Are you claiming this is done without a force carrier? If you are working outside the standard model, I guess that’s fine, but I don’t want to spend time arguing with you.
The electromagnetic field does have a force carrier. It is the photon.
The photon mediates the force between electrically charged particles. It cannot mediate any reaction between two neutral photons.
Ah, I see. Sorry for the snark. I was thinking more in line with the Compton effect, and thought you were talking about something like that too. (Even though it’s clear that you were explicitly not. I thought you were denying photon-virtual photon interaction because I was talking about it in a funny way.)
I would still say it’s still philosophical whether photons experience acceleration, but I concede that photon-photon interaction is not done by virtual photon exchange.
I am indeed denying the existence of photons interacting with virtual photons. I am also saying there is no tree level photon-photon interaction of on shell photons. Neither Compton scattering nor Bhabha nor pair production nor pair annihilation involves a photon-photon interaction. There is no photon-photon vertex in QED. There is no tree level Feynman diagram that you can look at and say “this is, at least philosophically, a photon changing its momentum”.
There is a 1 loop diagram that represents photon-photon scattering. But even that doesn’t have any photon-photon vertices, instead it is mediated by electron-positron pair.
Non-abelian gauge bosons (gluons) couple to themselves. So does gravity (gravitons). Abelian ones (photons) do not.
Photons don’t accelerate. They are emitted or absorbed. That’s their only interaction.