Classicality in Bell's original reasoning

[zonde]

I am disappointed, aren't we supposed to talk about science here ?

Then I can't propose you anything.

 

[zonde]

This is Griffiths response to it.

And Stapp's article already contains response to Griffiths response and Griffiths response contains response to response which basically says that: "The reader will have to judge".

 

[zonde]

Read his paper. He explains that his definition of locality derived from the assumption of CFD.

Can't read this article as it is behind paywall.

But when I look at his definition of "local" from this article http://dx.doi.org/10.1103/PhysRevA.47.R747 it seems that he very carefully avoids any counterfactual reasoning (btw reference [10] is the paper you gave):
"For a given theory, we consider all the possible sequences of N events that can occur in each setup. N is the same for the four setups and arbitrarily large. As in [9] and [10], a theory is defined as being "local" if it predicts that, among these possible sequences of events, one can find four sequences (one for each setup) satisfying the following conditions:
(i) The fate of photon a is independent of the value of β, i.e., is the same in an event of the sequence corresponding to setup (α1,β1) as in the event with the same event number k for (α1,β2); also same fate for a in (α2,β1) and (α2,β2); this is true for all k's for these carefully selected sequences.
(ii) The fate of photon b is independent of the value of α, i.e., is the same in an event k of the sequences (α1,β1) and (α2,β1); also same fate for b in (α1,β2) and (α2,β2).
(iii) Among all sets of four sequences that one has been able to find with conditions (i) and (ii) satisfied, there are some for which all averages and correlations differ from the expectation values predicted by the theory by less than, let us say, ten standard deviations."

 

[zonde]

But does this contextuality index describe global measurement arrangement as well? As I understand it does.

You understand wrong. In general, it doesn't refer to measurement arrangements at all. The KS theorem just tells us that there can't be a one-to-one mapping.

I found one Griffiths article where he tries to argue that QM is non-contextual Quantum Measurements Are Noncontextual
"The hidden variables approach seems almost inevitably to lead to the conclusion that quantum mechanics is infested with nonlocal influences, and the choice of a measurement at some spacelike separated point can influence what is going on here, a “contextual” influence."

Well, it seems that my understanding of common terminology (KS definition of term "contextual") is correct and you are using some private and rather uncommon terminology.

 

[rubi]

Am I right to understand that as 0% FTL signaling, and 100% instantaneous correlation (which is on what my little code is based on) ?

There is 0% action at a distance, independent of whether you can use it for signaling or not. I don't know what you mean by instantaneous correlation.

Can't read this article as it is behind paywall.

But when I look at his definition of "local" from this article http://dx.doi.org/10.1103/PhysRevA.47.R747 it seems that he very carefully avoids any counterfactual reasoning (btw reference [10] is the paper you gave):
"For a given theory, we consider all the possible sequences of N events that can occur in each setup. N is the same for the four setups and arbitrarily large. As in [9] and [10], a theory is defined as being "local" if it predicts that, among these possible sequences of events, one can find four sequences (one for each setup) satisfying the following conditions:

He refers to [10], precisely because he has introduced the his notion of locality and explained it in that article. And he clearly explains that it implicitely assumes counterfactual definiteness. I don't know how you get the idea that he "carefully avoids counterfactual reasoning", but you are definitely in disagreement with the author.

Well, it seems that my understanding of common terminology (KS definition of term "contextual") is correct and you are using some private and rather uncommon terminology.

It seems that you still didn't bother to understand the KS theorem. Griffiths is not talking about the KS theorem here. The KS theorem says nothing about the meaning of the $\chi$ index. It just says that a one-to-one mapping of observables to random variables is not possible. There are infinitely many ways to write down such a many-to-one correspondence. Making $\chi$ depend on non-local information is a possibility, but not a necessity. The KS theorem does not make statements about locality. Also, as I told you, it is completely irrelevant. The point is that Bell excludes contextual theories from his analysis (or do you see any contextuality index in his proof?)

 

[zonde]

He refers to [10], precisely because he has introduced the his notion of locality and explained it in that article. And he clearly explains that it implicitely assumes counterfactual definiteness.

Well, then please quote his particular point.

I don't know how you get the idea that he "carefully avoids counterfactual reasoning", but you are definitely in disagreement with the author.

I got the idea by very carefully reading his definition and doing some analysis afterwards. And please provide relevant quote from the author if you think I disagree with him.

It seems that you still didn't bother to understand the KS theorem.

Wrong. I just do not jump at conclusions about things I'm not sure I understand.

Griffiths is not talking about the KS theorem here.

This is first sentence from this paper:
"John Bell in Sec. 5 of [1] while discussing hidden variables in quantum mechanics raised the question of whether quantum theory is “contextual.”"
Reference [1] contains Bell's version of (B)KS theorem.

 

[rubi]

Well, then please quote his particular point.

Another justification of this property 3 relies on a concept which was called
(( contrafactual definiteness ~> (-m), a concept used in daily life whenever we
must make a choice. Contrafactual definiteness means that, in a given situation,
the consequence of each of the possible courses of action can be considered
even though the only sequence of events that can be known for certain is the
one produced by the tinal single choice. Thut is we can hypothesize about the
event sequences following the courses of action that will not be chosen.

