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2 points

There is no tree level photon-photon interaction. Photons scatter off electrons (or any other charged particle), not off neutral photons.

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4 points

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.

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2 points
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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.

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3 points
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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.

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