I Classicality in Bell's original reasoning

[Boing3000]

So when you "prove" there is something non-local occurring, you really aren't. You have a context which is in fact traced out by a light cone (or cones). The extent of the "non-locality" is the distance between points on a light cone and no further. QM fully qualifies as a local contextual theory, which matches what some of the theorems that Griffiths refers to would indicate.

Thanks a lot for that explanation.
It'll try to do my homework about what contextual theory means (in general, then with regard to QM) then how locality can still apply in that context.

 

[RockyMarciano]

No, it has nothing to do with determinism.

Then I guess somebody should correct the wikipedia article.

The question is whether one can model the quantum observables one-to-one as random variables on a classical probability space. If that is not possible, then the theory is called contextual.

I have seen that called non-EPR realist(i.e. non-classical) instead. So it seems to me that only those that want to keep classicality recur to contextuality, why is it better to drop counterfactual definiteness(wich I'd say leads to solipsism) than classicality(EPR realism)?

Of course, using classical probabilities has nothing to do with determinism. I can also write down a classical probability distribution for a coin tossing experiment ($p_i=\frac 1 2$), but of course that doesn't imply that the experiment is deterministic.

Clearly classical probabilities are compatible with classical determinism, and coin tossing is usually considered deterministic with the classical 1/2 probability atributted to lack of information about the initial state.

 

[rubi]

I have seen that called non-EPR realist(i.e. non-classical) instead. So it seems to me that only those that want to keep classicality recur to contextuality, why is it better to drop counterfactual definiteness(wich I'd say leads to solipsism) than classicality(EPR realism)?

Solipsism and realism are philosophical terms that have no place in physics. Physics has nothing to say about these things. For the rest of your post: I'm using the terms classicality, CFD, non-contextuality interchangeably, because for the purpose of Bell's theorem, it makes no difference.

Clearly classical probabilities are compatible with classical determinism, and coin tossing is usually considered deterministic with the classical 1/2 probability atributted to lack of information about the initial state.

Probabilities are always compatible with determinism, but they are also compatible with genuine randomness. Probabilities just don't care about such notions. Whether you can come up with a deterministic theory that underlies the coin tossing experiment is not relevant. You can also do that with QM (see Bohmian mechanics, which is in my opinion absurd).

 

[bohm2]

Assumption is that there is physical model that can explain results of measurements that show perfect correlations. There is no assumption of hidden variables per se.

A paper discussing whether the assumption of classicality is made by Bell is this paper by Maudin:

Werner has made quite clear and explicit the startling claim that Bell himself did not understand what he had proved. If so, then Bell’s own pronouncements about what he did, and what it means, are not reliable. Werner thinks that Bell and Einstein and I have all tacitly made an assumption of which we are unaware, an assumption he labels C for “classicality”. When Bell, or Einstein, or I write “theory” what we really mean (although we don’t realize it) is “classical theory”. And when we draw conclusions about what a theory with certain characteristics must be like, the conclusions really only hold for classical theories. Furthermore, Operational quantum theory is not a classical theory. Therefore, according to Werner, Bell’s and Einstein’s conclusions simply do not apply to Operational quantum theory. In particular, Operational quantum theory can be local in Bell’s and Einstein’s sense and still violate Bell’s inequality because it is not classical. Werner concedes that Bell proved that any classical theory that violates his inequalities must be non-local (again, in Bell’s and Einstein’s sense of “non-local”). But deny classicality and the arguments no longer go through...Since the main contention is that Bell and Einstein and I have all been blinded by tacitly presuming classicality, the main order of business ought to be demonstrating exactly where the argument presumes classicality.

Reply to Werner
https://arxiv.org/ftp/arxiv/papers/1408/1408.1828.pdf

Werner's reply to Maudlin's challenge can be found here:

What Maudlin replied to
https://arxiv.org/pdf/1411.2120v1.pdf

 

[Boing3000]

A paper discussing whether the assumption of classicality is made by Bell is this paper by Maudin:

Very interesting links, thanks you. I can't help to find Maudlin straightforward and coherent, and Werner hand waving and talking at cross purpose.

To the Maudlin's precise question "Which step of that argument, exactly, does not go through if the state space of the theory is not a simplex?" the answer is "QM is not a simplex".