(Property 3 is the locality definition from your paper)

I got the idea by very carefully reading his definition and doing some analysis afterwards. And please provide relevant quote from the author if you think I disagree with him.

Your method of carefully reading and doing some analysis doesn't seem to work very well.

Wrong. I just do not jump at conclusions about things I'm not sure I understand.

As I explained, it is totally irrelevant anyway.

This is first sentence from this paper:
"John Bell in Sec. 5 of [1] while discussing hidden variables in quantum mechanics raised the question of whether quantum theory is “contextual.”"
Reference [1] contains Bell's version of (B)KS theorem.

So what? QM is contextual. That's what the KS theorem says. However, it doesn't force any specific form of contextuality. It just says that the mapping must be many-to-one and nothing more.

 

[zonde]

Another justification of this property 3 relies on a concept which was called
(( contrafactual definiteness ~> (-m), a concept used in daily life whenever we
must make a choice. Contrafactual definiteness means that, in a given situation,
the consequence of each of the possible courses of action can be considered
even though the only sequence of events that can be known for certain is the
one produced by the tinal single choice. Thut is we can hypothesize about the
event sequences following the courses of action that will not be chosen.

(Property 3 is the locality definition from your paper)

Thanks. Now I understand where CFD comes into Eberhards definition of "local". It's when he refers to concept of "theory".

Hmm, so do you suggest that we should consider explanations that are not "theories"? Here ... on science forum?

 

[Boing3000]

There is 0% action at a distance, independent of whether you can use it for signaling or not.

That's a way better way to put it. And action at a distance means for me impossible (FTL) transfer of momentum/energy (as per SR)

I don't know what you mean by instantaneous correlation.

I mean the prediction of QM and how they have been verified experimentally.
That is: NO action at a distance (that means Einstein after all was right) but factual instantaneous correlation (when experimenter coerce the measurement timing of A & B to be as close to identical as possible in the labs-frame)

I take also for granted that instantaneous is not to be confused with "very fast", because instantaneous has no unit of speed (and even less an infinite one), does not concern movement nor any kind of space-time related quantity.
But when other type of quantities (not space-time related, like up/down spin information) "are" observed to change simultaneously ("are" because of to separate observation, not because of two separate quantities), the only logical conclusion is that there is only one of this quantity all along (non-locality/nowhere and everywhere).

 

[rubi]

Thanks. Now I understand where CFD comes into Eberhards definition of "local". It's when he refers to concept of "theory".

Hmm, so do you suggest that we should consider explanations that are not "theories"? Here ... on science forum?

I have of course anticipated an absurd response, but I couldn't imagine that it would be that absurd. What did you think? Of course, we are talking about theories. Bell's theorem is talking about theories; Eberhard is talking about theories.

The point is the following: Contrary to what you claimed, Eberhard admits that his definition of locality includes CFD, so his derivation of Bell's inequality and Bell-type inequalities does not make less assumptions than anyone elses derivations.

I mean the prediction of QM and how they have been verified experimentally.
That is: NO action at a distance (that means Einstein after all was right) but factual instantaneous correlation (when experimenter coerce the measurement timing of A & B to be as close to identical as possible in the labs-frame)

Now you explain the term "instantaneous correlation" by putting the word "factual" in front of it. Anyway, nothing is instantaneous about quantum correlations.

 

[zonde]

The point is the following: Contrary to what you claimed, Eberhard admits that his definition of locality includes CFD, so his derivation of Bell's inequality and Bell-type inequalities does not make less assumptions than anyone elses derivations.

First, Eberhard's derivation is different as he does not use hidden variables.
Second, all his requirements can be realized in single chronological sequence of events with no parallel counterfactual sequences. So the only sense in which he is using CFD is that he requires that theory makes predictions. That's all.

 

[rubi]

First, Eberhard's derivation is different as he does not use hidden variables.
Second, all his requirements can be realized in single chronological sequence of events with no parallel counterfactual sequences. So the only sense in which he is using CFD is that he requires that theory makes predictions. That's all.

Ok, once again:
Eberhard's locality definition requires that the theory makes predictions about unperformed measurements. If a theory does not make such predictions, for instance, because it is contextual, then Eberhard's locality definition doesn't apply. The situation is identical to ordinary derivations of Bell's inequality. If you had read paper [10], you would see that his locality definition is just Bell's usual definition with the additional possibility for experimental noise. If a theory violates CFD, then it needn't be local, as usual.

 

[zonde]

Eberhard's locality definition requires that the theory makes predictions about unperformed measurements.

From dictionary:
prediction - a statement made about the future

All future measurements are not (yet) performed. So any theory that makes predictions is making counterfactual statement.
Is it so hard to understand?

 

[rubi]

From dictionary:
prediction - a statement made about the future

All future measurements are not (yet) performed. So any theory that makes predictions is making counterfactual statement.
Is it so hard to understand?

