Bell's theorem is silly, false, misleading

[Gordon Watson]

1. I've lodged a 6-page DRAFT (titled as above) at viXra.org. Abstract (and some discussion): http://vixra.org/abs/1510.0320. PDF: http://vixra.org/pdf/1510.0320v1.pdf

2. Version 2 of the above will have (at least) paras #1.2 and #1.3 rewritten. In #2.5, "Bell's theorem" should read "the Bell-d'Espagnat explanation".

3. I'm seeking to have the main CRITICAL discussion, questions, etc., HERE at sciphysicsforums.com! NB: Small and critical comments are often of great benefit to me.

4. Given increasing numbers of quantum professors, theorists, philosophers and experimentalists hyping that our world is NONLOCAL:

Can a common-sense EINSTEIN-LOCAL theory and its realisable thought-experiments prove them wrong?

With best regards; Gordon
.

[Xray]

I see that your paper was posted ahead of the BIG announcement, http://www.nature.com/nature/journal/va ... 15759.html (see this too http://arxiv.org/pdf/1508.05949.pdf) to which the following press-release (sourced from, hansonlab.tudelft.nl/wp-content/uploads/2015/10/Bell_test_Delft-PressRelease_vOct16.pdf) refers. I have underlined some "scientific statements" that amaze me and would welcome your comments based on your paper. The contact person for the Nature and arxiv papers is Professor Ronald Hanson at r.hanson@tudelft.nl

*** Draft press release for “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres” by B. Hensen et al. ***

Loophole-free Bell test crowns 80-years-old debate on nature of reality: Einsteins “spooky action” is real.
In 1935, Einstein asked a profound question about our understanding of Nature: are objects only influenced by their nearby environment? Or could, as predicted by quantum theory, looking at one object sometimes instantaneously affect another far-away object? Einstein did not believe in quantum theory’s prediction, famously calling it “spooky action”.
Exactly 80 years later, a team of scientists led by professor Ronald Hanson from Delft University of Technology finally performed what is seen as the ultimate test against Einstein’s worldview: the loophole-free Bell test. The scientists found that two electrons, separated 1.3 km from each other on the Delft University campus, can indeed have an invisible and instantaneous connection: the spooky action is real.
The experiment, published in Nature today, breaks the last standing defence of Einstein’s iconic 1935 paper: it closes all the loopholes present in earlier experiments. The Delft experiment not only closes a chapter in one of the most intriguing debates in science, it may also enable a radically new form of secure communications that is fundamentally impossible to ‘eavesdrop’ into.

In two places at the same time?
“Quantum mechanics states that a particle such as an electron can be in two different states at the same time, and even in two different places, as long as it is not observed. This is called ‘superposition’ and it is a very counter-intuitive concept”, says lead scientist Professor Ronald Hanson. Hanson’s group works with trapped electrons, which have a tiny magnetic effect known as a “spin” that can be pointing up, or down, or - when in superposition - up and down at the same time. “Things get really interesting when two electrons become entangled. Both are then up and down at the same time, but when observed one will always be down and the other one up. They are perfectly correlated, when you observe one, the other one will always be opposite. That effect is instantaneous, even if the other electron is in a rocket at the other end of the galaxy”, says Hanson.
Already in 1935, just a few years after the development of quantum theory, this counterintuitive effect was seen as a reason to doubt the new theory. These objections were published in a famous scientific paper, known as ‘the EPR-paper’ (1935), named after its three authors: Einstein, Podolsky and Rosen. They stated there could still be undiscovered properties of particles, so called ‘hidden variables’, which would provide a more intuitive explanation of the predicted correlations: the two particles were just pre-programmed to be opposite, we just did not know it.

