Local realism ruled out? (was: Photon entanglement and )

[nanosiborg]

Who are such "loophole people"?

People who think that a loophole-free test will change the current situation, which is that qm predictions are in line with results and violate BI, and lhv predictions are not in line with results.

 

[akhmeteli]

People who think that a loophole-free test will change the current situation, which is that qm predictions are in line with results and violate BI, and lhv predictions are not in line with results.

Whether I am one of those "loophole people" or not, I respectfully disagree with your assessment of the current situation, e.g., with the following phrase: "lhv predictions are not in line with results." As long as there are loopholes in experiments (and there have been no loophole-free experiments so far), the results of the experiments cannot rule out all lhv theories, so at least some lhv theories' predictions are in line with the results.

 

[nanosiborg]

As long as there are loopholes in experiments (and there have been no loophole-free experiments so far), the results of the experiments cannot rule out all lhv theories ...

Strictly speaking, this is correct. But I think the evidence is overwhelming that if a loophole-free test were done, then qm would correctly predict the results and lhv would not.

... so at least some lhv theories' predictions are in line with the results.

Assumptions are required because of the inability to close all loopholes in the same test. So far, given the (reasonable, imo) assumptions used by the testers, qm agrees with experiment and lhv doesn't.

The incompatibility between qm and lhv has been mathematically proven. They necessarily predict a different correlation between θ and rate of coincidental detection. So, if qm is correct, then (Bell) lhv models of quantum entanglement are ruled out.

I'm betting that qm will continue to be confirmed, even in a loophole-free test.

 

[akhmeteli]

Strictly speaking, this is correct. But I think the evidence is overwhelming that if a loophole-free test were done, then qm would correctly predict the results and lhv would not.

This is an opinion, not a fact. Somebody believes the evidence is overwhelming, somebody believes there is no evidence, as there have been no loophole-free experiments. How do you like the following "overwhelming evidence" that planar Euclidean geometry (PEG) is wrong (I already offered it in this thread)? PEG predicts that the sum of angles of any triangle is 180 degrees, whereas experiments demonstrate with high confidence that the sum of angles of a quadrangle and the sum of angles of a triangle on a sphere are not equal to 180 degrees. The obvious "loopholes" will certainly be closed simultaneously in future experiments:-)

Assumptions are required because of the inability to close all loopholes in the same test. So far, given the (reasonable, imo) assumptions used by the testers, qm agrees with experiment and lhv doesn't.

My question is: what assumption is more reasonable: local realism or, say, fair sampling? Apparently, you'd vote for the latter one, I would vote for the former one. So who's right? I believe so far this is just a matter of opinion.

The incompatibility between qm and lhv has been mathematically proven. They necessarily predict a different correlation between θ and rate of coincidental detection. So, if qm is correct, then (Bell) lhv models of quantum entanglement are ruled out.

I agree, the Bell theorem proves incompatibility between standard quantum theory and local realism. I argue though that this is not a problem for local realism, as, strictly speaking, standard quantum theory is incompatible with itself (I have in mind the notorious problem of measurements in quantum theory), so, strictly speaking, it cannot be completely correct. To prove incompatibility of standard quantum theory and local realism, you need to prove that the Bell inequalities can be violated in quantum theory. To this end, you need to use two mutually contradictory postulates of standard quantum theory: unitary evolution and, say, the projection postulate.

I'm betting that qm will continue to be confirmed, even in a loophole-free test.

Strictly speaking, this phrase just attests to the strength of your opinion, not to its correctness. I don't believe local realism will be ruled out in loophole-free experiments, but again, this is just my opinion, not a fact. Maybe we should just wait and see.

 

[akhmeteli]

Andy, While we're waiting, please, would you mind spelling out what you mean by "local realism"?

Accepting that by "local" you mean "Einstein-local", maybe we could just focus on what "realism" means to you, please?

Locality, in my book, means that no effect can have its cause anywhere beyond its past light-cone. I guess this is what you call "Einstein-local".

Realism, in my book, is not the realism of the EPR article, i.e. I don't believe that, say, a particle has definite values of coordinates, momentum, spin projections, etc., whether the relevant observables are measured or not. You may say that I do not seek noncontextual hidden variables. The version of realism that I accept is contextual: any state can be described by some set of parameters that uniquely define the state's evolution. I would not call those parameters "hidden variables", as, say, in the models of my articles, they are not exactly hidden: they are the potentials of the electromagnetic fields and their derivatives. This version is "contextual" as the set of parameters must describe the relevant instruments as well.

