Classicality in Bell's original reasoning

[rubi]

If you mean CFD as validity of "what if?" type of questions then I completely agree with you.

I mean the mathematically precise requirement that $A_{\alpha\beta}^\chi=A_{\alpha\beta}$.

But take into consideration that while it is meaningless to apply CFD to reality it is valid for any model of reality that is capable of making predictions.

No, it is not. The KS theorem undeniably proves CFD must be invalid in any model that reproduces all QM predictions. There is no way out of this and if you claim that you can have a model that reproduces QM and maintains CFD then you are factually wrong and you are denying a rigorously established mathematical theorem. So assuming CFD in the proof of Bell's inequality is definitely an extra assumption that precludes the applicability of the inequality to QM models.

 

[zonde]

Because it is the main assumption of the Bell inequalities that distant(separated) independent points have prefixed measurement outcomes for any possible measurement(the perfect anticorrelation of same direction measurements required fixes all possible orientations simultaneously in the plane determined by the basis chosen). Alice and Bob are not of course obligated to check this premise simultaneously, but the existence of those simultaneous outcomes existing is assumed by Bell by assigning hidden variables determining A and B outcomes in a linear independent way(in a way such that the determination of A is independent of the determination of B by $\lambda$.

I do not follow you. We assume that two measurements are independent and to make it more convincing we chose to make them simultaneously at two distant points. If we believe that they are independent there is no particular need to perform them simultaneously. The key point here is that they are independent.

 

[zonde]

I mean the mathematically precise requirement that $A_{\alpha\beta}^\chi=A_{\alpha\beta}$.

What is $\chi$ in your statement?

 

[RockyMarciano]

I do not follow you. We assume that two measurements are independent and to make it more convincing we chose to make them simultaneously at two distant points. If we believe that they are independent there is no particular need to perform them simultaneously. The key point here is that they are independent.

Yes, it is the key point, and there is no need to perform anything simultaneously. The hidden variable determines both A and B independently at any given time t, that is what simultaneously mean.

 

[rubi]

What is $\chi$ in your statement?

The Kochen-Specker theorem proves that an assignment of random variables to quantum observables can't be one-to-one. It must be many-to-one. Hence, there must be an index that labels this many-to-oneness. I chose to name this index $\chi$. If you don't put this contextuality index, you are excluding all contextual theories (and thus QM) right from the start.

(I have already explained the very same thing to you in another thread just a few months ago, but apparently you didn't read or understand it. If you pretend to understand Bell's theorem better than all the experts in QM foundations (who disagree with you), then you are supposed to understand at least the most basic theorems of that field. Otherwise, we can't productively discuss this.)

 

[zonde]

The Kochen-Specker theorem proves that an assignment of random variables to quantum observables can't be one-to-one. It must be many-to-one. Hence, there must be an index that labels this many-to-oneness. I chose to name this index $\chi$. If you don't put this contextuality index, you are excluding all contextual theories (and thus QM) right from the start.

But does this contextuality index describe global measurement arrangement as well? As I understand it does. So that it is assumed right from the start that the model is either superdeterministic or non-local.

I have already explained the very same thing to you in another thread just a few months ago, but apparently you didn't read or understand it.

Hmm, surely you noticed that I replied to your post.

If you pretend to understand Bell's theorem better than all the experts in QM foundations (who disagree with you),

Yes, yes, I already understood that I am misunderstanding all the experts that seem to say the same things as me. For example I totally misunderstood Bell as you explained earlier:

Assuming hidden variables and assuming determinism is not the same thing. What you need to assume is a hidden variables model. Those hidden variables may be deterministic or they may be stochastic. That doesn't matter and that's what Bell said in that quote.

This time I will give longer quote of Bell that includes the sentence that you commented:

It is important to note that to the limited degree that determinism plays a role in the EPR argument, it is not assumed but inferred. What is held sacred is the principle of “local causality” or “no action at a distance”. Of course, mere correlation between distant events does not itself imply action at a distance, but only correlation between the signals reaching the two places. These signals, in the idealized example of Bohm, must be sufficient to determine whether the particles would go up or down. For any residual undeterminism could only spoil the perfect correlation. It is remarkably difficult to get this point across, that determinism is not a presupposition of the analysis.

 

[Boing3000]

This time I will give longer quote of Bell that includes the sentence that you commented:

Why are you quoting Rubi ?

That doesn't matter and that's what Bell said in that quote.

And then confirm what he says ?