<Mentor's note: edited for distraction>

What is meant is that the theory needs to be able to assign values to quantities that can't be measured simultaneously, like spin along different directions. Eberhard requires this, but it is not satisfied by QM. Hence, QM is compatible with locality.

<Mentor's note: edited for distraction>

 

[Boing3000]

Now you explain the term "instantaneous correlation" by putting the word "factual" in front of it.

Sorry, sloppy language again. "Experimental/observed" is what I meant.

Anyway, nothing is instantaneous about quantum correlations.

I feel like I am back to square one now. Do you meant that QM predict some minimal delay before Bob and Alice can make they observation about an entangled pair state ? I always though they can do them whenever they want to.
Can you point me to this non-instantaneous computation, for example in the case of spin entangled electrons, and eventually the experimental testing of that prediction ?

 

[DrChinese]

I feel like I am back to square one now. Do you meant that QM predict some minimal delay before Bob and Alice can make they observation about an entangled pair state ? I always though they can do them whenever they want to.
Can you point me to this non-instantaneous computation, for example in the case of spin entangled electrons, and eventually the experimental testing of that prediction ?

Time is not a factor (variable) in this case, so it is meaningless to discuss delays, instantaneous, etc. Do you recall my comment (post #64) about "when" and entanglement? That is the point I was making. There is no "when" in the normal sense of the term.

I can tell you that 2 particles were not entangled before time T1 (when we first set things up), and they were not entangled after time T2 (after everything to observe was observed). But I cannot tell you specifically when the entanglement began or when it ended outside of that, nor what is occurring in between. Keep in mind that entangled particles do not need to have even interacted to be entangled, so that complicates things further.

Regardless of all that, QM makes good predictions as to what will be observed.

 

[RockyMarciano]

QM is contextual. That's what the KS theorem says. However, it doesn't force any specific form of contextuality. It just says that the mapping must be many-to-one and nothing more.

But isn't quantum contextuality used when trying to understand QM deterministically?(at least that is what Wiki says:"Quantum Contextuality means that in any theory that attempts to explain quantum mechanics deterministically..."
Could you clarify why would anyone insist on explaining QM deterministically, if that's what you are doing? I thought that was precisely what Bohmian mechanics pursued, is the only basic difference between BM and CH the disagreement about locality?

 

[rubi]

But isn't quantum contextuality used when trying to understand QM deterministically?(at least that is what Wiki says:"Quantum Contextuality means that in any theory that attempts to explain quantum mechanics deterministically..."
Could you clarify why would anyone insist on explaining QM deterministically, if that's what you are doing? I thought that was precisely what Bohmian mechanics pursued, is the only basic difference between BM and CH the disagreement about locality?

No, it has nothing to do with determinism. 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. 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.

CH has nothing to do with BM. BM is a hidden variables theory, while CH is just standard QM. Everything works exactly like in Copenhagen.

 

[Boing3000]

Time is not a factor (variable) in this case, so it is meaningless to discuss delays, instantaneous, etc. Do you recall my comment (post #64) about "when" and entanglement? That is the point I was making. There is no "when" in the normal sense of the term.

But I totally agree, and I would be very happy not to use "instantaneous", in favor of "non-locality". But that is the term I see everywhere to describe that entanglement (perfect correlation) is, with no evolution with respect to time (and space) (between t1 and t2). I have always understood Bell's theorem as being a way to prove that hypothesis (by observation).

The problem I have is to understand rubi, which seems to say that Bell's theorem is about something else, and that QM can explain (global?) entanglement using locality (thus evolution with respect to space-time). Has Griffith proved that ? In one of its paper he starts to say:

The opinion is widespread that quantum mechanics is nonlocal in the sense that it implies the existence of long-range influences which act instantaneously over long distances, in apparent contradiction to special relativity

How can "nonlocal" means "long-range influences which act instantaneously over long distances", when non-local means no space-like nor time-like characteristic. How something with no-size be long, or something with no evolution in time be anything but instantaneous ?

A few sentences below he writes

The widespread belief in the existence of such nonlocal effects seems a bit surprising in view of theorems [36, 37], whose validity does not seem to be in doubt, to the effect that these (supposed) quantum nonlocal influences cannot be used to transmit signals or information

It cannot if the entanglement broke at first interaction. It can otherwise.

Thus they are not detectable by any ordinary experimental test.

Isn't it trivial to measure by ordinary test (after A and B get back together), that the correlation was indeed non-local ?

How could anyone could "suspect any conflict between quantum theory and special relativity", when non-locality is explicitly defined as not to contradict SR ?

 

[DrChinese]

How can "nonlocal" means "long-range influences which act instantaneously over long distances", when non-local means no space-like nor time-like characteristic. How something with no-size be long, or something with no evolution in time be anything but instantaneous ?
...

You are not following the argument in its entirety. 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.

Yes, it is ALSO true as follows: There does "appear" to be something non-local going on. I want to stress appear. You can't say A causes B, B causes A, or A and B are mutual causes/effects (where A and B are non-local to each other).

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.

 

[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?