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I have read these questions:

Can virtual particles be 'boosted' into becoming real particles by fields other than gravity?

where dmckee specifically mentions J/Ψ meson production as a clear example when a pair of virtual particles is knocked on shell from the nucleon see.

and where annav says "With the above background it is evident that virtual particles turn into real when they acquire mass and keep their quantum numbers: The photon hitting an electron and exchanging a virtual electron with the field of some atom (through a virtual photon or Z) creates a pair by the electron becoming real."

Can virtual particles become real?

where Solenodun Paradoxus says " But it is only an analogy, and it has its limitations. Most of the newbie questions about virtual particles can and should be addressed in the full mathematical framework which is interacting Quantum Field Theory. Any kind of explanation involving virtual particles is just hand-waving."

and Arnold Neumaier says "Virtual particles have no dynamics. The latter is always tied to a state, which - unlike virtual particles - necessarily respects causality. Hence they cannot ''become'' anything."

And I got curious, but confused. Some answers say:

  1. it is not possible,

  2. some answers say it is possible (J/Ψ meson production),

  3. some say it is only possible as far as we say that virtual particles mediate forces between real particles, so they have real effects.

I would like to settle this for good.

Question:

  1. Which one is it really:

    1. Virtual particles can be knocked on shell and become real

    2. Virtual particles can never become real

    3. Virtual particles have real effects on real particles

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    $\begingroup$ Virtual particles can never become real because they aren't particles. They're more like a topological (graph-like) representation of perturbation theory made up by Feynman when he created his diagrams. I'm not well aquainted enough with the formalism of QFT but I'm sure someone here would be able to walk you through a tree-level propagator using perturbation theory and show what I mean. $\endgroup$ – Gabriel Golfetti Sep 23 '18 at 0:44
  • $\begingroup$ @safesphere I understand what you are saying, though, real photons, not having rest mass, have a speed in the time dimension of 0. So real photons are not moving in time either right? When you are saying "A wave function of a real photon is a spiral stretched in time. A wave function of a virtual photon is a circle at one moment." Don't you mean that the wave function of a real photon is stretched in space and time so it evolves, meaning it propagates in space as time passes? And that the wave function of a virtual photon does not evolve? It does not propagate in space as time passes? $\endgroup$ – Árpád Szendrei Sep 23 '18 at 16:52
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One has to keep clear what elementary particle physics is about. It is about modeling mathematically the behavior of elementary particles so that predictions can be made and validated by future experiments.

The models are quantum mechanical, i.e. probabilistic, using the field of complex numbers and the tools of integration and differentiation. Given the upper and lower limits in the integrals under consideration, real numbers can be predicted for observations.

The calculations were simplified by Feynman when he discovered the representation with diagrams of the scattering process.

em

This is the simplest process, the intermediate line is called a photon because it has the quantum numbers of a photon, even though the mass given by the four vector is variable. The variable mass is what gives the line the title virtual.

The photon of the above diagram cannot become real, by real meaning on mass shell, because the total reaction would have the zero energy of the mass of the photon.

This type of diagram for e+e- scattering describes the experimental plot, with different virtual exchanges

epl

It models very well the measured crossections, where one sees that as the energy of scattering approaches certain values resonances appear with specific masses that can be fitted and assigned quantum numbers and a real number for the mass from fitting the resonance shape. In this sense only, of continuity in the mathematical model, one can say that virtual particles become real, as the energy scans the on mass shell range.

Virtual particles can be knocked on shell and become real

No,virtual particles are just a tool in the mathematics describing the interaction, transferring the quantum numbers from the initial state to the final state.

Virtual particles can never become real

Their only reality is in the mathematical formula describing the model that will give the real numbers to compare with experiment.

Virtual particles have real effects on real particles

Virtual particles exist in the mathematics that describes interactions of real particles. They are a mathematical tool, as much as integrals themselves. They affect the calculations, but cannot be experimented upon in the lab because they only have a mathematical existence, useful in keeping track of quantum numbers.

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  • $\begingroup$ 99% of mass of everything around us is the energy of virtual gluons. Apparently their "mathematical existence" is quite tangible. $\endgroup$ – safesphere Sep 23 '18 at 7:07
  • $\begingroup$ @safesphere it is the energy that we model mathematically as carried by virtual particles, but we cannot pick up and experiment with a virtual particle. $\endgroup$ – anna v Sep 23 '18 at 10:14
  • $\begingroup$ @annav thank you i appreciate the answer. Can you please tell me if we know that it is the energy that we model mathematically as carried by virtual particles, for EM, virtual photons. Then why can't we do the same for gravity, model the energy (gravitational force) as carried by virtual gravitons? Why is doing this for gravity so much harder? $\endgroup$ – Árpád Szendrei Sep 23 '18 at 17:06
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    $\begingroup$ Effective quantizations of gravity do just that,but there is a problem as solutions do not converge and one has to wait for a strict definite quantization with no infinities that are ignored in the effective ones because they presuming a solution will be found eventually. $\endgroup$ – anna v Sep 23 '18 at 17:24
  • $\begingroup$ @annav can you please tell me what you mean by " there is a problem as solutions do not converge " i understand they go to infinity. Which solutions do you refer to, is there something I could read about the specific non-converging solutions problem? $\endgroup$ – Árpád Szendrei Sep 23 '18 at 17:27

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