Surprising that the author of such a technical piece talks about “particles and waves” in the expository paragraphs. Let’s be clear. We are talking about bosons

Surprising that the author of such a technical piece talks about “particles and waves” in the expository paragraphs. Let’s be clear. We are talking about bosons and fermions. Now let’s consider what is going on. We have two photons in and two photons out in different energies and directions although the total energy and momentum must be conserved. Anything could be happening in between, so let’s stick with known phenomena. We know about photon -> particle/antiparticle, and the reverse. We also know about particle/antiparticle -> dual photon, and the reverse, which must exist by time symmetry. So it’s not hard to see that dual photon -> particle/antiparticle -> dual photon interactions are very possible. So how do we get scattering? First, if the input photons are opposite momentum, then the output photons may be in any opposite directions. Actually, any two incident photon momenta define a cone of output direction possibilities, and the lifetime of the +/- particle system translates that cone along the total momentum vector. Thus, many observations are possible at the detector.