Does vacuum polarization turn Newton's gravity into Einstein's gravity?

UPDATE October 7, 2021: We were not able to find a reasonable model where vacuum polarization makes the gravitational field infinitely strong at the event horizon. Instead we found out that newtonian mechanics explains the effect. See our blog post today.

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There is a similarity in the gravitational force in general relativity and the Coulomb force in QED.

In both cases, the force at long distances is from a pure 1 / r potential, but at short distances the force grows stronger.

In QED we can explain the growth with vacuum polarization.

                e-  •    ----------->

                     +     vacuum

                     -      polarization

                    ●

                proton

                  

The acceleration of the electron causes a virtual pair to appear between the electron and the proton. The pair is a dipole which attracts both the electron and the proton.

In gravity, the analogous diagram is the following:

          

                     -    vacuum

    Mercury  •     ----------->

                     +    polarization

                    ●  Sun

The acceleration of Mercury causes virtual pairs of photons to appear. The positive energy photon flies between Mercury and the Sun, while the negative energy one flies behind Mercury. The photons must have extremely small positive/negative energy because they have to move over large distances.

In recent weeks we have claimed that in QED, the large-distance physics is the "true" physics, and it is modified at short distances through vacuum polarization and other processes.

Maybe newtonian gravity is the "true" gravity, and it is modified at short distances through vacuum polarization and other processes. General relativity would have its origin in quantum physics.

In QED we have single particles while in gravity we have lumps of 10⁶⁰ particles. We need to figure out how to handle a large number of particles in quantum field theory.

In QED, the electromagnetic field couples to electrons and positrons. The interaction is a source for the Dirac field. Conversely, an electron couples to the electromagnetic field and acts as a source.

Gravity couples to all matter fields. All matter particles act as a source of gravity. Conversely, gravity should act as a source for all kinds of matter fields.

There is a problem: if all matter fields contribute to making gravity stronger, why are the Einstein equations independent of quarks and so on? The reason might be that only photons can have low enough energy so that they can stay off-shell long enough to contribute to vacuum polarization. The lifetime of a virtual pair has to be minutes if it has to travel over planetary distances.