Is Bell's Logic Aimed at Decoupling Correlated Outcomes in Quantum Mechanics?

[DrChinese]

The conclusion with respect to standard QM is that standard QM (SQM) cannot be embedded within a locally causal theory of hidden variables, because SQM predicts nonlocal correlations between measurement outcomes at spacelike separated detectors. SQM is a causal theory because the time-evolution of the SQM wavefunction is fixed by only an initial condition, and not, for example, by "two-time" boundary conditions. So one can deduce that SQM is incompatible with local causality because SQM is a nonlocal causal theory.

What could it mean to say that there is no "cause"? One (admittedly vague) possibility might be if the wavefunction was defined in terms of Block Time (where there is no objective distinction between past, present, and future instants of time). Then there would be no objective direction of causation, because the wavefunction would be defined throughout an eternal 4-D Block Universe.

Re my drift, essentially yes. The fact that standard QM is a nonlocal causal theory, naturally suggests (just as a logical possibility) that it might be possible to embed it into a nonlocal causal theory of hidden variables. And the deBB theory just happens to be an example of such a logically possible theory (though it is by no means uniquely implied by Bell's theorem).

Very well said! As you are meaning these terms, I agree with everything you are saying. I think it is interesting that nonlocal can properly be used in several contexts here.

 

[Maaneli]

Very well said! As you are meaning these terms, I agree with everything you are saying. I think it is interesting that nonlocal can properly be used in several contexts here.

Cool, so ... would I be right to conclude that you now agree that realism and locality are not independent assumptions in Bell's theorem?

 

[DrChinese]

Cool, so ... would I be right to conclude that you now agree that realism and locality are not independent assumptions in Bell's theorem?

As said, it comes down to the words. You said: "...standard QM (SQM) cannot be embedded within a locally causal theory of hidden variables..." To me, that is essentially the same as saying "standard QM cannot be embedded within a local realistic theory."

I also like the way you say that QM makes predictions which are nonlocal causal. Yet that kind of nonlocality is quite different that the nonlocal connections in Bohmian type theories. In entanglement situations, the nonlocal connection relates to spin conservation. The nonlocal connection is associated with the entangled particles and apparently none other. And there is no apparent cause to the spin value.

In BM, there are nonlocal influences between all particle positions, and these are sufficient to explain the appearance of spin values. So in my book, these are very different uses of the term nonlocal (not that you were saying otherwise).

I believe the Heisenberg Uncertainty Principle is essentially something which implies both nonlocality and contextuality. So that could be construed as to imply nonlocal nonrealism. So yes, you could say that those are not separate independent assumptions from that side. But either way, the question is: could a local contextual theory be feasible? I still don't see why not.

 

[Maaneli]

DrC,

Thanks for your comments. Unfortunately, I'm very busy at the moment and may not be able to give a thoughtful reply any time soon. But I do intend to reply eventually.Maaneli

 

[Eye_in_the_Sky]

... the definition of local causality that Bell uses in his theorem relies on his realism assumption (the existence of beables).

The part in the parentheses can be made more precise so as to read:

... (that (certain relevant) beables exist as local beables).
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... What one can conclude ... is that standard QM is nonlocal causal.

I thought the conclusion was a denial of local causality. What you say is almost the same thing, but then I get stuck on the word "causal".

What one concludes is that, according to standard QM, the "Alice-and-Bob scenario" involves a phenomenon which is either:

(i) causally nonlocal ,

or

(ii) nonseparable – (i.e. "state" nonseparability) across a spacelike region of spacetime .
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Or, equivalently in Ruta's words:

(at least) one of the following applies:

(i) causal nonlocality ,

or

(ii) constitutive nonlocality .
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Or, equivalently in Bell's language:

(at least) one of the following is the case:

(i) violation of "local causality" ,

or

(ii) existence of "nonlocal beables" .
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And finally, equivalently, in DrC's words:

(i) "causal locality" does not hold ,

or

(ii) "reality" is dependent upon "observation" (i.e. Alice's reality is dependent upon Bob's choice of measurement, and/or vice versa – but not necessarily causally so) .
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e.g. from two posts from another thread:

... either [causal] locality does not hold, or reality is dependent on observation.

... Bob's reality is determined by a choice of measurement by Alice [along with the associated outcome].

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... Okay, now going back:

... but then I get stuck on the word "causal". What if there is no cause? Not that I would know what that means.

This sounds like one of the places I have been stuck at for some time now, namely:

What does it (really) mean to say the following?

Alice's reality is dependent upon Bob's choice of measurement (and/or vice versa) – but not causally so.

(... Or is that not even (really) how to say it?)

 

[DrChinese]

And finally, equivalently, in DrC's words:

(i) "causal locality" does not hold ,

or

(ii) "reality" is dependent upon "observation" (i.e. Alice's reality is dependent upon Bob's choice of measurement, and/or vice versa – but not necessarily causally so) .
_____

e.g. from two posts from another thread:


... Okay, now going back:


This sounds like one of the places I have been stuck at for some time now, namely:

What does it (really) mean to say the following?

Alice's reality is dependent upon Bob's choice of measurement (and/or vice versa) – but not causally so.

(... Or is that not even (really) how to say it?)

See, it turns into a bit of a sticky wicket.

All I ever end up with is realizing that one classical notion - at a minimum - must go. If you juggle around enough, you can pick it yourself. Determinism, causality, observer independence, locality, separability, ...