I'm afraid that it really isn't a question of interpretation; in QED, the only interactions which can ever take place between charged particles are via the electromagnetic field, and the only interactions which can ever take place between photons are via the charged fields. I gave a quick explanation of that above, but I will expand on it here to see if I can't clear up a few potential misunderstandings.

The QED Lagrangian for electrons, positrons and photons is

where

Every prediction of the theory, every statement it has to make about nature, is contained in that Lagrangian.

1. Which terms have to do with

*direct* interactions between the charged particles and the photons? Easy; we just look for the terms which involve both types of field. There is only one such term:

(Note that this is also, and not coincidentally, the only term which includes

*e*.)

2. Which terms involve

*direct* interactions between the electron-positron field and itself? Easy; we need to find terms involving three or more factors of ψ. There are none.

3. Which terms involve

*direct* interactions between the photon field and itself? Easy again; we need to find terms involving three or more factors of

*A*. There are none.

4. What happens if we delete the interaction term identified in #1 above? We are left with a simple Lagrangian describing two

*free fields*, something so simple we can solve it exactly without perturbation theory. There is a massive fermion ψ and a massless boson

*A*, and neither field has any interactions whatsoever. There is, of course, no sensible notion of "charge". There are no scattering processes, no bound states, no annihilations, no pair productions, etc. We see quite clearly that the deleted interaction term is responsible for

*all* of the interactions of the theory.

5. Returning to the full QED Lagrangian, with the interaction term restored, does this mean the electrons cannot interact with each other? No! Of course they will interact (or what a poor theory of electrodynamics this would be!), but they do so

*indirectly*, via the processes predicted by the coupling term

. For example, an electron can introduce a kind of condition in the electromagnetic field which in turn influences the behaviour of other electrons, and so on.

6. How about photons? Are they forbidden to interact by QED? No! They too will interact, but they do so

*indirectly* via processes predicted by the same coupling term

. For example, a photon can introduce a kind of condition in the electron-positron field and thereby affect other nearby photons, if the conditions are just right.

7. We see that it is the interaction term

, coupling the charged particles to the photons, which permits - in fact,

*demands* - the flow of energy and momentum between the charged field and the photon field in precisely-goverened ways. It is this term which gives rise to the Lorentz force. It is also this term which makes electrons and positrons contribute to the charge and current density terms in Maxwell's equations in the classical limit, and which predicts annihilation and pair production processes. It is this term which predicts that photon-photon scattering must occur.

The quality of being "satisfactory" is subjective, of course. As it happens, I find QED, and gauge theories generally, deeply satisfying. QED explains how what we observe as "charge" arises from very deep symmetries of the laws of physics. Those same principles that explains how "charge" arises also gives rise to precise, quantitative laws which tell us how "charged" objects interact. Those principles, in fact,

*demand the existence of the electromagnetic field!* Above all, the theory of electrodynamics resulting from those principles has performed truly superbly in experiments. But it doesn't even end there! The same principles, generalised, underlie electroweak unification and quantum chromodynamics. There's no denying that there is room for improvement in the Standard Model, but it is truly amazing that such a simple idea, gauge symmetry, should work at all, never mind as amazingly well as it does.

In my previous post, I attempted to express something in human language which, unfortunately, cannot easily be so expressed without discarding the greater part of its precision and elegance, the two very traits which make the idea so theoretically attractive in the first place. Nature apparently speaks mathematics, not English, and in particular seems to speak abstract, difficult mathematics. As such, I have not been able to do the idea proper justice in a forum post (although I have given you a decent pointer in Zee's book, and you can learn the precise details if you wish). However, forget that for a second. Suppose for argument's sake that the idea were not satisfactory, even when fully understood. The question is:

*why should it be?* We do not have any

*a priori* reason to suppose that nature should behave in a way which any one of us feels is satisfactory. A pearl of wisdom from one of the founders of modern QED is apt here;

*"We are not to tell nature what she's gotta be... She's always got better imagination than we have!"*