I QM objects do not have properties until measured?

This model concludes instantaneous change of particle state:

1. Initially spin directions for particles A and B are undetermined.
2. A measurement for spin is randomly ± 1 with 50/50 outcome
3. If A measures +1 at direction α then B particle collapses to state with spin direction Φ = Π - α
4. If A measures - 1 at direction α then B particle collapses to state with spin direction Φ = α
5. Later when B measures spin at direction β he gets +1 with probability cos² (β-Φ)/2
and -1 with probability sin²(β-Φ/2

And in this experimental result, particles having definite spin orientation before measurement is rejected.Consider 3 particles;

1. Particle a is spin + at 0^ο and spin - at 45^ο
2. Particle a is spin + at 45^ο and spin - at 90^ο
3. Particle a is spin + at 0^ο and spin - at 90^ο
Following conservation laws the entangled particle b that is paired with particle a would be expected to be spin + at 45^ο and in both cases at 90^ο
Then with sin²(θ/2) the probability that an entangled pair will be P++ with θ angle between detectors the inequality:
sin² (45^ο/2) + sin²(45^ο/2) ≥ sin²(90^ο/2 is violated;
.1464 + .1464 ≥ .5

I question both conclusions in both cases above:

 

It only means that "QM objects usually do not have the measured properties before their measurement", since the measurement setting changes these properties - except in so-called nondemolition measurements.

 

A QM object always has uncertain properties (not no properties). For example, the position of a (for simplicity scalar) particle in a beam is not known precisely, but it is known that it is within the confines of the beam. Thus if the beam is in z-direction, one knows (by preparation) the x- and y-coordinates quite well, whereas the z-coordinate is very fuzzy. However (consistent with the Heisenberg uncertainty relations) one knowns the momentum in z-direction quite well. Thus one has good knowledge of a particular complete set of commuting observables.

If you measure a quantum system you change some of its properties through the interaction with the detector. In exchange for it you gain information about the object at the moment of measurement.

This has been known since the early days of quantum mechanics, hence has nothing to do with Bell. Bell's novelty was to study nonlocality in a tractable framework.

 

Why is the uncertainty of the properties before measurement important here? No properties is usually intended here as no local properties (which can become no properties in some interpretations).

 

I talked about properties of a quantum system, not about errors is a classical view.

Bell's question is different - he asks whether there is a different, classical theory underlying quantum mechanics and showns that it must have nonlocal laws if his inequalities are violated (which they are according to experiments performed later). Bell's theorem says nothing at all about quantum mechanics - it is a purely classical theorem!

 

Because it is the correct description.

Observables with a continuous spectrum can never be known without uncertainty since there are no associated normalized eigenstates!

 

I mean, the change of properties through the interaction with a detector doesn't address the reason behind bell inequalities violation. Or does it?

 

Bell inequality violations have nothing at all to do with the measurement problem, hence should be off-topic in this thread. They address a completely different problem - that of local hidden variable theories.

 

This is not quite right. Prior to Bell one could imagine that non-locality of QM could be explained by preexisting hidden physical configuration that obeys locality. Bell's work demonstrated that such an explanation is in conflict with predictions of QM.
Maudlin explains this in his article
In other words Bell demonstrated that the only realistic solution to non-locality of QM doesn't work.

 

Maudlin is a crackpot whose views are rejected by the vast majority of working physicists. His paper is debunked in this article. He fails to recognize some subtle assumptions that are undoubtedly made in the proof of the theorem.

 

Maudlin is not a crackpot. Werner is wrong because if we assume the wave function to be real, the state space is still a simplex. However, if the wave function is real, then collapse is real, and operational QM is nonlocal.

Werner's reference [8] is an article by Wiseman. Wiseman's article supports Maudlin's view. Wiseman shows how Werner's argument and definitions need to be modified to support something like what Werner is trying to get at. But then it turns out that after the appropriate corrections to Werner's view, Werner is talking about something different from Maudlin, and there is nothing wrong with Maudlin's view.