It is remarkably difficult to get this point across, that determinism is not a presupposition of the analysis.

I have a hard time to understand what this discussion is about, and on what you are disagreeing...

 

[zonde]

And then confirm what he says?

Bell does not say that determinism does not matter. He says that determinism is inferred, not assumed. Here:

It is important to note that to the limited degree that determinism plays a role in the EPR argument, it is not assumed but inferred.

And another quote:

My own first paper on this subject ... starts with a summary of the EPR argument from locality to deterministic hidden variables. But the commentators have almost universally reported that it begins with deterministic hidden variables.

 

[rubi]

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. This leaves us with infinitely many ways to construct many-to-one mappings. Also, it is not relevant. The point is that if you drop this index, you are excluding QM from the analysis (which is fine, since the inequality is supposed to exclude certain classical models, but not QM). Thus, Bell's inequality says nothing about QM.

Hmm, surely you noticed that I replied to your post.

Yes, and I also noticed that you don't address the arguments, which is why it is so pointless to discuss with you.

Yes, yes, I already understood that I am misunderstanding all the experts that seem to say the same things as me. For example I totally misunderstood Bell as you explained earlier:

This time I will give longer quote of Bell that includes the sentence that you commented:

Bell is wrong and this is well understood by all experts today. QM respects the EPR notion of locality, as I have told you uncountably many times. A rigorous proof can be found here. Either you find an error in that proof or you should refrain from making the same false claim over an over. From reading your posts, I conclude that you haven't even looked at the article.

If you again don't address the arguments, I won't waste any more time to respond to your posts.

 

[zonde]

The point is that if you drop this index, you are excluding QM from the analysis (which is fine, since the inequality is supposed to exclude certain classical models, but not QM). Thus, Bell's inequality says nothing about QM.

Of course Bell's analysis does not cover QM as the question is about models that can say something more than just give statistical predictions. And as I understand KS is addressing the same question.

Bell is wrong and this is well understood by all experts today.

Except Norsen, right? Or is he non-expert?

From reading your posts, I conclude that you haven't even looked at the article.

No, I haven't. It's behind paywall.
But as I understand from this Griffiths article that his take on Bell inequality violations is that there is assumption of "classical" hidden variables and it does not hold:

Quantum theory predicts correlations in the spin-singlet state that do not satisfy Bell inequalities (Shimony 2009), and by now there is ample evidence from experiments on the analogous property of pairs of correlated photons that quantum theory is correct, and therefore one or more of the assumptions that go into the derivation of a Bell inequality must be faulty. While the claim has been made that the key assumption is locality, and therefore a violation of Bell inequalities implies that the real (quantum) world is nonlocal, a histories analysis identifies the problem as a different assumption made by Bell: the existence of classical hidden variables that are inconsistent with Hilbert space quantum mechanics.

So I don't see that this adds anything to discussion unless CH provides some explanation for perfect correlations under assumption of "local causality".

 

[Boing3000]

a histories analysis identifies the problem as a different assumption made by Bell: the existence of classical hidden variables that are inconsistent with Hilbert space quantum mechanics.

Zonde, what do you think Giffiths means by that. That a "classical" model must exist that disagree with QM prediction (which seems pointless), or that such a classical non-local cannot exist (which is wrong, that's easy to build one, but only with non-locality)

So I don't see that this adds anything to discussion unless CH provides some explanation for perfect correlations under assumption of "local causality".

Can you point me to a example of "perfect correlations under assumption of "local causality"" ?

 

[rubi]

Of course Bell's analysis does not cover QM as the question is about models that can say something more than just give statistical predictions. And as I understand KS is addressing the same question.

The point is that Bell's assumptions don't cover theories that can reproduce the QM predictions, even if you ignore the locality assumption. Bell's theorem is solely a theorem about certain classical theories. The fact that QM violates the inequality means that one of the assumptions is wrong (dropping the contextuality index or the locality assumption). It is plain as day that Bell dropped the contextuality index and thus it is a non-trivial assumption of the theorem.

Except Norsen, right? Or is he non-expert?

Norsen is not an expert. He has never contributed anything to the subject. Most of his papers just reproduce Bell's writings.

No, I haven't. It's behind paywall.
But as I understand from this Griffiths article that his take on Bell inequality violations is that there is assumption of "classical" hidden variables and it does not hold:

So I don't see that this adds anything to discussion unless CH provides some explanation for perfect correlations under assumption of "local causality".

