questionpost said:
I get the point of view your talking about, where it's not just some interaction, it's just a sort of probability shift.
You might need to read up a bit on probability, including stuff like probability distributions, expectation values, and correlations. The latter are certain quantities which are calculated from probability distributions.
I usually recommend Ballentine as a QM textbook, but it's more upper-undergrad or graduate level. Maybe some of the other SAs here can recommended other books. Otherwise, try asking for recommendations over on the "academic guidance" forum.
Even while considering that though, things still interact in the real world, so I'd kind of like to know how an interaction itself changes probability and whether that breaks relativity.
In general, time evolution is determined by Hamiltonian operator. If the Hamiltonian contains a term representing interaction, then states can evolve into new states.
Probability distributions in QM are determined by (the square of) a product between states. So if you have an initial state, then allow it to evolve (interact), and then compare to all the possible other states, you get a probability distribution. (That's outrageously oversimplified of course.) Also remember that "initial state" should be thought of in terms of a large ensemble of identically prepared systems -- not a "one-off".
Importantly, such interaction terms in the Hamiltonian never break the underlying principles of relativity. (If they did, they'd be unphysical rubbish.) Indeed, relativity is one of the guiding constraints when constructing mathematical models of interactions.
Even still, how does that "instantaneousity" in the real world actually get like, recognized by the universe?
If by "instantaneousity in the real world" you mean instantaneous causation of effects on one particle by another, well, there is no such thing in the real world. Interactions happen as part of time evolution, which respects relativity.
(Sorry -- got to go now.)