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Why can't the pair production process occur in empty space? I have read that a nucleus must exist and this is how it is useful: that the photon turns into virtual loops of e+ e- and one of them interacts with the field of a real charged particle exchanging enough energy and momentum so that both e+e- become real while energy and momentum are conserved in a three body diagram. What I don't understand is how the photon turns to virtual loops of e+e- what do they mean what are they... You know there are lots of info from the Internet that now I knew them, my professor doesn't explain much, he just says that positron with a nucleus gives.... Etc so he just writes the equation but I'd really like to know specific details and it takes so much time from me.. :(

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    What is empty space for you? Pair production needs, at least, one incoming and two outgoing particles, so that's not empty, already. Are you asking why still another particle is needed to facilitate it? That question would, I believe, have an answer in http://physics.stackexchange.com/questions/13513/spontaneous-pair-production – CuriousOne Dec 26 '15 at 08:08
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    See the linked question. Spontaneous pair production cannot occur because it would violate conservation of momentum. – John Rennie Dec 26 '15 at 08:15

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