Bell Test
A major step was taken in 1964, when CERN scientist John Stewart Bell devised an experiment that could prove that ‘spooky action at a distance’ existed - the Bell Test - as it can rule out any ‘hidden variable’ as an explanation. During the past four decades, many Bell experiments were performed, showing results that conflicted the ‘hidden variables’ explanation. Nonetheless, the debate didn’t just end there: as the opposing scientists stated: the Bell tests performed still contained ‘loopholes’, or back-doors that could invalidate the proof.
Basically, a Bell Test does a measurement on two sides of an entangled pair, choosing randomly between two possible ‘questions’ at both sides. Depending on which question is asked, a different property of the particle is measured. In a Bell test, quantum mechanics predicts that the outcomes, or ‘answers’ will be strongly correlated in a way that can’t be explained by any ‘hidden variable’ theory. Nonetheless, as opposing scientists said, alternative explanations could still not be fully excluded.
Firstly, it might be possible that the particles or the detectors were ‘secretly’ communicating to each other in some unknown way that might be beyond our current understanding of nature. By secretly sharing questions or answers between them (the locality loophole), they could be producing the observed correlations in a perfectly local manner. Secondly, if the experiment only detected a subset of prepared entangled pairs, they might not be representative of all of them (the ‘detection loophole’). With these loopholes open, the possibility of an alternative explanation cannot be fully excluded.

Loopholes
Over the last decade, advances in nanoscale technology allowed experiments to close these loopholes individually. For the first time, a group of scientists from The Netherlands, Spain and United Kingdom have now managed to close all loopholes simultaneously.
The scientists placed two diamonds on opposite sides of the Delft University campus, 1.3 km apart. Each diamond contained a tiny trap for single electrons, which have a magnetic property called a “spin”. They managed to entangle the electron spins and perform a Bell Test.
“We have two labs, one in the Faculty of Applied Sciences, and one on the other end of the campus in the Reactor Institute. The large distance between our detectors ensures that neither the detectors, nor the electrons can exchange information within the time it takes to do the measurement, and so closes the locality loophole. This exchange is limited by the speed of light, and the distance is too far for light to travel in the time it takes us to ask our electron spins a question and get an answer”, explains PhD-student Bas Hensen, lead-author of the study.
“We also close the detection loophole, because in this experiment we measure all our entangled pairs. This is the first time all loopholes are closed at the same time in a single experiment, and we still find that the invisible bond between the electrons is there: the first loophole-free Bell test”.

Secure communications
The experiment in Delft closes a chapter in one of the most intriguing debates in science. “It is one of the few experiments in physics that can directly test and even reject fundamental principles of nature” says Hanson. However, the experiment has practical value as well, as entanglement allows for a form of secure communication.
The measurement outcomes can be used as an encryption key: the key is fundamentally impossible to eavesdrop on as it doesn’t travel between two points, but is created through the instantaneous entanglement link. However, loopholes are potential backdoors for hackers, so quantum communication will only be inherently secure if all the loopholes are closed.***

????? There is more at http://hansonlab.tudelft.nl/teleportation/

[FrediFizzx]

Donald Graft will be doing an independent analysis of the raw data from the Delft experiment.

https://pubpeer.com/publications/B74AEB ... 88#fb39529

I suspect that he is "barking up the wrong tree" though in trying to show errors in the experiment.

[Heinera]

Donald Graft will be doing an independent analysis of the raw data from the Delft experiment.

https://pubpeer.com/publications/B74AEB ... 88#fb39529

I suspect that he is "barking up the wrong tree" though in trying to show errors in the experiment.

Donald Graft doesn't believe that experiments can significantly violate 2 for the CHSH-inequality (he thinks experimental violations are due to manipulations of the raw data), so implicitly he doesn't believe in Joy's theory either.

[Xray]

Donald Graft will be doing an independent analysis of the raw data from the Delft experiment.

https://pubpeer.com/publications/B74AEB ... 88#fb39529

I suspect that he is "barking up the wrong tree" though in trying to show errors in the experiment.

Donald Graft doesn't believe that experiments can significantly violate 2 for the CHSH-inequality (he thinks experimental violations are due to manipulations of the raw data), so implicitly he doesn't believe in Joy's theory either.