Yes, Griffiths (like everyone else) agrees Bell critically assumes the existence of some classical hidden variables, which one can rightfully deny. It follows that one doesn't need to reject locality. CH provides a perfectly clear explanation for the correlations: The measurements are correlated, because the particles have been prepared this way locally. Griffiths proves in his paper that the probability for EPR locality to be violated is zero. There is no contradiction to Bell's theorem, because Bell is just wrong about the idea that the EPR argument implies his assumptions. It doesn't. If you don't agree with this, then you must point out an error in Griffiths analysis. (If you can't get hold of the paper, then you can also look in his book, which contains the proof as well.)

You forgot to quote Griffths next sentence:

In addition, the histories approach makes it possible to establish on the basis of quantum mechanics itself a principle of Einstein locality (Griffiths 2011b):

Objectively real internal properties of an isolated individual system do not change when something is done to another non-interacting system

 

[DrChinese]

Bell is wrong and this is well understood by all experts today. ...

Which Bell? There is nothing wrong in his original paper, which starts with the EPR reasoning. Some of Bell's later writings meandered a bit in his descriptions and intent, but I don't consider those "gold". From Griffiths:

"While the claim has been made that the key assumption is locality, and therefore a violation of Bell inequalities implies that the real (quantum) world is nonlocal, a histories analysis identifies the problem as a different assumption made by Bell: the existence of classical hidden variables that are inconsistent with Hilbert space quantum mechanics."

So what? It is precisely those classical hidden variables that EPR brings up ("elements of reality") and Bell disposes of. Nothing wrong about that. If those are per se inconsistent with "Hilbert space quantum mechanics", so much the better.

 

[DrChinese]

Norsen is not an expert. He has never contributed anything to the subject. Most of his papers just reproduce Bell's writings.

I thought I was the only one who thought that.

Norsen specifically likes to twist Bell to "prove" that locality must be rejected. I completely disagree with his reasoning, which I consider circular.

 

[rubi]

Which Bell? There is nothing wrong in his original paper, which starts with the EPR reasoning. Some of Bell's later writings meandered a bit in his descriptions and intent, but I don't consider those "gold". From Griffiths:

"While the claim has been made that the key assumption is locality, and therefore a violation of Bell inequalities implies that the real (quantum) world is nonlocal, a histories analysis identifies the problem as a different assumption made by Bell: the existence of classical hidden variables that are inconsistent with Hilbert space quantum mechanics."

So what? It is precisely those classical hidden variables that EPR brings up ("elements of reality") and Bell disposes of. Nothing wrong about that. If those are per se inconsistent with "Hilbert space quantum mechanics", so much the better.

The point is that the EPR argument is informal and thus no mathematical statement can be derived from it. Thus, the assumption of hidden variables is really an assumption and not a necessity that can be derived. One just can't derive the existence of hidden variables. It is perfectly possible that hidden variables just don't exist and that's what most people actually agree with. zonde, on the other hand, believes that the non-existence of hidden variables is not a viable alternative, because the EPR argument presumably proves their existence. Of course he is wrong.

 

[physika]

Alice's and Bob's measurements do not have to be simultaneous. Why we should burden ourselves with such restriction?
.

Indeed.

and there is really, simultaneity?

I do not follow you. We assume that two measurements are independent and to make it more convincing we chose to make them simultaneously at two distant points. If we believe that they are independent there is no particular need to perform them simultaneously. The key point here is that they are independent.

and not necessarily independent.

.

 

[stevendaryl]

[Bell]: It is important to note that to the limited degree that determinism plays a role in the EPR argument, it is not assumed but inferred. What is held sacred is the principle of “local causality” or “no action at a distance”. Of course, mere correlation between distant events does not itself imply action at a distance, but only correlation between the signals reaching the two places. These signals, in the idealized example of Bohm, must be sufficient to determine whether the particles would go up or down. For any residual undeterminism could only spoil the perfect correlation. It is remarkably difficult to get this point across, that determinism is not a presupposition of the analysis.

Where did this come from? I'm always trying to find this quote when someone describes Bell's argument as assuming deterministic hidden variables.

 

[zonde]

Where did this come from? I'm always trying to find this quote when someone describes Bell's argument as assuming deterministic hidden variables.

It's in Bertlmann's socks and the nature of reality in p.C2-46 in this link

 

[A. Neumaier]

Where did this come from? I'm always trying to find this quote when someone describes Bell's argument as assuming deterministic hidden variables.

