[lisper]

That's right, except that the opposite of "local" in this case is not "global". (This is physics, not software engineering.) The opposite of "local" in this case is "non-local", which refers to state that propagates faster than the speed of light. Bell's theorem shows that describing reality requires some kind of non-local state. In the case of both Copenhagen and Bohm, that non-local state resides in the wave function. But here's the thing: you cannot know the state of the wave function because of the no-cloning theorem. The best you can do is prepare sub-systems in known states. So QM really is different. You cannot predict the outcome of a quantum experiment even in principle and even with arbitrarily advanced technology.

[bluepoint]

Best, most precise and accurate comment. Thank you.

[nobodyandproud]

Hold on.

Maybe I’m splitting hairs here, but surely there’s a difference between “not knowable in advance” and “doesn’t exist”?

[lisper]

What matters is the reason that it's not knowable. Some things are knowable in principle but not in practice because of technological or economic constraints, like whether or not there are life-supporting planets in the Andromeda galaxy. But in principle, if you could build a big enough telescope, you could know. Quantum experiments are not predictable even in principle. Even with arbitrarily advanced technology and unlimited resources, you can never know the outcome of a quantum experiment (assuming QM is correct, of course). That is an operational definition of the idea that the information required to predict a quantum experiment does not exist in our universe.

[nobodyandproud]

Yes, but that’s still different from saying that a particular quantity doesn’t exist prior to measurement.

The uncertainty principle makes this inherent, but the uncertainty principle itself is a consequence of the wave nature of particles.

[lisper]

This is the reason I hedged with "assuming QM is correct, of course". You are recapitulating the EPR argument. The reason the Bell inequalities are a thing is that they refute the EPR argument. It is not possible for QM to be completed as a local hidden-variable theory. If it turns out that the information required to predict the result of a QM experiment actually exists, then QM is not merely incomplete, but actually wrong. That is possible, of course. But I'll give long odds against.

[nobodyandproud]

What I wrote was confusing.

Heisenberg says that we cannot know both position and velocity with arbitrary precision.

This is inherent to any wave-based system. BUT, this only means we cannot know (as in theoretically prevented) all of the variables to arbitrary enough precision to accurately predict the outcome.

It doesn’t mean, however, that there aren’t any initial conditions even prior to measurement.

Nor does Bell’s inequality doesn’t negate this. Note Lso that non-local does not imply that causality is broken (you cannot transmit information FTL via decoherence).

In fact, one of the more interesting (and unexplored) possibilities is that the boolean-logic law of excluded middle is wrong.

This is because Bell’s derivation is pure arithmetic and logic. It’s the one bit of QM that any student can follow.

Lest this is handwaved away, know that there are entire branches of constructivist mathematics that do just this.

[lisper]

> It doesn’t mean, however, that there aren’t any initial conditions even prior to measurement.

This is the EPR argument.

> Bell’s inequality doesn’t negate this.

Bell shows that there is no measurement you can make, even in principle, that will give you the information you need to predict the outcome of a quantum experiment.

You can, if you wish, insist that those initial conditions exist notwithstanding our inability to measure them even in principle. But you could equally well insist that the outcomes of quantum experiments are determined by an invisible pink unicorn. Both hypotheses are equally unfalsifiable (if QM is correct).

I have actually coined the term IPU (Invisible Pink Unicorn) as an intentionally derisive description of hypothetical constructs that cannot be measured even in principle. Many QM interpretations contain IPUs. Bohmiam particle positions, for example, are an IPU.