"Probably is not deterministic" is not quite the same as "provably is not deterministic." Physicists have opinions on a lot of things, but I don't think they can fundamentally answer this.
In your original post, you state that we might as well assume determinism. Why? Given the widely accepted nondeterminism of quantum behavior, why wouldn't we assume nondeterminism instead?
I realize what you're grasping at is that deterministic behavior might somehow underly this seemingly nondeterministic behavior. Bell's theorem, however, has made it difficult to reject that the this fundamental aspect of the universe is hard to explain without assuming nondeterminism (or superdeterminism).
I agree you can't prove it. You just haven't really explained why you're leaning toward the deterministic side.
I didn't make myself clear. I meant assume in the mathematical sense, as in, to take as an axiom. If you do a science experiment, you are assuming that you will get back a repeatable result, and you won't be measuring something perfectly random. Otherwise, people might assume you're crazy. :)
I realize what you're grasping at is that deterministic behavior might somehow underly this seemingly nondeterministic behavior. Bell's theorem, however, has made it difficult to reject that the this fundamental aspect of the universe is hard to explain without assuming nondeterminism (or superdeterminism).
I agree you can't prove it. You just haven't really explained why you're leaning toward the deterministic side.