It's in Bertlmann's socks and the nature of reality in p.C2-46 in this link

But the first sentence of the quote as given by zonde is an unjustified assertion made by Bell in a quite informal context. See post #5 of this thread.

 

[zonde]

The point is that Bell's assumptions don't cover theories that can reproduce the QM predictions

Bell's analysis does not cover theories that give only statistical predictions. And there is no point repeating statements about which we disagree. My position was that there is only one assumption.

Norsen is not an expert. He has never contributed anything to the subject. Most of his papers just reproduce Bell's writings.

Norsen is defending Bell's own position. Sounds like a contribution to me.
Ok, you don't like Norsen, but what do you say about Eberhard?

Yes, Griffiths (like everyone else) agrees Bell critically assumes the existence of some classical hidden variables, which one can rightfully deny. It follows that one doesn't need to reject locality. CH provides a perfectly clear explanation for the correlations: The measurements are correlated, because the particles have been prepared this way locally. Griffiths proves in his paper that the probability for EPR locality to be violated is zero. There is no contradiction to Bell's theorem, because Bell is just wrong about the idea that the EPR argument implies his assumptions. It doesn't. If you don't agree with this, then you must point out an error in Griffiths analysis. (If you can't get hold of the paper, then you can also look in his book, which contains the proof as well.)

You are trying to put the burden of proof on me. And why do I have to agree with that?

 

[stevendaryl]

But the first sentence of the quote as given by zonde is an unjustified assertion made by Bell in a quite informal context. See post #5 of this thread.

Well, I think that Bell's right, and you're wrong, in this regard. When Alice measures spin-up along axis $\hat{a}$, she knows definitely that Bob will not measure spin-up along axis $\hat{a}$. She doesn't know what Bob's going to do, but she does know a constraint on the pair:

$\langle$ What Bob will measure, What his result will be$\rangle$

I think that should count as certain knowledge.

 

[rubi]

Bell's analysis does not cover theories that give only statistical predictions.

The situation is much worse: Bell's analysis doesn't cover contextual theories.

My position was that there is only one assumption.

Your position is wrong and falsified. If locality was the only assumption, QM could not be local. However, as I have explained several times now, QM is pefectly compatible with locality. You are contradicting established scientific facts.

what do you say about Eberhard?

Eberhard acknowledges that every derivation of the BI assumes CFD, so I have no problem with him.

You are trying to put the burden of proof on me. And why do I have to agree with that?

Yes, of course, if you contradict an established scientific fact, the burdon of proof naturally is on you. Griffiths has proved that QM is compatible with locality, so if you don't agree, then you have to find a mistake in his proof. This is how science works. You can of course disagree, but then you disagree with scientific practice. Disagreeing with facts that have undeniably been established is completely unscientific. If you think it is admissible to disagree with a proven fact without pointing out a mistake in the proof, then you are acting like a little child. It is on the same level as stubbornly claiming that $1+1=5$.

 

[zonde]

Zonde, what do you think Giffiths means by that. That a "classical" model must exist that disagree with QM prediction (which seems pointless), or that such a classical non-local cannot exist (which is wrong, that's easy to build one, but only with non-locality)
My guess would be that he suggest there is assumption of locally deterministic hidden variables.
Can you point me to a example of "perfect correlations under assumption of "local causality"" ?

You mean example that agrees with QM predictions, right? I can't give you example that is consistent with scientific approach. There are some unscientific ones. Superdeterministic and maybe interpretation where measurement results can't be considered as physical facts.

 

[zonde]

The situation is much worse: Bell's analysis doesn't cover contextual theories.

You have not defined the "context" term, just given some vague statements what it does not include.

Your position is wrong and falsified. If locality was the only assumption, QM could not be local. However, as I have explained several times now, QM is pefectly compatible with locality. You are contradicting established scientific facts.

Falsified because I don't accept the burden of proof, right?

Eberhard acknowledges that every derivation of the BI assumes CFD, so I have no problem with him.

Then point out assumption of CFD in his own proof.

Yes, of course, if you contradict an established scientific fact, the burdon of proof naturally is on you. Griffiths has proved that QM is compatible with locality, so if you don't agree, then you have to find a mistake in his proof. This is how science works. You can of course disagree, but then you disagree with scientific practice. Disagreeing with facts that have undeniably been established is completely unscientific. If you think it is admissible to disagree with a proven fact without pointing out a mistake in the proof, then you are acting like a little child. It is on the same level as stubbornly claiming that 1+1=5.

Bell has proved that QM is incompatible with locality. He did that before Griffiths "proved" the opposite.