 

[nanosiborg]

My question is: what assumption is more reasonable: local realism or, say, fair sampling? Apparently, you'd vote for the latter one, I would vote for the former one. So who's right? I believe so far this is just a matter of opinion.

Yes, I'd vote for the latter one. We could argue about the merits of our apparently different processing of certain articles, but I prefer to just wait for a loophole-free test.

What do you think is the likelihood of a loophole-free test in the foreseeable future?

I agree, the Bell theorem proves incompatibility between standard quantum theory and local realism. I argue though that this is not a problem for local realism, as, strictly speaking, standard quantum theory is incompatible with itself (I have in mind the notorious problem of measurements in quantum theory), so, strictly speaking, it cannot be completely correct. To prove incompatibility of standard quantum theory and local realism, you need to prove that the Bell inequalities can be violated in quantum theory. To this end, you need to use two mutually contradictory postulates of standard quantum theory: unitary evolution and, say, the projection postulate.

There's no measurement problem of the sort you mention (ie., qm being incompatible with itself due to contradictory dynamical laws or postulates) with a minimalist statistical interpretation. So, in the minimalist view, if a loophole-free test affirms qm, then local realism (at least in the form of Bell lhv models) will be definitively ruled out.

 

[harrylin]

Strictly speaking, this is correct. But I think the evidence is overwhelming that if a loophole-free test were done, then qm would correctly predict the results and lhv would not.[..]
[..]
What do you think is the likelihood of a loophole-free test in the foreseeable future?

I wonder if such a conclusive test will be possible; the failure to accomplish that feat in the course of decades suggests to me that it may be a law of nature that such a test is not possible (similar to the relativity and uncertainty principles).

 

[akhmeteli]

What do you think is the likelihood of a loophole-free test in the foreseeable future?

I don't know. Just don't have enough information. Some knowledgeable people believe such a test is imminent, they say something like "in a year or two". I won't be surprised though if such a test will take much, much more time. Whenever it happens though, I don't expect any violations in a loophole-free test.

There's no measurement problem of the sort you mention (ie., qm being incompatible with itself due to contradictory dynamical laws or postulates) with a minimalist statistical interpretation.

I did not consider the minimalist statistical interpretation, just standard quantum theory. However, based on the discussion of some other interpretations (such as Bohmian one) in this thread, I tend to think that if there are no contradictions in an interpretation, it is either impossible to prove that the Bell inequalities can be violated, or predictions of the interpretation differ from those of standard quantum theory, making dubious the experimental status of the interpretation.

So, in the minimalist view, if a loophole-free test affirms qm, then local realism (at least in the form of Bell lhv models) will be definitively ruled out.

Irrespective of any interpretation, I agree that loophole-free experimental demonstration of violations would make a local realist's life much more difficult, although "definitively" would be a strong word even then - e.g., there would still be a possibility of superdeterminism.

 

[nanosiborg]

I don't know. Just don't have enough information. Some knowledgeable people believe such a test is imminent, they say something like "in a year or two". I won't be surprised though if such a test will take much, much more time. Whenever it happens though, I don't expect any violations in a loophole-free test.

Whatever the results it will be exciting when (if) it happens.

I did not consider the minimalist statistical interpretation, just standard quantum theory.

I was thinking of the minimalist statistical interpretation as being standard quantum theory.

Irrespective of any interpretation, I agree that loophole-free experimental demonstration of violations would make a local realist's life much more difficult, although "definitively" would be a strong word even then - e.g., there would still be a possibility of superdeterminism.

I consider superdeterminism (a metaphysical conspiracy theory) to be an unacceptable stretch anyway. Given a loophole-free test that confirms qm and falsifies lhv I don't see superdeterminism being taken seriously by anybody. I mean, local realists will have to admit, if that happens, that their program has been definitively refuted and Bell lhv models of quantum entanglement are definitively ruled out.

 

[akhmeteli]

I was thinking of the minimalist statistical interpretation as being standard quantum theory.

If this interpretation adopts both unitary evolution (UE) and the projection postulate (PP) of standard quantum theory, it also adopts its contradictions. If you believe you have a solution to the problem of measurements in standard quantum theory... Well, congratulations... Good luck "selling" your solution to physics community... If, however, this interpretation does not adopt UE and PP, it's not standard quantum theory. Moreover, it would be difficult, if not impossible, to prove that there can be violations in this interpretation.

