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SeventhSigma

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I always hear that quantum particles exhibit "intrinsic" randomness in the states they take on, but how is this any different from me tossing a die repeatedly and saying "Look, this die is intrinsically random -- notice how the rolling average gets closer and closer to 3.5." But let us pretend that a skeptic looks at this and wonders if there are hidden variables that account for what I think is "random."

Of course, we may later find that "Well, if we know something about gravity, the type of die, the weight, the air resistance, the distance between the die and the surface it strikes, any deformation that occurs between the die and surface, the physical makeup of the die and surface, the initial position of the die, the forces acting on it when the die is released, etc -- we can know something about what value we'll get."

Would these variables be considered "local hidden variables?" How is any of this different from the case of quantum particles? I always hear that "local" quantum variables have been ruled out and that "non-local" variables may still be in the running, but what does it mean for something then to be local or non-local? How do we know all variables have been accounted for when we have not yet penetrated down to the fundamentally small and fast (namely I refer to Planck fundamentals, here, of which we're supposedly 20 orders of magnitude away from or something like that)?

How can we tell that quantum randomness is "intrinsically/fundamentally random" if there are possible variables to explain the actions?

Regarding the non-local variables, I've heard of Bell's Theorem even though I don't know *why* it rules out local variables for QM (if we applied Bell's Theorem to a die system, would we be able to show that there are other variables involved?). I hear quantum entanglement is a common misconception explaining that information still doesn't travel FTL, but the wavefunction collapse still occurs despite the object distance, implying that collapse is purely an observer phenomenon. This makes me wonder if wave collapse really occurs at all -- is it possible that these "potential states" don't really exist, but that one state just IS and we won't know about it until it acts on something else in a discernible way that allows us to derive its state? As in, we don't know what something IS until we look but we model its potential states via probability? What evidence is there for non-local variables in QM or that particles can all communicate with each other?

I've become increasingly frustrated with these questions because despite the hours I spend pouring over this stuff, I can't seem to find answers.