 

[rubi]

You have not defined the "context" term, just given some vague statements what it does not include.

I have defined it precisely. Contextuality means that the random variables must carry an index.

Falsified because I don't accept the burden of proof, right?

No, falsified because someone has proved you wrong.

Then point out assumption of CFD in his own proof.

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

Bell has proved that QM is incompatible with locality. He did that before Griffiths "proved" the opposite.

Bell did not prove that QM is incompatible with locality. I explained precisely where he makes an extra assumption. It is consensus among physicists that Bell makes extra assumptions. It is also consensus that Griffiths proof contains no errors. You are the only one in disagreement with established science. The burden of proof is on you. If something is wrong with the proof, then you should be able to point out a mistake. Griffiths paper is from 1998 and it is well known and has many citations. If there was an error, someone would have pointed it out by now.

 

[DrChinese]

Bell's analysis does not cover theories that give only statistical predictions.

That's incorrect. The Bell paper absolutely considers such theories. The requirement is that there be some function or set of functions that would determine an outcome, based on some set of input parameters. You don't need to be able to actually predict each outcome. So lack of knowledge could lead to statistical predictions in such cases.

 

[Boing3000]

There are some unscientific ones. Superdeterministic and maybe interpretation where measurement results can't be considered as physical facts.

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

 

[Boing3000]

Griffiths has proved that QM is compatible with locality

As a layman I suppose it would be impossible for me to get a tone down version of that proof (or a free reading at least ?)

I found this article but it doesn't sound right. I am quite disturb by the apparent confusion between FTL "influence" and its opposite : non-local/instantaneous.

I also have always taken for granted that when a particle with an entangled property is measured, the corresponding entanglement is destroyed by the measurement.. am I correct ?

 

[DrChinese]

I also have always taken for granted that when a particle with an entangled property is measured, the corresponding entanglement is destroyed by the measurement.. am I correct ?

In most cases, I would say you are correct. There are a few complicating issues: 1) When does the entanglement end (when both are measured or just one) ? 2) The entanglement does not end if entanglement swapping is made to occur.

 

[rubi]

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

Consistent histories is an example of a quantum theory, which is local according to the EPR definition. It's often considered to be the modern version of the Copenhagen interpretation.

As a layman I suppose it would be impossible for me to get a tone down version of that proof (or a free reading at least ?)

Griffiths essentially proves that the probability for a non-local influence is $0$. The argument is too long for me to type it here. Maybe you can get hold of Griffiths book "Consistent Quantum Theory" or maybe he has some version of the argument on the arXiv.

I found this article but it doesn't sound right. I am quite disturb by the apparent confusion between FTL "influence" and its opposite : non-local/instantaneous.

This is Griffiths response to it.

I also have always taken for granted that when a particle with an entangled property is measured, the corresponding entanglement is destroyed by the measurement.. am I correct ?

This is the naive view, which is good enough for practical purposes. If you take QM seriously, you would instead expect the particle will become entangled with the measurement apparatus und the environment, i.e. the entanglement is still there, but you cannot see it in the reduced picture.

 

[Boing3000]

1) When does the entanglement end (when both are measured or just one) ?

I would say it make no difference, because the other particle is the only one connected with that property thus future correlation became irrelevant (maybe not for 3 particle entanglement, if it exists, and should be testable).

2) The entanglement does not end if entanglement swapping is made to occur.

Thank you, for pointing that out, I had to look it up !

 

[Boing3000]

Griffiths essentially proves that the probability for a non-local influence is $0$

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

]This is Griffiths response to it.

My next read, thanks !

This is the naive view, which is good enough for practical purposes. If you take QM seriously, you would instead expect the particle will become entangled with the measurement apparatus und the environment, i.e. the entanglement is still there, but you cannot see it in the reduced picture.

I deduce that from the fact that no signaling is possible. So it seems logical that measurement apparatus must somewhat erase the "link" between the particles (or add so much other state to the point of making it random).
If a "delicate" measurement (not forbidding the possibility to redo the same measurement on the same particle) was possible, it would be straightforward to communicate between Alice and Bob

 

[Nicky665]

There's this guy who in one page derives bell inequality starting only from the assumption of non-locality (being in two different places at the same time). Anyone wants to see it ?

 

[PeterDonis]

There's this guy

Is it a textbook or peer-reviewed paper?

 

[Nicky665]

No. But its one page with 7 equations ... I don't know if there's anything to his arguments, by the way.