I consider superdeterminism (a metaphysical conspiracy theory) to be an unacceptable stretch anyway. Given a loophole-free test that confirms qm and falsifies lhv I don't see superdeterminism being taken seriously by anybody. I mean, local realists will have to admit, if that happens, that their program has been definitively refuted and Bell lhv models of quantum entanglement are definitively ruled out.

I agree that superdeterminism does not look good. However, I don't know how to refute 't Hooft's reasoning in favor of superdeterminism (by the way, 't Hooft is not "anybody"): "if you believe in determinism, you have to believe it all the way." (http://arxiv.org/abs/1112.1811)

 

[lugita15]

If this interpretation adopts both unitary evolution (UE) and the projection postulate (PP) of standard quantum theory, it also adopts its contradictions.

akhmeteli, I discussed this with you earlier this thread, but I don't know why you keep insisting that unitary evolution and the projection postulate are logically contradictory. What's wrong with saying that the wave function evolves unitarily until a measurement is made, at which point it undergoes collapse in accordance with the projection postulate? It may be philosophically undesirable for there to be two processes, but where is the logical contradiction? I don't think most physicists would agree with you that the measurement problem involves a logical contradiction.

 

[DrChinese]

(by the way, 't Hooft is not "anybody")

I don't think 't Hooft has been very convincing to date. I think nanosiborg was being fair using the word "anybody", I think it is obvious that the meaning was "other than the author himself". And was not intended to be literal anyway, the idea has not gained much traction since it was first thrown out there many years ago.

 

[akhmeteli]

akhmeteli, I discussed this with you earlier this thread, but I don't know why you keep insisting that unitary evolution and the projection postulate are logically contradictory. What's wrong with saying that the wave function evolves unitarily until a measurement is made, at which point it undergoes collapse in accordance with the projection postulate? It may be philosophically undesirable for there to be two processes, but where is the logical contradiction? I don't think most physicists would agree with you that the measurement problem involves a logical contradiction.

Dear Lugita15,

It is my understanding that you discussed this issue with me in just one post in this thread - post 758. If I am mistaken, please let me know. I gave my answer to your post 758 in post 760.

In your last post (822) you did offer an additional (von Neumann's) argument - that unitary evolution and the projection postulate "take turns". Maybe you can avoid a logical contradiction in this way (see though http://plato.stanford.edu/entries/qt-measurement/, section 3, second and subsequent paragraphs), but you buy into more problems, and not just philosophical ones. I already gave the conclusions of Schlosshauer's analysis (M. Schlosshauer, Annals of Physics, 321 (2006) 112-149) of experimental data in this thread (post 41). He wrote, in particular, that "the universal validity of unitary dynamics and the superposition principle has been confirmed far into the mesoscopic and macroscopic realm in all experiments conducted thus far;", and "no positive experimental evidence exists for physical state-vector collapse;"

So one may ask: if measurement leads to collapse, does this mean that we cannot consider unitary evolution of the measured system together with the instrument (and with the observer, if you wish)? Would unitary evolution give wrong results in this case? Not according to Schlosshauer's analysis. There is no positive experimental evidence of collapse, and there is no experimental evidence of violations of unitary evolution. On the other hand, in some cases, collapse can be a good approximation for a measurement process fully described by unitary evolution ( http://arxiv.org/abs/1107.2138 (accepted for publication in Physics Reports - http://www.sciencedirect.com/science/article/pii/S0370157312004085 )), but just an approximation.

Some other difficulties of von Neumann's approach are discussed in http://plato.stanford.edu/entries/qt-measurement/.

So I insist that unitary evolution (UE) and the projection postulate (PP) are indeed mutually contradictory for reasons given in my post 760 in this thread. Logic might allow UE and PP "take turns", but if you believe that they do take turns, you have to believe that UE is not always correct, and there is no experimental basis for that.


Let me just ask you: do you seriously believe that unitary evolution is not always correct?

 

[akhmeteli]

I don't think 't Hooft has been very convincing to date.

Dear DrChinese,

I don't want to and I don't need to defend superdeterminism. I am just saying that there is some logic behind it. However, if a theory does not defy logic, that's good, but not enough:-)

I think nanosiborg was being fair using the word "anybody", I think it is obvious that the meaning was "other than the author himself".

