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Some people consider all elementary particles to be non-existent. They tell us that they are changes in the field configurations that last which are called "real particles", while those that not last long enough are called "virtual particles".
But field configurations refer to wavefunctions that are a part of the entire field. Seen in this light, particles do exist, with an associated wavefunction. And so do virtual particles, though they don't last long enough to be "real". They find themselves (only by saying this already gives some "realness" to their existence) not on mass-shell and appear in the interaction between real particles, which do find themselves on mass-shell (or in the field configuration of the vacuum).

In the interaction case (as well as in the vacuum field configuration case or, for that matter, even in the case of changing field configurations, representing real particles), they are taught to be just mathematical constructions.

One can read [here][2] (a nice exchange of views, questions, and answers):

However, it appears to be a very good question whether virtual particles actually "exist" i.e. if they play a causal role. There is the common talk about virtual particles being exchanged and thus mediating interactions. This view was criticized e.g. by Mario Bunge (1970) in his „Virtual Processes and Virtual Particles: Real or Fictitious?”, International Journal for Theoretical Physics, Vol. 3, No. 6, 507-508. A rather forceful argument to the same effect was given by Weingard in his „Virtual Particles and the Interpretation of Quantum Field Theory“, in: H. R. Brown und R. Harré (Hrsg.) „Philosophical Foundations of Quantum Field Theory” 1988, Oxford: OUP. Weingard's bottom line is, that virtual particles are an artifact of perturbation theory only.

It's also possible to execute a Feynman diagram without the use of virtual particles, i.e., without the use of particles that not lay on their mass shell, but I didn't take a "deep" look into that possibility. It can be found here.

My question is very simple: If it is said that virtual particles are just mathematical constructs (just as real particles), does that imply that there are no real correspondences with the real world? It seems to me that something real must happen in the reaction between two particles. Or that elementary particles must be real particles and not mathematical constructions (changes in field configurations). As I said, changes in the field configurations correspond to wavefunctions which in turn correspond to real particles. These can be point-like or have some other form (I'm not referring to string theory).

Deschele Schilder
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    Please see http://profmattstrassler.com/articles-and-posts/particle-physics-basics/virtual-particles-what-are-they/ for an interesting take on virtual particles, but also see https://physics.stackexchange.com/a/275099/123208 – PM 2Ring Oct 07 '20 at 09:13

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Virtual particles can influence physical processes.

The Casimir effect predicts an attractive force between massive objects in a vacuum, due to a destructive self-interference of virtual particles confined between them. There is some experimental support for this claim, although not everybody accepts the evidence as valid.

Hawking's model of black holes suggests that they should evaporate through a mechanism involving virtual particles. When a virtual pair appears very close to the event horizon, one may "steal" energy from the other and escape as a real particle, while the other is drawn back in and disappears - effectively stealing the energy from the black hole. I am not sure to what extent the suggestion has been verified, but it is certainly very widely acclaimed.

Static magnetic and electric fields are also sometimes described as comprising virtual photons, being continuously emitted and re-absorbed by the charge concerned. However I have never come across any underlying theory that ties together quantum properties and classical field equations in the way that QFT does for ordinary photons.

Guy Inchbald
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  • due to destructive interference between virtual particles I don't understand the destructive interference. Aren't there just less quantum fluctuations due to the confinement? Anyway, your answer is "yes"? Virtual particles are real? – Deschele Schilder Oct 06 '20 at 18:46
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    I changed the wording. Any better? As to their reality, virtual particles are not really real, they are really virtual (or is that virtually real?) Real, solid existence is not a binary on/off property. – Guy Inchbald Oct 07 '20 at 08:57
  • That's better indeed. And I like your comment (I couldn't hold my laugh, in a positive way; there is of course a reason they are called virtual, but I think it's not in the sense of non-existent). – Deschele Schilder Oct 07 '20 at 09:26
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    Neither the Casimir force nor Hawking radiation was originally found through a virtual-particle argument. I'm not sure Hawking radiation can be derived that way at all, and the Casimir virtual-particle argument doesn't generalize to other surface shapes. It's a myth that these effects have some special connection to virtual particles. See R. L. Jaffe on the Casimir force and Sabine Hossenfelder on Hawking radiation. – benrg Oct 11 '20 at 01:35
  • @benrg There is of course a vast conceptual gulf between a quantum description of a "particle" and a classical localised description. It is equally over-simplistic to dismiss virtual quantum particles based on classical notions of a localised particle. – Guy Inchbald Oct 11 '20 at 08:45
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If you look at some problem in the Classical Electrodynamics (CED), say, at scattering of two charges, you will have two equations - one for each particle, containing a retarded field from the other one. These retarded fields are virtual particles. They have "sources" and "sinks"; the latter is the other particle for which it serves as an external field.

Vladimir Kalitvianski
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  • So in CED virtual particles do also exist? It's a Lorentz invariant theory (CED) but the concept of virtual particles (off-shell particles) is applicable in QED only. Retarded fields are classical fields. – Deschele Schilder Oct 06 '20 at 16:22
  • No, the "definition" as off-shell particles is inexact since perturbative. I have given the exact definition: sourced with one particle and affecting another one. Here retardation shows who emits the retarded field for the other charges. It is off-shell too, but more exact. – Vladimir Kalitvianski Oct 06 '20 at 18:14
  • I don't understand. In CED virtual particles are not defined, even not as you define them. In CED. They are particles defined in QED only. The retarded fields in CED may have a source and a sink (the particles) but these fields are defined in the context of CED. But your answer is useful as far that it makes you think about it. – Deschele Schilder Oct 06 '20 at 18:37
  • I've appealed to CED in order to simplify the definition. And I made a mistake: actually I meant a near retarded field, without radiation. It is implicit in my answer, but I meant the near field. In QED the corresponding lines are all "internal", not with free ends. – Vladimir Kalitvianski Oct 07 '20 at 06:08