I have been reading similar discussions on how protons and electrons interact, using virtual photons and such. Yet, I can find little information regarding the subject in question. Can a beam of photons posses the characteristics of that of a virtual photon in a proton-electron interaction where the electron “thinks” there is a proton when there is not?

  • $\begingroup$ What energy is this interaction? In particular, does the internal structure of the proton matter? Also, for how long should this illusion last? For only an instant, for eternity, or otherwise? $\endgroup$ – probably_someone Jan 24 at 18:42
  • $\begingroup$ What energy? I assume electromagnetic, but with real photons? And the illusion, for some amount of time (e.x. one second or more, but not eternal). I am guessing the internal structure of the proton shouldnt matter since that isnt really involved in this interaction (to my knowledge). $\endgroup$ – Terran Jan 24 at 19:57

It is commonly said that the electric force is due to the exchange of virtual photons but you need to be very cautious about this statement. The electric force is calculated as if it was due to the exchange of virtual photons, but this is a computational device and virtual photons do not actually exist. There are no virtual photons being sent and received by your proton.

If you shine light at the proton there will indeed be an interaction. With high energy light we get Compton scattering or at lower energy Thomson scattering. But neither of these resemble the electrostatic force. The (real) photons do not produce anything like the electrostatic force because the electrostatic force is not transmitted by photons - it is just calculated that way.

  • $\begingroup$ So, what is it then? $\endgroup$ – Terran Jan 26 at 1:34
  • $\begingroup$ @Terran the interaction between charges is described by quantum field theory, which I'm afraid is pretty complicated. $\endgroup$ – John Rennie Jan 26 at 5:40

No, you cannot. Virtual photons are mainly the famous Coulomb field, it does not propagate like photons to infinity.

  • $\begingroup$ Is there some kind of intrinsic property of virtual photons that disallow this kind of interaction, assuming that the photons dont need to maintain this property at infinity, and only for a short while? $\endgroup$ – Terran Jan 24 at 20:01
  • $\begingroup$ Not really. In QED there is a notion of "equivalent photons" in collision description for high energies. But it is an exotic case, and it does not give virtual photons the status of real ones. $\endgroup$ – Vladimir Kalitvianski Jan 24 at 20:09

An electron accelerates towards a proton with the exchange of series of virtual photons. In principle, you could produce the same acceleration by bouncing photons of the same energies off the electron with the same timings. It's the electromagnetic equivalent of the equivalence of gravitational and inertial interactions. Though at this scale the Uncertainty Principle makes it virtually impossible in practice.

  • $\begingroup$ Is this true when the relevant photons are off-shell? As far as I know, you can't make a beam of off-shell photons; the best you can do is stick a charge near the electron, which I'm pretty sure isn't what the OP is asking about. $\endgroup$ – probably_someone Jan 24 at 18:58
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    $\begingroup$ The answer is incorrect. You cannot pull an electron with real photons, but only push. $\endgroup$ – safesphere Jan 24 at 19:31

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