This … "Donald Graft doesn't believe that experiments can significantly violate 2 for the CHSH-inequality (he thinks experimental violations are due to manipulations of the raw data)" … is my reading of Donald Graft's work also.

So while I 100% agree that he is "barking up the wrong tree," I trust it is good motivation for his critical examination of the raw-data. While he waits for that data, I would encourage him to have a go at Gordon Watson's essay. That way he might show why the naive-realism behind CHSH makes CHSH a valid "gold-standard" against which EPRB-style experiments are to be evaluated for accuracy/honesty/integrity/correct raw-data analysis. Though, since all such experiments are NOT amenable to a naive-realistic explanation, he will surely fail.

Xray

[Gordon Watson]

I see that your paper was posted ahead of the BIG announcement, http://www.nature.com/nature/journal/va ... 15759.html (see this too http://arxiv.org/pdf/1508.05949.pdf) to which the following press-release (sourced from, hansonlab.tudelft.nl/wp-content/uploads/2015/10/Bell_test_Delft-PressRelease_vOct16.pdf) refers. I have underlined some "scientific statements" that amaze me and would welcome your comments based on your paper. The contact person for the Nature and arxiv papers is Professor Ronald Hanson at r.hanson@tudelft.nl

*** Draft press release for “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres” by B. Hensen et al. ***

<BIG SNIP>

Xray, over many years I've seen some classic boo-boos in Press Releases and from sub-editors. One that always springs to mind is an introductory byline to a d'Espagnat article (in Sci. Am. and clickable from Refs. in my essay).

So, for me, an important part of the Press Release -- apart from: who wrote it? -- is the quote from Hanson: "... the effect is instantaneous …" I claim to refute the need for such $&#*## expressions, so see para. #4.15 in my old essay. It's the same in my new one at http://vixra.org/abs/1511.0035 , which I hope answers some of the other problems with their P/R and the research paper itself. (NB: I'm not disputing the experiment.)

With best regards, and apologies for my delay; Gordon

[Don]

Donald Graft doesn't believe that experiments can significantly violate 2 for the CHSH-inequality (he thinks experimental violations are due to manipulations of the raw data), so implicitly he doesn't believe in Joy's theory either.

Allow me to clarify my thinking about Joy's work, which is perhaps misrepresented above.

While I'm not familiar with the gory mathematical details of Joy's work, I also don't know of any reasons to doubt it. I can grant that given a physical system that is governed by such mathematics a local violation may be possible, and I know of no reason that such physics cannot be instantiated in Nature. Where I differ, however, is that I do not believe that this mathematics applies to the physics of a standard EPRB experiment. If it does not, then I would expect the inequalities to apply. So Joy is both right and wrong in my opinion. He is right (I suppose) that there may be physical systems embodying his mathematics that could locally violate the inequalities, but he is wrong to claim that this mathematics applies to standard EPRB. Of course, I am open to hearing him justify the applicability of his mathematics to standard EPRB. While Joy's work, if correct, undermines the validity of the inequalities in general, which is surely an important result, it does not explain the claimed inequality violations for standard EPRB.

My work is unique in that I make the following two claims:

1. Quantum mechanics does not predict inequality violation! I don't think Joy holds this view.

2. The experiments when properly designed and analyzed do not violate the inequalities, and therefore they confirm local realism. So, where I seek to show this, Joy appears to accept the experimental violations as valid and seeks to explain them. That is standard thinking in the foundations community. I hope to change that thinking.

My new model (http://arxiv.org/abs/1507.06231) is a killer for the whole Bell Test program because it shows with simple mathematics that in an EPRB experiment any emission rate higher than 0 can violate the CH inequality, given an appropriate classical system that saturates the inequality. The violation, however, is an artifact of the analysis, and not a real physical thing. I encourage people to read my last paper carefully, especially Section 2 and the final equation derived there. This is a totally new mechanism, never before described, that is unrelated to the known "loopholes". After discovering this I have mostly lost interest in analyzing data from specific experiments, because I believe my new proof invalidates all experiments that require the analysis to pair detections. The pseudo-heralded experiments like Christensen et al, while they may avoid this mechanism, do so at the expense of post-selecting the data, and I do not regard post-selection (systematic data discarding) as a valid form of analysis. I am working on a model that shows this.

