Feynman diagrams arise mathematically essentially as neat graphical ways of organising the terms in Wick's theorem for time-ordering. But at the same time we're supposed to interpret them as some sort of "physical process". Like nucleons "exchanging" a meson and so on. But why should the neat mathematical tool have anything to do with what's happening in reality? All they are is a way of doing perturbation theory with pictures instead of integrals. So why should they have physical interpretation?
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4Does this answer your question? On the interpretation of Feynman diagrams – Amit Apr 02 '23 at 00:04
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1Physical theories are justified by experiments. Feynman diagrams are part of a theory. Theories are not real, although they may be useful. – John Doty Apr 02 '23 at 00:08
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Your question has a false premise. Nothing justifies Feynman Diagrams as being a physical process, for the reasons you describe. They are just a way of calculating the probability amplitude. It is even known that adding all Feynman diagrams leads to an infinite result. In theories such as Lattice QCD, a nonperturbative approach is taken, and there aren’t diagrams.