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I was reading this post, that discusses whether if virtual particles do exist; stating that they are only a mathematical artifact that arises from perturbation theory. My question is, if virtual particles (which in Feynman Diagrams are said to be the mediators of a force) do not really exist, how the theory predicts this interactions? Do this interactions happens smoothly? Is something really interchanged between particles to know they are near each other; or the mathematical model is too simple to describe this interactions (maybe the way the model is done works, so why ask it for more)? Does this interactions have finite speed?

I remember a something I read from Newton in which he stated that something he hated from his theory of gravitation is "action at a distance", like if the force of gravity was some kind of magic acting on all particles instantaneously. If virtual particles does not exist and nothing mediates the force (because the model does not account for this), wouldn't this be a case of "action at a distance"?

EDIT: I don't want to know the equation that governs this particles interactions, I want to know what the model predicts during this interactions and understand whether if all of this are only mathematical procedures or if there is physics underlying the process.

Álvaro Rodrigo
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Forces are mediated by fields. That is the F in QFT. You can write the fields in many different ways. Sometimes it makes sense to write them in terms of "real" particles and sometimes it makes sense to write them in terms of "virtual" particles. But regardless of how you write them and regardless of the reality that you assign to the terms that you use in writing them, it is always the field that mediates the force.

Be aware that many times you cannot write a field in terms of a definite number of photons. For example, a coherent state has a sort of uncertainty relationship between the number of photons and the phase.

Dale
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