Why do antimatter and matter annihilate when they collide?
That's what physicists would like to know. The short answer is "Thems the rules", i.e. that's the way Nature is. We know that anti-matter and matter annihilate because we observe that they do. And we observe the opposite, the a high energy photon (E >= 1.022 MeV) may interact with a nucleus (nuclear field) to produce a positron/electron pair.
Why it happens is one of those fundamental (and mostly philosophical) questions.
Anything that can happen will happen.
Generally speaking, many physicists do not answer questions starting by "Why"...
I think there should be a finite cross section for such an annihilation.
And the total additive quantum number is Zero, so it can happen.
LOL. Not being a physicist myself I can respond to that. (Though you probably weren't entirely serious, I kind of feel as though this might be the place for a “Why did the physicist cross the road?” joke.)
I think it's probably because at a certain level, responses to questions that demand conceptual answers cannot be made without making unverified claims or generalizations. In that case the guaranteed-accurate and safest way to avoid misstating things is to essentially only provide data in response to questions.⚛
Actually, it is a consequence opf marrying quantum mechanics with special relativity. When you do that (or, when dirac did that I should say) you have no choice than to introduce the concept of antiparticles. It is forced upon you by the formalism. And then, once you couple the electron (and its antiparticle) to an electromagnetic field, you have no choice than to accept that an electron and a positron will annihilate into photons. When you couple them to the weak gauge bosons, you find that they will also annihilate into Z bosons.
So if you accept quantum mechanics and special relativity, annihilation is forced upon you.
I would rather agree with kdv's answer, especially considering that Dirac's prediction of antimatter is probably one of the most spectacular ever. And in Feynman's space-time picture this becomes quite trivial.
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