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Suppose a positron/electron pair were produced in a vacuum chamber with a very strong magnetic field, so strong that the particles circle around and meet after, say, 3 ns. Would the particles annihilate, or would they not due to the positron existing in backward time? That is, when occupying the same point in space, the electron would do so at +3 ns, the positron at -3 ns, and they would be "separated" by 6 ns.

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    $\begingroup$ Antiparticles evolve in normal time. You are stretching a shared metaphor on virtual particles best forgotten in this context. $\endgroup$ Jul 11, 2017 at 18:57

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The problem is that the pair cannot be produced in vaccum, because of conservation laws. The gamma has to hit something. The gamma has zero mass , and in the system of the hypothetical pair, the invariant mass of the added four vectors of the e+e- would be at least 2x$m_e$.

pairprod

So the interaction with a nucleus in the vacuum (the vacuum is never complete) would take away part of the momentum of one of the e+or e- and therefore the circles would be different and would never meet, as the geometry of two circles with no ionization energy loss would suggest.

So the answer is no. Nothing to do with the fictitious backwards in time variables of the feynman diagrams any way, because once produced, both of them are going forward in real time. Please see my answer here to a related question.

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