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In vacuum, high-energy photons interact via virtual electron-positron pairs: photon-photon interaction

Is this interaction attractive or repulsive? In other words, if two photons are initially parallel and they are observed, will the distance between them increase (repulsive) or decrease (attractive). Can we get the answer from calculating the amplitude?

Rd Basha
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    How do you define attractive for the purposes of this question? – Roger V. Jul 08 '22 at 09:48
  • Let's say I have two parallel (high-energy) lasers with some distance between them. Does the light that hits the screen hit closer or farther? Does it depend on the energy? on the distance? – Rd Basha Jul 08 '22 at 10:40
  • Just to narrow it down, the two photons start with the same wavector (direction) and frequency? – Mauricio Jul 08 '22 at 11:10
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    Each vertex brings down the crossection of photon photon scattering by $(1/137)^{1/2}$ ( http://www-pnp.physics.ox.ac.uk/~barra/teaching/feynman.pdf) and at the level of photons this means effectively no interaction, between beams of photons, as the extra statistical probability of photon interacting coherently , all zilions of them in a laser beam. will be zero, imo .https://physics.stackexchange.com/questions/242184/probability-of-photon-to-photon-collision/242289#242289 – anna v Jul 08 '22 at 11:27
  • Of course this effect is very small in an actual laser. But we can still ask the question: If I send on photon at a time, and wait a long time- there will be interaction. Is it attractive? This is a measurable effect- it was measured in the LHC. – Rd Basha Jul 08 '22 at 11:33
  • @RdBasha could you provide a source for the LHC measurement? – Mauricio Jul 08 '22 at 11:52
  • https://home.cern/news/news/physics/atlas-observes-light-scattering-light – Rd Basha Jul 08 '22 at 11:56
  • https://cdsweb.cern.ch/record/2667214 – Rd Basha Jul 08 '22 at 11:56
  • Correct me if I am wrong, but those are not collisions of parallel photons. Right? – Mauricio Jul 08 '22 at 12:01
  • Right. I'm just saying that the effect exists and is measurable. That means that in principal two light beams should interact. – Rd Basha Jul 08 '22 at 12:07
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    You are asking about two laser *beams . "two parallel (high-energy) lasers with some distance between them" , There might be measurable effects if two high energy laser beams are split from one original, as coherence is established , There are interesting experiments in the MIT site with lasers example https://www.youtube.com/watch?v=J4Ecq7hIzYU . High photon energy does not look an active research subject https://www.quora.com/What-is-the-highest-frequency-laser-and-what-challenges-exist-for-making-a-higher-frequency-laser – anna v Jul 08 '22 at 13:25
  • related:https://physics.stackexchange.com/questions/561326 and https://physics.stackexchange.com/questions/1361 – AlmostClueless Jul 08 '22 at 13:37
  • I doubt the nanobarns involved here would scare you; I assume you appreciate this is a very *short distance* phenomenon... – Cosmas Zachos Jul 08 '22 at 15:28
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    Note the conventional Coulomb potential derived from the Born amplitude of the one photon exchange in QED has no intrinsic scale, unlike the γγ scattering amp, which is limited by the Compton wavelength of the electron (the lightest charged particle). So there is no long range "classical" potential and your title question is meaningless. – Cosmas Zachos Jul 08 '22 at 15:52

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