Initially Wheeler and Feynman postulated that, the electromagnetic field is just a set of bookkeeping variables required in a Hamiltonian description. This is very neat because makes the point of divergent vacuum energy a moot point (i.e: an example of asking the wrong question)
However, a few years later (1951), Feynman wrote to Wheeler that this approach would not be able to explain vacuum polarization.
Anyone knows what was the argument for saying so? I don't see how allowing both processes with entry and exit particles and processes that begin in pair-creation and end in pair-annihilation makes the existence of a field a requirement.
Answer
the original strategy of Feynman and wheeler was really about the desire to get rid of all self-interactions. In the modern language, it would eliminate most loop diagrams.
In particular, consider an electron propagator, in the modern language. One may attach a photon propagator on it. That modifies the electron's self-energy, and this is the kind of a term that the Wheeler-Feynman program wanted to eradicate completely. However, if you add another complexity to the photon propagator - namely an electron-positron loop in the middle - then it is a nontrivial contribution, especially because the vacuum polarization loop may be attached to different parts of the diagram as well.
Their very idea would be that it is impossible for the same electron propagator to have two photon end points attached - that would be connected with one another. That would throw the baby out with the bath water. At any rate, no complete theory of their picture exists (or is mathematically possible) and their dreams and partial hints have only been a motivation for them to get the really important insights.
Best wishes Lubos
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