The process

Two electrons approach each other, repel, and fly apart. That is Møller scattering ¹, and it is the simplest thing two pieces of ordinary matter can do to one another.

It is also the first process in this course where a question you have been answering without noticing suddenly has no answer.

Here is the question. Two electrons come in; two electrons go out. Which outgoing electron is the one that came in from the left?

You cannot say. Not because the experiment is imprecise, and not because you lack information — because electrons are identical. There is no serial number, no dye, no property whatsoever that distinguishes one electron from another. Swap the two outgoing electrons and you have not produced a different final state. You have produced the same final state, described twice.

Every process so far kept its particles apart for you. In $e^+e^- \to \mu^+\mu^-$ the outgoing pair were a muon and an antimuon — different charge, different name. In Bhabha the outgoing pair were an electron and a positron. You could always point at a leg and say which one it was.

Here you cannot, and the amplitude will have to answer for it.