As 't Hooft was not in the context of nanosiborg's post 820, this is not obvious:-)

And was not intended to be literal anyway, the idea has not gained much traction since it was first thrown out there many years ago.

I agree. However, while we may have a similar opinion of superdeterminism, this is an opinion, not a fact. nanosiborg finds superdeterminism unacceptable, but 't Hooft's example shows that superdeterminism's alternatives may seem even more disgusting to some people:-)

 

[DrChinese]

I agree. However, while we may have a similar opinion of superdeterminism, this is an opinion, not a fact. nanosiborg finds superdeterminism unacceptable, but 't Hooft's example shows that superdeterminism's alternatives may seem even more disgusting to some people:-)

I feel 't Hooft has not done step A in the presentation of this idea: tell us the weaknesses as well as the strengths! For a scientist NOT to take the time and effort to do this is, in my opinion, a very serious issue. I consider it a matter of integrity in the sense that I would expect similar behavior from a salesman. 't Hooft is a highly respected scientist (deservedly so) and not a salesman, but in this case that is what I see. So if I were talking to him, I would say: be your own critic before you write on this again.

Specifically: there are in fact HUGE requirements on a superdeterministic (SD) theory. For example: exactly how is the information locally maintained so that spatially distant relationships can be honored in keeping with the predictions of QM? And does SD posit new relationships between the 4 fundamental forces?* And since QM does NOT properly describe the true** relationship between entangled particles, what is it? These are just a few starter questions. So when it comes to "disgusting", I would prefer to see clearly the ugly side of SD so I can choose. I already know what is "disgusting" in the various usual interpretations.

*Since I can develop Bell tests that exploit these relationships, this is a very serious problem. For example, I have a radioactive sample that randomly drives the selection of Bob's measurement setting. This requires a very complex explanation which will inevitably be inconsistent with the Standard model.

**Instead only describes the apparent relationship. Obviously that is different otherwise we wouldn't need to have SD in the first place.

 

[nanosiborg]

If this interpretation adopts both unitary evolution (UE) and the projection postulate (PP) of standard quantum theory, it also adopts its contradictions. If you believe you have a solution to the problem of measurements in standard quantum theory... Well, congratulations... Good luck "selling" your solution to physics community... If, however, this interpretation does not adopt UE and PP, it's not standard quantum theory. Moreover, it would be difficult, if not impossible, to prove that there can be violations in this interpretation.

I think of standard qm as the minimal set of maths necessary to calculate accurate predictions. The minimalist statistical interpretation (MSI) of qm is simply standard qm without any accompanying assumptions about deep reality. There's no measurement problem (in the foundational sense that I think you mean it) re MSI. Whatever you want to call it, it's just qm without reification of any of the maths used in calculating predictions.

I can appreciate that foundationalists have a problem with standard qm having reversible and irreversible dynamical processes, and that this seems illogical to you. It doesn't seem illogical to me because I don't think of standard qm as saying anything about deep reality, and qm works quite well in its present form. Why do what seem to some like disparate, even contradictory, elements of the theory produce such accurate results?

I agree that superdeterminism does not look good. However, I don't know how to refute 't Hooft's reasoning in favor of superdeterminism (by the way, 't Hooft is not "anybody"): "if you believe in determinism, you have to believe it all the way." (http://arxiv.org/abs/1112.1811)

I think one can accept the assumption of determinism without adopting superdeterminism, which I consider as a conspiratorial extension of it. I'm ready to accept the results of a loophole-free Bell test. I just hope that when this is done and qm is confirmed and lhv is contradicted, then the lhv people won't grasp at increasingly absurdly fashioned straws (such as superdeterminism).

 

[akhmeteli]

I think of standard qm as the minimal set of maths necessary to calculate accurate predictions. The minimalist statistical interpretation (MSI) of qm is simply standard qm without any accompanying assumptions about deep reality. There's no measurement problem (in the foundational sense that I think you mean it) re MSI. Whatever you want to call it, it's just qm without reification of any of the maths used in calculating predictions.

I can appreciate that foundationalists have a problem with standard qm having reversible and irreversible dynamical processes, and that this seems illogical to you. It doesn't seem illogical to me because I don't think of standard qm as saying anything about deep reality, and qm works quite well in its present form. Why do what seem to some like disparate, even contradictory, elements of the theory produce such accurate results?

