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Lies in education [was Re: The "loop and a half"]

Steve D'Aprano wrote:
> I've seen (or at least, I remember seeing)
> diagrams of matter/antimatter annihilation with the two particles coming
> together and a single photon coming out: a simplified and strictly wrong view
> of the physics.

It may or may not be wrong, depending on what the diagram was
supposed to represent.

Each vertex in a QED Feynman diagram involves one electron,
one positron and one photon. That much is perfectly true.

But if you work out the probability of that process happening
on its own, it turns out to be zero. You need a diagram with
at least two vertices to get a non-zero probability.

Another way to say it is that a single-vertex diagram
correctly represents a virtual process (involving virtual
particles, which don't have to conserve energy or
momentum), but it doesn't correspond to any real process
(since real particles have to conserve both).