In the book - The Elegant Universe
In quantum field theory, a particle and its antiparticle can momentarily annihilate one another, producing a photon. Subsequently, this photon can give rise to another particle and antiparticle traveling along different trajectories.
Does a photon have any information that it was created by the annihilation of particle-anti-particle? If not so, then always a photon can create a particle-anti particle irrespective of whether itself was created by such annihilation?
Answer
The quote in the question is the caption to figure 6.6, which shows the following Feynman diagram:
It is important to understand that this diagram does not show an actual physical process. The two incoming particles do not annihilate to create a photon then reform from that photon. Apart from anything else this would violate conservation of momentum and energy.
The diagram is a graphical representation of a function called the propagator that is telling us about the probability that the electron and positron will interact. The photon (the wavy line) shown in that diagram is a virtual particle and is not something that actually exists. For more on this see the question Do virtual particles actually physically exist?
So your question cannot be answered because the photon in the diagram doesn't really exist. If we allow an electron and positron to annihilate this always produces two photons not one, and the converse is that a single photon cannot pair produce an electron and photon, or at least not without some other particle present to balance the momentum. For more details see Why can't a single photon produce an electron-positron pair?
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