I can't shake up the impression that some people don't understand why no FLT influence is a consequence of non-locality, whatever additional characteristic the candidates theories want to imbued themselves with (excluding magic of course).

 

[rubi]

Maudlin's argument is exactly the same as the one that has already been debunked in this thread, so if you want to understand why he is wrong, you just have to read the thread again. The challange is to prove Bell's inequality with the contextuality index $\chi$ in place. You won't be able to.

 

[Boing3000]

The challange is to prove Bell's inequality with the contextuality index $\chi$ in place. You won't be able to.

I don't think I'll be able either. But I also don't think that this "contextuality index", is required by the original proof.

Maybe adding it extend the proof in some way, by making it more useful to distinguish experimentally between theories, by making additional predictions. But I totally fail to understand those points. I'll try anyway, and re-read the whole thread

Thanks a lot for all you posts !

 

[rubi]

But I also don't think that this "contextuality index", is required by the original proof.

Well, this is exactly the point. The original point is not concerned with contextual theories (because it tacitly suppresses the contextuality index), so a violation of Bell's inequalities says nothing about contextual theories such as QM.

 

[zonde]

But I also don't think that this "contextuality index", is required by the original proof.

Well, if you attach some index to measurement results themselves then you can't get Bell inequalities. But then you are back at superpositions of Schrodinger cat states (MWI without preferred basis or something like that).

I can't shake up the impression that some people don't understand why no FLT influence is a consequence of non-locality, whatever additional characteristic the candidates theories want to imbued themselves with (excluding magic of course).

Non-locality is taken just as approximation of FTL influence with very high speed. Your model of shared "variable" is just too solipsistic and too far from physics (but time to time people bring up these ideas here).

 

[Boing3000]

Non-locality is taken just as approximation of FTL influence with very high speed.

I strongly disagree, on simple and straightforward logical bases. A thing that have no spatial nor temporal coordinate, cannot move nor influence nor have speed.

Your model of shared "variable" is just too solipsistic and too far from physics (but time to time people bring up these ideas here).

That I agree with. But that model does not pretend at all to model physical reality. It "implements" Bell's theorem logic. It is a Bell's proof "simulator", using objects made of logic(classic/not magic), stochastic(but deterministic inside, because computer cannot create true random value), classic(no complex n-dimensional space), SR compliant (no FLT influence). But then you can switch non-locality(spookiness/non-realism) on or off (uses state/value without(or with) unique "observational window").

 

[bohm2]

Rubi/Neumaier/Griffiths line is as follows (and I am referring to comments in concurrent threads as I do this): Bell excludes local realistic (non-contextual) theories; and QM is contextual. So a successful theory need not be non-local.

But KS theorem already rules out any models that are non-contextual. Surely Bell's shows something further?

 

[DrChinese]

But KS theorem already rules out any models that are non-contextual. Surely Bell's shows something further?

I'm not sure Bell literally goes much farther than KS. I think of their results as analogous but different. Bell's result is much more influential because it is easier to follow, and was a specific response to a well known paper (EPR). It says:

- No physical theory of local hidden variables (contextual or not) can ever reproduce all of the predictions of quantum mechanics.

KS relates to the state independent of the measuring device, and says:

- No physical theory of non-contextual hidden variables (local or not) can ever reproduce all of the predictions of quantum mechanics*.

You could say that Bell rules out contextual local realistic theories (which KS would not), which would clearly rule out any attempts at classical representations. If you are going to have hidden variables, they must be non-local and contextual. If you keep locality, it must be non-realistic and contextual. (I can't really envision the difference between non-realistic and contextual though.)*when the dimension of the Hilbert space is three or more.

 

[Jilang]

For spin I would go with random in two dimensions (is that non-realistic?) and contextual and local. Would that work?

 

[zonde]

But KS theorem already rules out any models that are non-contextual. Surely Bell's shows something further?

KS theorem shows that there is conflict between non-contextual HV models and QM (only theoretical argument). Bell not only shows conflict between local theories and QM but in addition opened a way how to test this conflict experimentally.

 

[bohm2]

If you keep locality, it must be non-realistic and contextual. (I can't really envision the difference between non-realistic and contextual though.)

How would you interpret experimental violations of Legget's inequality?

 

[Dale]

Closed pending moderation

Edit: after discussion we have decided to leave this thread closed