The bare charge of the electron is the same as the apparent charge?

Let us assume that there really is a sign error in the traditional way that the vacuum polarization diagram is added to the plain photon propagator. Instead of weakening the electric attraction, the diagram strengthens it.

   virtual photon p

             ~~~~~~~~~~~ O ~~~~~~~~~~~

                                       virtual pair loop

Let us study the consequences.

1. Keep the cutoff very large. Then the diagram greatly enhances the electric attraction. The "bare charge" of the electron has to be minuscule in the absolute value. We see that little charge greatly magnified when we measure the electron from a macroscopic distance, for example, in the Millikan-Fletcher experiment.

2. Put the cutoff at the natural value |p|, where p is the exchanged momentum. In this case, the natural interpretation is that the bare charge is what we measure from a macroscopic distance. At short distances, creation of virtual pairs enhances the attraction.

In Case 1, we do "renormalization": the bare charge is hidden from us. We use the charge measured from a macroscopic distance. This is an ugly complication.

In Case 2, we have to find good grounds for using |p| as the cutoff. In this blog we have studied throughly destructive interference of the created virtual pairs. The interference is not trivial, because we have two particles, not just one. Case 2 is the beautiful solution. There is no need for an arbitrary cutoff or renormalization.

We can, of course, take as an axiom that there is destructive interference in this case. But it is better to prove the claim from general principles of quantum mechanics.

http://meta-phys-thoughts.blogspot.com/2021/08/feynman-vacuum-polarization-and.html

See the note at the start of the link. We got the correct Uehling potential with a 7% accuracy by putting the cutoff at |p|.

Is there destructive interference in virtual pairs?

We could model the two particles in the nonrelativistic case as a single particle in 6 + 1 dimensions. Then we probably get destructive interference for large 7-momenta.

What is the 7-dimensional wave function of the single particle? 

The Dirac wave function of the positron rotates to the opposite direction to the wave function of the electron. If we take the product of the two, we get a strange non-rotating wave function. Note that the classic Dirac problem of negative energy states of the electron resurfaces here. There probably is destructive interference for this strange wave, too, for large 7-momenta.

Maybe we should interpret that the Dirac wave is a classical wave, and calculate the product from abstract complex waves? Then we could make both waves to rotate to the same direction. Then there is destructive interference.

Yet another model is that the electron wave in the loop "turns back in time". Then we have just one particle which travels back in time as a positron. In this case, there is destructive interference.