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I have read these questions:

Virtual Photon transmission speed of a Static Electric Field?

where John Rennie's comments say:

Virtual photons can travel faster than light

Is there a "difference" between photons that act as virtual particles and photons that act as the quanta of EM radiation?

where D.W.'s and Neuneck's comments say:

Re (1) - Do you really mean "...immediately caught by another particle"? Wouldn't it need to still move at the speed of light? – D. W. Jun 5 '14 at 18:02 1 upvote flag No. Since they are not required to have energy and momentum on the mass shell (see rob's answer), other limits do not apply either. One naive way of picturing this is that the interaction between two electrons via a photon takes place as a small lightning bolt, connecting the two electrons for an instant, allowing momentum to be exchanged. After the lightning bolt disappears the electrons change their direction and are oblivious of each other again. – Neuneck

https://profmattstrassler.com/articles-and-posts/particle-physics-basics/virtual-particles-what-are-they/

Speed of electromagnetic interactions

How fast does the electrostatic force travel?

And it made me curious.

We know that virtual photons are off mass shell, and they do not have to obey some physical rules.

But still they are the mediators of EM interactions, and the speed of the static fields (the interaction between static fields) seems to be instantaneous based on the answers.

We know that there are instantaneous processes as per QM, like the absorption/emission of real photons, and the electron's movement to a higher energy level as per QM by absorbing a real photon.

Now in the case of an electron moving to a higher energy level, that is explained by the probability distribution of the wavefunction, where the wavefunction describes the probability to find the electron at a certain energy level, and that wavefunction changes instantaneously.

I do not know if the virtual photons exchange is the same, described by the wavefunction and it can change instantaneously.

Question:

  1. Are virtual particles traveling faster then c mathematically (because of the wavefunction's instantaneous change)?

  2. If they are just a mathematical description of the interactions (that we cannot explain in a classical view), then how does the math count for the instantaneous interactions speed? Is it the same as per QM, the instantaneous processes like photon absorption/emission, energy level movement of electron?

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  • $\begingroup$ Just curious, HOW do we know "there are instantaneous processes as per QM, like the absorption/emission of real photons, and the electron's movement to a higher energy level as per QM by absorbing a real photon."? We know they are going to go to completion, always, once started, but instantaneously? $\endgroup$ – user198207 Jul 7 '18 at 18:55
  • $\begingroup$ As I like to stress , the equations of quantum field theory are fully on agreement with causality. $\endgroup$ – my2cts Jul 7 '18 at 20:37
  • $\begingroup$ Have a look at his paper arxiv.org/pdf/gr-qc/9909087.pdf for gravity. treats electromagnetism too. It has to do with the classical picture. Nowphotons by construction when superposed into the classical field should follow the same rules. The" virtual" will be a mathematical complication for the quantum level, not one to negate the classical proofs. (like using a needle to move a haystack). $\endgroup$ – anna v Jul 8 '18 at 7:31
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Are virtual particles traveling faster then c mathematically (because of the wavefunction's instantaneous change)?

Why virtual photons appear in the science about electromagnetism? Because the description of what is the nature of electric fields, magnetic fields and photons is not subject of consideration. Indeed, did you read anything about the consistency of these fields? Fields have a potential and this can be visualised by field lines. That’s all. Or, more worse, that it is declared an overall existing EM field even without any charges in it.

Not having any model about fields the virtual photon is a lousy try to explain interactions between charges. I have a naive explanation but not the status of a scientist. The last is enough not to go into discussion about this naive model or about the dry-written foundation About complex one-dimensional structure of space. Going into the statement of this model there is no need in virtual photons. The field of a charge is finite and at the end of the structures (strings) the charges start to interact. Easy model, which explains futhermore the annihilation of opposite charges of the same mass and the stopp of the annihilation process for charges of different mass (electrons near the nucleus).

If they are just a mathematical description of the interactions (that we cannot explain in a classical view), then how does the math count for the instantaneous interactions speed?

No need in instantaneous actions with the model of finite extension of fields.

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