Wiseman and Cavalcanti have a very thorough analysis of all the different routes to the separability criterion: http://arxiv.org/abs/1503.06413. While there are certainly some subtleties to Maudlin's view, it is Maudlin that is essentially correct, and Werner that is essentially wrong.

 

Bell's theorem is not trivial, as he derives general limits of LHV. But the question about locality of QM becomes much more trivial if you ask very specific question: can there be explanation that obeys locality for particular prediction of QM with specific values. It turns out the answer is "no" and one such a counterexample type argument you can find here. It does not use probability spaces or assumptions about micro world.

 

That's what Werner pointed out. You are taking realism for granted. The Bell violations only prove that "locality + realism" is wrong. You need both assumptions. Locality alone isn't enough. Maudlin doesn't recognize this and claims that locality is enough. This is clearly wrong, but instead of admitting is mistake, he is being polemic, which makes him a crackpot.

Maudlin's view is that no realism assuption needs to be made in the proof of Bell's theorem. This is wrong without any doubt, since the realism assumption can be isolated precisely. It is definitely there and it's crackpottery to doubt that.

Here is another paper, published in the same issue, where the failure of such arguments as Maudlin's is pointed out clearly:
http://iopscience.iop.org/article/10.1088/1751-8113/47/42/424009

It nevertheless uses assumptions beyond locality. This is adressed in this book.

 

No, Werner is wrong. The realism assumption is not equivalent to the state space being a simplex.

That is not Maudlin's view. His view is that realism is a precondition for reality. There is no locality without realism, and this is correct. This of course depends on how one defines locality, but it is true for Maudlin's definition. He sums it up: the world is local. If one wants to define a nonreal world - one can do so, but then the nonreal locality is something else that is not addressed by Bell's theorem. For example, consistent histories does escape the Bell theorem - but consistent histories is not locally causal - the notion of locality in consistent histories is something else.

 

Mathematically, Bell's theorem requires the assumption of a simplicial state space, whose extremal points are the Dirac measures. Of course, one can state that in simpler terms and say that this means that Bell needs to assume that all random variables are defined on a single probability space. This is what Werner means when he talks about "realism" (in fact, he doesn't use that word at all and rather calls it "classicality") and it is a necessary assumption in every proof of Bell's theorem. No proof exists that doesn't assume this.

Maudlin claims that the violation of Bell's inequality proves that the world is non-local. This is false. The world might as well just be non-classical, which is in fact the mainstream position.

That's right, a non-classical world can still be local. A relation "causes" (##\sim##) one spacetime must satisfy ##x \sim y \Rightarrow x \in I^-(y)## (read: "if ##x## causes ##y##, then ##x## is in the chronological past of ##y##"). Quantum theory can be consistently supplemented with such a relation (a trivial example would be the empty relation, but there are of course non-trivial ones) and thus quantum theory is at least compatible with locality.

Bell's notion of "local causality" is a misnomer. It should really be called "classical local causality" (see the last paper that I quoted). It is just not a universal criterion for locality and can only be applied to theories, whose state spaces are simplices. So not surprisingly, quantum theory doesn't satisfy it. However, this says nothing about the status of locality in quantum theory.

 

But in operational quantum mechanics, which Werner claims to be local, there is wave function collapse. If we take the wave function to be real, then operational quantum mechanics is manifestly nonlocal. The state space in operational quantum mechanics is not a simplex, and that doesn't seem to depend at all on whether one assumes the wave function to be real or not real.

 

If you assume both that the wave function is a classical field on spacetime ("the wave-function is real") and the collapse postulate, then I agree that quantum theory is non-local. However, operationalists usually don't assume the former hypothesis.

 

Yes, but how does assuming reality of the wave function change the state space from not being a simplex to being a simplex? It seems that in both cases the state space is non-simplicial.

[Just to be clear, I do agree that there is a version of Bell's theorem in which one needs "some form of locality" + "something else".]