Dear nanosiborg,

I conclude from the above that you admit that standard qm has both reversible and irreversible processes. That probably means that it includes both unitary evolution (UE) and the projection postulate (PP). They give different predictions for the same quantum state. (If you believe, following von Neumann, that UE and PP "take turns", you add some extra problems (please see my post 824)). So it seems that "the maths used in calculating predictions" gives ambiguous predictions. This is a contradiction, or inconsistency, in my book. It isn't, in yours? You know, I like very much this one about a don't-give-a-damners' contest:

- How do you feel about work?
- Don't give a damn about work.
- How about money?
- Don't give a damn about money.
- How about women?
- Well, broads are always on my mind.
- Well, there seems to be some inconsistency with the goals of our contest.
- Don't give a damn about your inconsistency...

Well, I might be a don't-give-a-damner myself, but it looks like standard quantum theory might give ambiguous predictions for Bell tests.

As for "why accurate results?" Because PP can be a very good approximation to the results of UE in some cases (please see the arxiv / Physics Report article quoted in my post 824). Let me remind you that thermodynamics gives very accurate results, but its irreversibility still contradicts the reversibility of the underlying microscopic theory. You may say: if it's so accurate, why should we care? Because Nature cannot be "approximately nonlocal" - that does not make any sense. It's either local or not. The Coulomb law or Newton's gravity are very accurate, but they fail exactly where they predict nonlocality.

I think one can accept the assumption of determinism without adopting superdeterminism

I agree

, which I consider as a conspiratorial extension of it.

, however, 't Hooft's argument (please see my post 821) is not completely lost on me.

I'm ready to accept the results of a loophole-free Bell test. I just hope that when this is done and qm is confirmed and lhv is contradicted, then the lhv people won't grasp at increasingly absurdly fashioned straws (such as superdeterminism).

I guess, some of them won't, some of them will... What would I do in such case? I honestly don't know, and I hope I won't need to choose:-)

 

[DrChinese]

... it looks like standard quantum theory might give ambiguous predictions for Bell tests.

I have only seen one set... ever... and for polarization it always follows the cos^2 rule. I have never seen a published reference to ambiguity regarding this point.

Besides your own statements or work, can you show me a suitable published prediction that is different than those in usual experiments? Weihs et al (1998) being a great example of the usual QM predictions. Who has predicted otherwise?

In other words: I am flat out saying your statement is merely a reflection of your personal non-standard theory. If I am correct, please label as such rather than lead unknowing readers to an inappropriate conclusion.

 

[akhmeteli]

I have only seen one set... ever... and for polarization it always follows the cos^2 rule. I have never seen a published reference to ambiguity regarding this point.

Besides your own statements or work, can you show me a suitable published prediction that is different than those in usual experiments? Weihs et al (1998) being a great example of the usual QM predictions. Who has predicted otherwise?

In other words: I am flat out saying your statement is merely a reflection of your personal non-standard theory. If I am correct, please label as such rather than lead unknowing readers to an inappropriate conclusion.

I am sure you have seen published references on the measurement problem in quantum theory, see, e.g., http://plato.stanford.edu/entries/qt-measurement/ and references there, e.g., Albert or Bassi/Ghirardi. Let us consider some measurement in quantum theory for a pure state. You can make a prediction using the projection postulate (PP) of standard quantum theory. According to PP, the resulting quantum state will be a mixture of eigenstates of the measured observable, and the measurement is irreversible. On the other hand, you can make a prediction using unitary evolution (UE) of standard quantum theory for the measured system, the instrument, and the observer, if you wish. Unitary evolution can only give a superposition of the eigenstates (if the initial state is not an eigenstate of the observable), and the measurement is reversible. That means that standard quantum theory definitely gives two contradictory predictions. For a specific model, Allahverdyan e.a. (please see the arxiv / Physics Report article quoted in my post 824) show that in some cases PP can be a good approximation to what UE predicts, but it is an approximation. If you demand that I reproduce the tedious calculations of Allahverdyan e.a. for Weihs et al (1998) or John Doe et al (2004), I flat out reject such demand as arbitrary and unreasonable.

