level diagrams) observed? For example, we can increase distance between two electrons, so that virtual photon becomes almost real.

Or is there any way to experimentally show that electromagnetic forces are caused by discrete particles - photons?

Answer 1

It does't really make much sense to talk about a tree-level truncation (it helps for calculations, but that's it) or to take the first Feynman diagram as a true representation of reality. By the way, in your $e^- e^- \to e^- e^-$ example, the whole notion of spatial separation is ill-defined since this is a t-channel process.

If going from virtual to real photon were possible here, you'd be able to create a single photon out of the annihilation of an electron-positron pair ... however, energy-momentum conservation forbids such a thing to happen (see this discussion for instance).