Is It true that matter cannot be created or destroyed?

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Dale said:
By “matter” I mean the fermions of the Standard Model and by destroyed I mean that the Feynman diagrams for the interaction has the fermion entering but not leaving.

This is a good precise definition, yes.
 
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Dale said:
By “matter” I mean the fermions of the Standard Model and by destroyed I mean that the Feynman diagrams for the interaction has the fermion entering but not leaving.

A fine definition. But note that conservation of angular momentum prevents the sort of processes you are describing.
 
Vanadium 50 said:
conservation of angular momentum prevents the sort of processes you are describing.

?? A QED diagram with two entering fermion lines (electron and positron) and two exiting photon lines is perfectly consistent; it just has to have two vertices (at lowest order).
 
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PeterDonis said:
Whether matter can be destroyed depends on what you mean by "matter" and what you mean by "destroyed".

Agreed. They are almost weasel words when exact context is not nailed down.
 
Outhouse said:
They are almost weasel words when exact context is not nailed down

I think "weasel words" is a bit strong; the terms do have well-established meanings. They just don't have unique well-established meanings. But I agree that nailing down exact context is a good thing.