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Virtual photons are the interaction exchange particles between electrons and therefore responsible for the Coulomb electric force but also magnetic interaction between electrons. Therefore, virtual photons are responsible for the electromagnetic interaction phenomena.

Microscopically, these virtual photons coherent streams are the building blocks by which electric and magnetic flux is made up of and therefore also the electric E and magnetic M interaction fields. I don't know why this is not broadly mentioned in the literature which would resolve a lot of confusion around this subject, thus that both electric and magnetic flux therefore also the E and M interaction fields are made up from these same virtual photons and that only the curl and divergence of the flux lines of the field changes depending on the type of the field E or M generated by the charge.

My question is, can we calculate theoretically the wavelength of the exchanged Coulomb force virtual photon, between two electrons for example separated by distance $d$?

Secondly, as in the case of electrons, are all Coulomb force, virtual photons identical? Meaning can all have the same wavelength?

Could a calculation be as following?:

Virtual particles break conservation of energy in the classical sense. The maximum amount of extra energy can be $ΔE=2ℏc/d$ , where $d$ is the distance between the two interacting electrons, $c$ the speed of light and $λ=πd$ the minimum allowed wavelength of the virtual photon exchanged between the two electrons separated by distance $d$. From there we can calculate $d$ το be $d=2ℏc/ΔΕ$.

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    $\begingroup$ "Microscopically, these virtual photons coherent streams are the building blocks by which electric and magnetic flux is made up of" A deeply questionable claim. For the "reality" of virtual particles, see e.g. physics.stackexchange.com/q/230113/50583, physics.stackexchange.com/q/700012/50583 and their linked questions. $\endgroup$
    – ACuriousMind
    Commented Sep 1, 2022 at 12:44
  • $\begingroup$ @ACuriousMind If not, from what quanta is for example the magnetic flux of a magnet made up of? Can you specify an elementary particle? It is a Boson interaction field between fermions. Therefore, the only theoretical explanation is that magnetic flux is a coherent stream of virtual photons. If they are not physical quanta of propagated energy then what else? There is no interaction without energy transfer (except maybe entanglement) therefore virtual photons must be real physical energy quanta. $\endgroup$
    – Markoul11
    Commented Sep 1, 2022 at 13:48
  • $\begingroup$ The other honest answer we could give is, "we do not know what consists the EM flux in space". $\endgroup$
    – Markoul11
    Commented Sep 1, 2022 at 13:56
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    $\begingroup$ Several wavelengths (momenta) are involved in the infinite sums of virtual photons comprising classical EM fields. Required review, and also, and also, $\endgroup$ Commented Sep 1, 2022 at 14:02
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    $\begingroup$ ...as well as... $\endgroup$ Commented Sep 1, 2022 at 14:02

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One must first clarify the concept of "virtual." This concept exists because of a calculational tool of Quantum field theory, the Feynman diagram.

For photons in particular:

virtualphot

In this particular diagram the cross section for scattering of two same charge electrons is depicted by the diagram, and the virtual photon represents the energy and momentum transfers in the integral that will calculate the cross section.

The four momentum carried by the virtual particle does not have a fixed invariant mass, but varies within the limits of the integration.

When the concept of virtual particles is used in order to describe quantum mechanically the classical fields, again it is a mathematical representation, the energy /momentum four vector of the virtual photons follow the limits of the mathematics and do not have a unique energy to be associated with a unique frequency. This article in Wikipedia may help.

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  • $\begingroup$ But virtual photons still represent physically momentary distortions in the quantum photon scalar field. $\endgroup$
    – Markoul11
    Commented Sep 1, 2022 at 18:56
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    $\begingroup$ no frequency of light can be assigned to that quantum, hν, because it has an invariant mass different than zero $\endgroup$
    – anna v
    Commented Sep 1, 2022 at 20:28
  • $\begingroup$ physics.stackexchange.com/a/147053/183646 This comes now down to the subject of mathematical effective interpretation of the phenomenon. This however does not mean that virtual particles are not representing a real physical interaction between fermions. Some kind of photon energy manifold is released from one charged fermion to the other in an energy exchange. Therefore, virtual particles in general are viewed by the Standard Model as real particles physical processes, in vacuum space. tinyurl.com/2p8s4yy9 $\endgroup$
    – Markoul11
    Commented Sep 2, 2022 at 11:36
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Photons cannot be the force carriers of the individual E and M fields. Photons carry away energy from the system.

Consider an electroscope: When charged, the foil leaves will repel each other against gravity, which tries to bring them back together. As long as the electrostatic potential remains unchanged on the leaves, the leaves will self levitate forever. No energy is lost in the system despite the fact that the E field is doing work against gravity to keep the leaves apart. The honest answer was stated somewhere above: we have no idea how electric and magnetic forces are propagated through space. The force carriers of the individual E and M fields remain to be properly characterized. Never forget that photons are the physical manifestations of both fields, not just one. The force carrier of the electromagnetic field, the photon, always carries energy away from its source. The “virtual” photon is a placeholder for the unknown.

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