In summary, I see Joy's work and my own as complementary and not in conflict. We differ on a few things, but both approaches to show the nonsensical nature of Bell tests are important and valuable.

Donald A. Graft

[FrediFizzx]

My work is unique in that I make the following two claims:

1. Quantum mechanics does not predict inequality violation! I don't think Joy holds this view.

2. The experiments when properly designed and analyzed do not violate the inequalities, and therefore they confirm local realism. So, where I seek to show this, Joy appears to accept the experimental violations as valid and seeks to explain them. That is standard thinking in the foundations community. I hope to change that thinking.

Hi Don and welcome,

1. Which inequalities? If you are speaking of Bell inequalities, of course QM doesn't predict that as they are mathematically impossible to violate. For EPR-Bohm, QM predicts -a.b and that is all it predicts. Joy's model for EPR-Bohm also predicts -a.b so I believe Joy holds the view that his classical local-realistic model does in fact explain the strong correlation.

2. Again... of course the experiments do not violate Bell inequalities as they are impossible to violate. I believe that Joy accepts that his model matches the prediction of QM and ineed explains it in a classical local-realistic way. All the experiments do is validate that the prediction of QM is correct. Bell's theory has been dead for a long time now so really has nothing to do with this any more. Loopholes are totally gone and don't matter. Bell "tests" are a complete joke and hoax on the physics community.

[Joy Christian]

Allow me to clarify my thinking about Joy's work, which is perhaps misrepresented above.

Hi Donald,

Welcome to the forum. And thank you for your thoughtful remarks. Let me begin with what we agree on. I agree with your executive summary:

In summary, I see Joy's work and my own as complementary and not in conflict. We differ on a few things, but both approaches to show the nonsensical nature of Bell tests are important and valuable.

Here is my position in broad terms:

(1) The whole business of Bell type inequalities is misleading and even fraudulent, if not entirely misguided in the light of the original EPR argument (considering its conceptions of realism, locality, and completeness). Theoretically, the inequalities do provide useful ideas about bounds on possible strong correlations, but experimentally their supposed "violations" are nothing but a bad joke, as you know very well.

(2) Neither Bell type inequalities nor Bell's so-called theorem is my primary concern. To me they are just unavoidable distractions, imposed upon us by some topologically naïve, general-relativistically uninformed, and politically powerful people.

(3) My primary interest and concerns are the physical origins of strong or "quantum" correlations. As such, I am obviously interested in Bell's claim that such strong correlations cannot be reproduced by any local-realistic model, even if we dispense with determinism. More specifically, Bell made the following mathematical claim:

Let A(a, h) = +/-1 and B(b, h) = +/-1 be two functions such that their product AB(a, b, h) = +/-1 is factorizable as follows:

AB(a, b, h) = A(a, h) x B(b, h),

where the "hidden" variable h is a shared randomness between A and B, and "a" and "b" are freely chosen, "non-hidden" parameters. Note that A does not depend on either B or "b", and B does not depend on either A or "a" --- thus A(a, h) and B(b, h) are manifestly local functions in the sense of Einstein and Bell.

Bell then claimed that with such manifestly local functions it is mathematically impossible to reproduce the strong correlations, such as the singlet correlations -a.b. It is this mathematical claim that I dispute. I couldn't care less about any inequalities in this context, although I have interest in them from a topological perspective.

It is easy to see that Bell's mathematical claim about the strong correlations, -a.b, is simply false, and in fact incredibly naïve from my topological perspective. It is, in fact, quite easy to reproduce the strong correlations, as you can verify for yourself: https://www.academia.edu/19235737/Macro ... fied_Proof.

As to whether or not the above local-realistic prediction of -a.b is compatible with the physics of an actual EPRB type experiment is an open question. Please do have a look at the above link and tell me what is it in my theoretical prediction that is incompatible with the actual experimental practice.

