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I know my question might have problems, but I am curious about it. In quantum field theory, particle-antiparticle pairs continuously pop in and out of existence from vacuum. These particles have a very short lifetime, at the scale of 10^-22 seconds. My question is, taking into account the QED which says that all electromagnetic forces are created by the exchange of virtual photons, can such shortly-living particles exchange any photon in their short lifetime and somehow perturb the electric field around them?

P.S. I know that according to the standard quantum mechanics, "vacuum fluctuations" only occur at the time of observation, and are NOT about dynamics of the system. I am talking in the scope of realistic observer-independent interpretations like Bohmian mechanics. In such interpretations, I think there is no explanation for the fluctuations other than that something is really happening in the real time.

I am going to write a careful answer, but I think it should be noted at the outset that the popular phrase "popped into existence" is entirely without meaning, as far as I can tell. Nothing ever has, or will, or even could "pop into existence". Physics is about cause and effect.

If I have a flat piece of paper and then I shake the paper, then a bump or a crease may appear where there was no such bump before. But it would be odd, I maintain, to say that the bump "popped into existence". The bump is a feature of the shape of the paper, and the paper has been manipulated. Such remarks can be transported quite straightforwardly to particle physics, where the paper is the quantum field and the bump is the type of excitation we call a particle.

Now you have in mind virtual particles, and you suggest that there are virtual particles in the vacuum. So let's consider that.

'Virtual particle' is the name we give to the internal lines in Feynman diagrams. There are plenty of Feynman diagrams having lines leading to loops, including virtual particle-anti-particle loops, and the result of the calculation represented by the diagram then does depend on the presence of these loops. So in this sense these virtual particles have physical effects. But this is putting the cart before the horse! The virtual particle is a part of the physical effect! The physical effect is the interaction of one quantum field with another. The virtual particles are a convenient way to lay out the calculation of that interaction.

All the diagrams I have discussed so far involve external lines: the incoming and outgoing physical entities whose interaction is being calculated. So they are not vacuum diagrams.

One can also draw diagrams containing "vacuum bubbles", i.e. a self-contained set of vertices and lines not connected to anything else. These diagrams represent integrals (as do all Feynman diagrams) and these integrals have strictly no effect on anything at all. They do not influence the outcome of any calculation involving external lines.

Finally, I note your P.S. and that your interest is in trying to figure out how field theory works from a Bohmian point of view. I guess the bottom line is that whatever view of quantum mechanics one takes, one wants ultimately to get accurate predictions of what measuring apparatuses will do. All my comments above are about that very thing: what the prediction is for observable behaviour such as detector clicks.

Yes, virtual electron-positron pairs in the quantum vacuum have electromagnetic effects. They modify the standard Lagrangian for electromagnetism into something called the Euler-Heisenberg Lagrangian.

One interesting physical effect caused by these vacuum fluctuations is the scattering of light by light. In classical electromagnetism, two light waves pass right through each other without interacting. In QED, the photons scatter off of the charged virtual electrons and positrons in the vacuum.

Another interesting physical effect is that if you create a sufficiently large electric field, the virtual electrons and positrons in the vacuum become real electrons and positrons. So you can create real matter and antimatter from just an intense, constant, uniform electric field.

As far as I know, neither of these effects has yet been observed, but they are predictions of QED, which is extremely well-verified.

Effects of vacuum fluctuations which have been observed include the “Lamb shift” of the energy levels of hydrogen, and the anomalous magnetic dipole moment of the electron. These are subtle effects which are essentially small corrections, as opposed to the first two effects I mentioned, in which vacuum fluctuations allow something totally new to happen.