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There is a polemic about whether virtual particles EXIST, or are only a tool for making our calculi easier. Here is a doubt about their existence, and on the other hand, an argument in support of their existence.

Against: consider a charge q regarded from an inertial frame in which it is in movement. Then, the movement of the charge q produces a magnetic field that can act on whatever other moving charge would appear. The magnetic field can be said to be transmitted through the vacuum by virtual particles. But, in a frame of coordinates where q is at rest, it produces NO magnetic field. So, NO virtual particles. Then, virtual particles EXIST in one frame and DON'T EXIST in another?

In favor: there is NO action-at-a-distance. The nature works in one and same way when propagating some type of influence. E.g., inside a dielectric, the electric field between two charged plates is propagated from one atom-dipole to another. Why should the nature behave differently in vacuum, i.e. without some sort of dipoles?

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    $\begingroup$ I don't quite follow your magnetic field argument. In the frame where there is no magnetic field there is an electric field instead. This is true of all charged particles, virtual or not. $\endgroup$ Nov 19, 2014 at 0:44
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    $\begingroup$ What's your question, exactly? $\endgroup$
    – ACuriousMind
    Nov 19, 2014 at 0:49
  • $\begingroup$ To the Curious Mind: My question is: by the first argument the virtual particles can't exist, because if a particle IS, or ISN'T, be it real or virtual, can't depend on the frame of coordinates. By the other argument, the virtual particles HAVE to exist; action-at-a-distance is not the way the nature works, so it seems to me according to the behavior of the dielectric. Then, which is the truth, they exist or not? In other words, which one of my arguments is correct (if any), the one against, or the one in favor? $\endgroup$
    – Sofia
    Nov 19, 2014 at 2:05
  • $\begingroup$ The invariant mass of a particle is not changed by relative motion, so the virtual or real character of a particle is likewise not changed. $\endgroup$ Nov 19, 2014 at 4:50
  • $\begingroup$ To dmckee: this is equivalent to my argument against the virtual particles. It can't be that in one frame they exist and in another one they don't. But, what about my argument in favor of them? It seems also correct. Then which one is wrong? $\endgroup$
    – Sofia
    Nov 19, 2014 at 10:38

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Your argument against is based on the fact that in one frame there is no magnetic field, but there is a magnetic field in a different frame. So there must be magnetic virtual particles in some frames but not in others. Hence magnetic virtual particles can't exist.

However there aren't separate magnetic and electric virtual particles. There are just virtual photons that are responsible for both magnetic and electric fields. Your argument simply shows the virtual photons look different when viewed from different inertial frames.

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  • $\begingroup$ To John Rennie: Thank you for your answer. But, I have some doubts, please see. Why virtual photons should be the mediators of the electrostatic and magnetostatic field? In a dielectric what propagates the electrostatic field is the atoms distorted into dipoles, not photons. What I was told is by other people, and seemed plausible to me is that in vacuum appear virtual electron-positron pairs. Is seems to me equivalent to the dipoles. But what about the magneto-static field? How does it pass through the vacuum? Why virtual photons and not virtual particles carrying magnetic momentum? $\endgroup$
    – Sofia
    Nov 19, 2014 at 19:21
  • $\begingroup$ An electron does not attract a virtual photon, the electron can move in the field of a virtual photon. But I think that nobody saw an electron changing its state of movement "out of the blue" (i.e. due to the virtual photons". Then how can the distant proton feel the electron? $\endgroup$
    – Sofia
    Nov 23, 2014 at 13:18
  • $\begingroup$ It's important to note here that photons are vector particles, and this is why they look different in different reference frames. $\endgroup$ Dec 19, 2014 at 23:46
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Virtual particles never been considered "real" in any serious interpretation of QFT for two reasons:

1) what we call virtual particles are just terms in a series at some order of a coupling constant,

2) there's no way to interact with them.

An interaction between two physical objects is a black box in QFT. The way people usually use to "see" inside this black box is via perturbation theory. The concept of virtual particle is there a convenient way to make sense of such computation, because it allows you to interpret each terms via Feynman's diagrams, and that's all it is. In QFT, the "primitive" physical objects are not particles at all but fields. So if you take QFT seriously, you would have to forget about the particles interpretation of physics.

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