> Does that mean that the positron is somehow "part" of the proton?
No, and the standard intuition that there are discrete things made out of smaller parts breaks down when you look closely enough. The proton is a bound state of the quark and gluon fields, but it only "contains" individual quarks and gluons in a loose heuristic sense, and positrons are a different thing entirely.
> Does it mean that their wave functions interact in some specific way?
Yes, or more precisely it means that the quark fields interact with the electron field (free electrons and positrons are different states of the same underlying bispinor field) and the W boson field in some specific way.
> Quantum physics has always bothered me, personally, since I find it difficult to understand reasons.
Ultimately, the sort of mechanistic explanations you're looking for do not exist: the universe runs on differential equations and linear algebra, not billiard balls and clockwork.
No, and the standard intuition that there are discrete things made out of smaller parts breaks down when you look closely enough. The proton is a bound state of the quark and gluon fields, but it only "contains" individual quarks and gluons in a loose heuristic sense, and positrons are a different thing entirely.
> Does it mean that their wave functions interact in some specific way?
Yes, or more precisely it means that the quark fields interact with the electron field (free electrons and positrons are different states of the same underlying bispinor field) and the W boson field in some specific way.
> Quantum physics has always bothered me, personally, since I find it difficult to understand reasons.
Ultimately, the sort of mechanistic explanations you're looking for do not exist: the universe runs on differential equations and linear algebra, not billiard balls and clockwork.