Although virtual photons are maybe best considered not to actually exist, it is said that electrostatic attraction and repulsion between two electrically charged particles can be mathematically modeled as being due to the exchange of virtual photons between the particles; in fact, in the (popular version of the) Standard Model (virtual, sometimes?) photons are the force carriers of the electromagnetic force. Can exchange of (virtual) photons really adequately model the electrostatic force? My problem with such an explanation is this (somewhat similar problems have been mentioned on PSE by others):
An electron might send out virtual photons, and another electron might be hit by one & be repelled from the first by conservation of momentum (there are, of course, problems with this involving simultaneous conservation of energy and momentum, which may be solved by not requiring this for virtual photons, [or perhaps by having only partial absorption of the incident photon, with the production of a lower energy one - is this experimentally disconfirmed?]), but what if a proton were hit by one? It would be repelled, also by conservation of momentum, but in actuality it is attracted. This problem is taken care of with the explanation using a classical electrostatic field by the field having a direction at each point, determined by the sign of the charge creating it, and a proton responding differently than an electron to that field because of the difference of the sign of its charge. However, conservation of momentum with the virtual photon would cause the proton to be repelled just as the electron is.
This could be taken care of by having the electron also emit negative mass virtual photons (which might be required anyway for conservation of mass/energy) and the proton interacting with those and so being attracted, but what would cause the proton to interact with the negative mass virtual photon & not the positive mass one? It can't be that protons always interact with negative mass virtual photons instead of positive mass ones, because, assuming protons also emit positive & negative mass virtual photons, another proton would have to interact with the positive mass one in that situation in order to be repelled. This can't be explained by the proton knowing whether the other emitting particle is positively or negatively charged, since under our assumption the interaction is to be explained by local interaction with the incident virtual photon, not by non-local, spooky action-at-a-distance direct interaction with the other particle.
The picture of the electromagnetic interaction via photons becomes more complex when some of the charged particles are accelerating, so that some of the photons are real - doesn't it?
Is it best to entirely give up the interaction via real and virtual photons picture, and just consider the electromagnetic interaction among charged particles as being the interaction of each with the quantized EM field of the others?