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Interactions between real and virtual particles?

  1. Jan 7, 2010 #1
    Hi folks,

    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!
  2. jcsd
  3. Jan 7, 2010 #2
    See my post here:

    It comes down to the statement that virtual particles are a reflection of the mathematical tools you use to compute stuff in quantum field theory. It's the only tool we have for a large class of quantum field theories. If you can find a new, better tool to calculate stuff (which indeed exists for certain QFT's) you will never come accross the idea of a virtual particle.

    The answer to you questions comes down to the fact that when you use this mathematical tool, which includes Feynman diagrams, you are summing over all possible ways that a physical configuration A evolves into another physical configuration at some other time B. All possible "ways" in which this evolution can take place is summed over -- these are the intermediate states. The whole idea is that these intermediate states themself might not be physical states, but that they still contribute to the overall process of A evolving into B.

    So the effect of an electron moving through space is a summation over all possible ways in which it can do that. That includes annihilation with the positron of a virtual electron-positron pair, but also processes such as emitting a photon and interacting with it at a later time (self-energy) or no interaction at all.

    But in the end all you can measure is the initial A and the final B. The virtual particles are a reflection of the underlying math.
  4. Jan 8, 2010 #3
    You're suggesting that virtual particle can not entirely of themselves be physical. But what about black hole radiation? Isn't that supposed to be caused directly from virtual particles interacting with the event horizon? The horizon is not a particle but it turns half of the virtual particles into real particles that radiate from the horizon, right?
  5. Jan 8, 2010 #4


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  6. Jan 8, 2010 #5
    I have only some vague knowledge with the computation itself, altough I agree with what Baez said in the link jtbell provided: the computation that I have seen doesn't even use virtual particles or Feynman diagrams. You're "just" comparing the same state seen from different observers (one in the past before the black hole is created and one in the future after the black hole has been evaporated). The very basic conclusion comes down to the idea that the vacuum state in the past corresponds to an excited, thermal state in the future.

    But all this is a statement about the observers far that sit far away from the black hole. We do not have a microscopic theory of black holes or the way they evaporate (leaving string theory aside for a moment -- I'm not familiar with those results). We simply do not know what kind of mechanisms are involved, since we do not have a theory of quantum gravity.

    So in this case the idea of virtual particles doesn't even correspond to the underlying math. It's just a mental picture, as Baez puts it.
  7. Jan 8, 2010 #6


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    I believe that the very definition of "virtual particle" demands that your question be answered in the negative. If it interacted with a real particle, it would no longer be virtual.

    Not a formal mathematical treatment of the question, just my personal musings.
  8. Jan 8, 2010 #7
    The idea behind the virtual particle pair is similar to that of the HUP, in that the particle pair can never be "observed", just as position can never be "observed" if momentum of the HUP particle is fully known. In other words, by having a virtual particle interact with an observable ("real") particle, you're effectively violating a law of nature. Remember, that law states that virtual particles can never be observed, even if that observation includes the physical contact (and hence annhialation) of the real particle.

    Think of it this way: By annhialating a virtual particle with a real particle, you're observing a virtual particle with a real particle. And observing virtual particles is against natural law.
  9. Jan 8, 2010 #8
    Hi all,

    Thanks for the replies. Regarding Neo's response above:

    Let's say I observe an electron, at some position 'A', moving to the right - then, some time later, I look again and observe an electron at position 'B' to the right of 'A'. In the classical picture, I would say that the electron has moved from A to B.

    However, from the quantum point of view (if I understand correctly), I would say that the electron takes every possible path from A to B. This would include moving from A to B without interacting with anything - but would also include the situation in which a virtual electron-positron pair pops into existence near the original, real, electron. In this latter case, the 'first' (real) electron could annihilate with the virtual positron, leaving the second electron ... which would then become 'real' (i.e. because it's forced to 'exist' due to its original partner, the positron, being annihilated with the first electron). Whew, I'm not sure that is at all clear :-)

    This all occurs without anything being observed, until I look for an electron at position B... and in both cases, as far as I can tell, the observed outcome is exactly that - an electron at position B (summing over all possible paths as per sum over histories).

    So I guess my question is more to what extent we can say that the electron-positron annihilation, or any states involving virtual particles, actually 'exist' ... is it at all possible to determine if the above series of events actually happens? Or, as Xepma said, are virtual particles really just bookkeeping? Perhaps this is more a question of 'identity' of the particle arriving at position B (is it the original electron?) ... although that concept is probably meaningless in quantum theory.

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