Many thing in quantum mechanics point to an underlying reality. And I'm not talking about bohmian mechanics and hidden classical variables. I believe that is obviously wrong, since "location" and "momentum" are obviously emergent properties, as you can easily see when you play around with a wave packet and derive the uncertainty relation.

There are so many equivalences between quantum theory and probability theory, beyond "QM is an extension of probability to complex numbers" and "square the amplitude to get the probability". For example, look at Feynman's path integral - where you sum up all possible ways to go from A to B, to get the transition amplitude. You can do a wick rotation (t -> it) and get a new expression related to a classical random walk. I hear you can even use a version of it in finance mathematics.

Another example is superluminal signaling. It would seem like something superluminal is going on with entanglement. But nature conspires just so that we cannot use it for transmitting information. A beginner would try to explain it classically - imagine you have two boxes, and put a marble in one. Now find the marble in one box, and obviously it will not be in the second. But classical analogies cannot give the same statistics as QM. (Sorry, it's been a while, I have difficulties recalling the argument :-).)

Anyway it seems like there must be an underlying reality that is "non-local" (in that it is not concerned with x, p, t, because these are emergent), and of which QM emerges as a statistical limit. There is an interesing idea from Gerard 't Hooft that this is a cellular automaton - the math seems to work out, but personally I feel that it should be a field theory (without any great justification as I'm just an armchair theorist).