The cellebrated works of the teams of S. Savasta and R. J. Schoelkopf, showed that virtual particle can have effects which can be indirectly testable. See for instance the famous article

L. Garziano et al., "A Single Photon Can Simultaneously Excite Two or More Atoms", arXiv:1601.00886v2,


R. Stassi et al., "Spontaneous Conversion from Virtual to Real Photons in the Ultrastrong Coupling Regime", arXiv:1210.2367v2

(I recommend to read these articles very attentively for understanding how the virtual photons influenced the final result. In the 1st article, the presence of virtual photons in intermediate stages - see diagrams in fig. 4 - is testified by the frequency of the oscillations in figure 3. See the formulas (4), (5), (6). I recommend, stop reciting that virtual particles are only a tool in Feynman diagrams. Virtual particles can also appear in reality, in some experiments, but cannot be detected because of their too short life, and different problems as mass, and others. In the process described in the first reference, their presence violates energy the conservation - this is why one cannot detect these intermediate states, which are, of course, very short. Though, their presence can be deduced indirectly from calculi, as in the (excellent) work of Savasta's team - first reference.)

My problem is that in these works only virtual photons are generated. My question is which other types of virtual particles are known? A colleague told me that only the particles in the table of the Standard Model can appear as virtual (of course, with abnormal mass or other abnormal features). Is that true? What about virtual protons, or virtual alpha-particles?

  • $\begingroup$ This seems more like a rant than a question. $\endgroup$ – knzhou Apr 9 '18 at 9:28
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    $\begingroup$ I'm not against trying to understand virtual particles intuitively (see my question here) but going on a long rant about whether they are really real is philosophy, not physics. A sufficiently careful physicist wouldn't even call an ordinary particle real -- even something as 'objective' as the number of ordinary particles differs between references frames. They're all tools to understand reality, not reality itself. $\endgroup$ – knzhou Apr 9 '18 at 9:36
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    $\begingroup$ And as a tool to understand reality, virtual particles are absolutely terrible most of the time. If you don't understand the math of QFT, and just imagine it as point particle mechanics where the virtual particles are little billiard balls, everything falls apart. You run into piles of contradictions. Even energy conservation doesn't work. (Indeed the notion of energy non-conservation in QM is just a convenient lie told to laymen to preserve the virtual particle picture, there is nothing remotely analogous to it in the actual math.) $\endgroup$ – knzhou Apr 9 '18 at 9:39
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    $\begingroup$ The only way to use virtual particle reasoning is to actually understand the mathematics, do the calculation the usual way, and then drape virtual particle intuition around the result. You can see that's exactly what happens in the papers you linked -- there is never a "virtual particle state" or a "virtual particle operator" anywhere, it's just standard QFT. That's why they can use virtual particle reasoning and get away with it: because they can actually do the calculation. $\endgroup$ – knzhou Apr 9 '18 at 9:41
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    $\begingroup$ I read the equations. They don’t contain virtual particles any more than standard QFT does. If you disagree, point to a specific equation to justify your claim — not a set of intuitive words. $\endgroup$ – knzhou Apr 9 '18 at 10:31

Virtual particles can be any type of particle. A good example would be virtual pions. Nuclear forces can be modeled in a simple way through a one-pion exchange potential.

If virtual particles could only be elementary particles, that would be too good to be true. Then we would have a magic way of detecting structure at all scales, because composite particles would behave differently than elementary ones, at all energies.

  • $\begingroup$ Did you see some article/work speaking of virtual atoms? If yes, please let me know, I would be very interested. $\endgroup$ – Sofia Apr 9 '18 at 10:29

Virtual particles are a mathematical construct in Feynman diagrams. They carry the quantum numbers of the named particle but are are off mass shell, under an integration for the process examined.

The virtual particle is a pole in the propagator under the integration from initial to final state.

I first learned field theory rules from a nuclear physics model, with creation and annihilation operators. If you can define a consistent quantum field theory for any set of particles , those particles can also be virtual in the Feynman diagrams for calculating measurable quantities. One has to make sure though that the system is consistent for the mathematics to work.

  • $\begingroup$ In the second paper you quote, there is not enough energy present in the setup to generate real particles with masses larger than zero. $\endgroup$ – anna v Apr 9 '18 at 6:44
  • $\begingroup$ Dear @annav , it seems to me that you DIDN'T READ carefully the first article. I read it with pencil and paper, checking each formula. Please look, I completed my question with explanations how one can see that the virtual photons appeared in intermediate states. I repeat, it's a very illuminating article. As to the virtual particles, they are photons. Of which mass > zero, do you speak in connection with the 2nd paper? Please be more clear. I tell you frankly, I am mainly asking about the possibility of virtual atoms, not only virtual elementary particles from the Standard Model Table. $\endgroup$ – Sofia Apr 9 '18 at 9:43
  • $\begingroup$ To everybody: If it can be proved that virtual atoms exist, even virtual molecules, that would help in clarifying one of the heavy problems in QM. This is why I asked my question, because I am far from being convinced that such heavy virtual particles can appear. The proof that heavy virtual particles can appear would be a remarkable acievement. $\endgroup$ – Sofia Apr 9 '18 at 9:49
  • $\begingroup$ Sophia, the only proof on existence of virtual particles is mathematical. If you make a field theory where whole atoms can be exchanged , they will be virtual, BUT THERE SHOULD BE ENOUGH ENERGY to turn virtual to real. In this diagram . Look at this pair creation diagram. i.stack.imgur.com/rnRys.gif The virtual electron becomes real IF THERE IS ENOUGH ENERGY supplied by the incoming gamma. In the links you give, the energy for turning virtual to real photons is given during the building of the setup of the experiment. $\endgroup$ – anna v Apr 9 '18 at 12:20
  • $\begingroup$ virtual particles are not only those Feynman diagrams. All the creatures violating different laws of physics, can't be detected and are short-lived. Look attentively at the diagrams in fig. 4. The virtual photons appear in intermediate states between the initial and final one, and are identical to the REAL photon in the initial state. But they popped out from the vacuum. The energy of the intermediate states differs from that of the initial state. That's why these states are called virtual - they can't be detected. Only the final state has the same energy as the initial state. $\endgroup$ – Sofia Apr 9 '18 at 12:51

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