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I have a question about virtual particles, and so far I haven't been able to find an answer. Do virtual particles ever annihilate with real particles? (Black hole evaporation aside)

For example, let's say we have a (real) electron, floating in space, and a virtual electron-positron pair pops into existence nearby. If the real electron and the virtual positron are close enough initially, I would expect that they would annihilate each other, leaving the remaining virtual electron - which would then become real (to maintain conservation of energy). Does something like this indeed happen? Or is it even possible to say, since you start with an electron and end up with an electron?

Also, more broadly, I keep reading two different takes on the 'existence' of virtual particles. Some physicists say they are indeed real, and pop into and out of existence all the time. Others say they're merely a mathematical tool used in perturbative quantum field theory (Feynman diagrams) and cannot really be said to exist. Any comments?

Thanks all!