Eliezer: There can be properties of the particles we don't know about yet, but our existing experiments already show those new properties are also identical
According to a specific theory, the experiments do, yes. But again I beg to know why you have 100% confidence that right now you think our understanding of sub-atomic particles is totally complete, such that there can't possibly be anything about particles that we haven't taken into account in our experiments so far. More specifically, I really doubt that any experiment will show two particles are exactly the same with absolute certainty, unless you subject the two particles to all possible interactions within this universe, which of course is unlikely in any experiment.
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Scott, I'm not dismissing QM's accomplishment, because yes it's significant, the point is simply that it's still just a theory, and so long as that's what it is, dismissing the possibility that it is incomplete, or wrong, is not scientific.
Eliezer, I get that you are highly confident in QM. Obviously, QM has a lot going for it. But that still doesn't mean that QM can't be incomplete, or even wrong. Of course, reality is what it is, but our mental representation of it can be arbitrarily accurate or innacurate, and we can continue to fool our selfs into thinking that "This is the point in which my scientific knowledge is complete", but that is completely unscientific. Now that is elementary cognitive science that I'm sure you agree with. So it is curious why you can't imagine how there might possibly be some high-level theoretical component to particle physics which QM simply doesn't take into account, despite how confident you feel that you haven't missed anything in the math or logic backing up the theory.
And making the claim that one aspect of a theory being wrong invalidates the whole, is just as presumptuous as saying that a theory is simply correct, no questions. So let's not go there.