 

[DrChinese]

I am sure you have seen published references on the measurement problem in quantum theory, see, e.g., http://plato.stanford.edu/entries/qt-measurement/ and references there, e.g., Albert or Bassi/Ghirardi. Let us consider some measurement in quantum theory for a pure state. You can make a prediction using the projection postulate (PP) of standard quantum theory. According to PP, the resulting quantum state will be a mixture of eigenstates of the measured observable, and the measurement is irreversible. On the other hand, you can make a prediction using unitary evolution (UE) of standard quantum theory for the measured system, the instrument, and the observer, if you wish. Unitary evolution can only give a superposition of the eigenstates (if the initial state is not an eigenstate of the observable), and the measurement is reversible. That means that standard quantum theory definitely gives two contradictory predictions. For a specific model, Allahverdyan e.a. (please see the arxiv / Physics Report article quoted in my post 824) show that in some cases PP can be a good approximation to what UE predicts, but it is an approximation. If you demand that I reproduce the tedious calculations of Allahverdyan e.a. for Weihs et al (1998) or John Doe et al (2004), I flat out reject such demand as arbitrary and unreasonable.

If there is no specific conflicting prediction to support your personal theory, and you refuse, then you are violating forum rules.

 

[akhmeteli]

If there is no specific conflicting prediction to support your personal theory, and you refuse, then you are violating forum rules.

This is your personal and arbitrary reading of the rules. The rules do not require that I fulfill your arbitrary demands. I gave all the references confirming that PP and UE give mutually contradictory predictions, so I fulfilled my duty under the rules: prove (using mainstream references) that the predictions do indeed differ, as I said. So I did not refuse to prove (by references) my statement, I did refuse to give a specific prediction, but I don't have any such obligation under the rules. The measurement problem of quantum theory is not my personal theory, furthermore, you yourself "freely admit it". I am sure you appreciate that UE cannot generate irreversibility or turn a pure state into a mixture, unlike PP, so there is no doubt that they do give differing predictions. Furthermore, strictly speaking, UE cannot even give a definite outcome of a measurement.

 

[bhobba]

I am sure you appreciate that UE cannot generate irreversibility or turn a pure state into a mixture

No it doesn't - but it turns it into an 'improper mixture' - see the early chapters of Decoherence and the Quantum-to-Classical Transition by Schlosshauer where he carefully explains what's going on. Here improper means no observation can tell the difference between it and an actual mixed state. The means with no contradiction one can assume it is an actual mixed state and the measurement problem is solved. The issue is not one of contradiction the issue is such an interpretation sweeps where the 'collapse' actually occurred, or even if one occurs at all, under the rug by saying it doesn't matter.

Or ,to put it another way, exactly how does an observation accomplish this marvelous feat - its one of (perhaps) incompleteness - but not of contradiction.

Thanks
Bill

 

[DrChinese]

This is your personal and arbitrary reading of the rules. The rules do not require that I fulfill your arbitrary demands. I gave all the references confirming that PP and UE give mutually contradictory predictions, so I fulfilled my duty under the rules: prove (using mainstream references) that the predictions do indeed differ, as I said. So I did not refuse to prove (by references) my statement, I did refuse to give a specific prediction, but I don't have any such obligation under the rules. The measurement problem of quantum theory is not my personal theory, furthermore, you yourself "freely admit it". I am sure you appreciate that UE cannot generate irreversibility or turn a pure state into a mixture, unlike PP, so there is no doubt that they do give differing predictions. Furthermore, strictly speaking, UE cannot even give a definite outcome of a measurement.

You gave an unpublished reference that does not indicate a specific difference from the standard QM predictions. You are obviously obsessed with the UE/PP elements of QM and certain specific conclusions you have drawn from this. That is your personal right, no issue with that.

The issue is that you consistently use PhysicsForums as a way to promulgate your ideas, and this is not the place for that. You typically operate right at the edges of forum rules, but this time you have crossed the line. They are not MY rules, they are OUR rules and we must all live by them.

The fact is: it is your personal theory that there are different predictions for Bell experiments in QM. There is not a single mainstream prediction for these experiments that differs from the norm, and certainly you have not identified a reference for anything different. I, on the other hand, can supply plenty of references for the CHSH inequality, the related QM prediction, as well as references for the standard QM predictions for matches of cos^2(theta).

Please retract your statement.

 

[jtbell]

Due to the length and digressiveness of this thread, it has been closed. For a more recent development, see here:

https://www.physicsforums.com/showthread.php?t=689717