Thanks,

Joy Christian

[Don]

Thank you for the warm welcome, guys.

1. Which inequalities? If you are speaking of Bell inequalities, of course QM doesn't predict that as they are mathematically impossible to violate. For EPR-Bohm, QM predicts -a.b and that is all it predicts. Joy's model for EPR-Bohm also predicts -a.b so I believe Joy holds the view that his classical local-realistic model does in fact explain the strong correlation.

I refer specifically to the CH inequality. If you read my paper http://arxiv.org/abs/1404.4329, you will see that your position that CH is impossible to violate is not correct. CH is not a tautology. Regarding the quantum prediction, -a.b is the quantum joint prediction. It cannot be recovered in an experiment with separated measurements, and reduced density matrices must be used instead of the joint distribution. Refer to http://arxiv.org/abs/1309.1153 and the Conclusion of http://arxiv.org/abs/1409.5158 for a full account of this important distinction.

You cannot consider all the inequalities as equivalent, and you cannot dismiss them as impossible to violate. This is an incorrect and naive view of the true situation, and you do yourself no good by espousing it. If you want to take your case beyond mere bald assertion, then please respond to the content of my papers (http://arxiv.org/find/quant-ph/1/au:+Gr ... /0/all/0/1), rather than asking me to reproduce all my arguments here, or give me some links to your own papers. Thank you.

2. Again... of course the experiments do not violate Bell inequalities as they are impossible to violate. I believe that Joy accepts that his model matches the prediction of QM and ineed explains it in a classical local-realistic way. All the experiments do is validate that the prediction of QM is correct. Bell's theory has been dead for a long time now so really has nothing to do with this any more. Loopholes are totally gone and don't matter. Bell "tests" are a complete joke and hoax on the physics community.

As I said, I do not agree with most of this. I do agree that the Bell test program is misguided, but not for the reasons you cite. Please read my papers for the justification.

@Joy

Thanks for your reply. My point in posting was not to question your work, simply to clarify Heinera's claim about my view of it. Also, this is Gordon's thread so we should not hijack it.

[Gordon Watson]

Thank you for the warm welcome, guys. … … … this is Gordon's thread so we should not hijack it.

Dear Don,

Welcome to the Forum and especially to this thread. For, please note: Your position is in no way a "hijacking" of this thread but (instead) adds much to its content. I say this because, as I presently understand your position, you are challenging the analysis of the experimental data and NOT Bell's position.

So I hope I'm not overstating your clear position (which I also welcome) when I summarise it thus: Donald Graft's position is that Bell's theorem is not silly, not false, not misleading. Rather, it is the analysis of the experiments that is flawed because local realism is true and Bell's inequalities properly reflect the related physical limits that apply in our local-realistic world.

If I have that right, then we at least agree to be local realists together and we can then move to discuss why our opinions differ so dramatically.

PS: As I understand your position: We agree that our world is Einstein-local. Which is a good staring point; and one not easy to establish in the quantum foundations community!

Looking forward to sorting things out, and with best regards; Gordon

[Edit: Don, I do not agree with this position: "Quantum mechanics does not predict inequality violation"! Please you point me to your reasoning.]

[Don]

Hi Gordon,

Nice to meet you and thanks for the welcome.

I had written above: "Regarding the quantum prediction, -a.b is the quantum joint prediction. It cannot be recovered in an experiment with separated measurements, and reduced density matrices must be used instead of the joint distribution. Refer to http://arxiv.org/abs/1309.1153 and the Conclusion of http://arxiv.org/abs/1409.5158 for a full account of this important distinction." These are the links you need to understand my position. Let me know if anything is unclear or you find it wrong in any way. This error of thinking that a joint distribution can be sampled via marginal measurements is the root of the whole befuddlement over EPRB.

[Gordon Watson]

Hi Gordon,

Nice to meet you and thanks for the welcome.

I had written above: "Regarding the quantum prediction, -a.b is the quantum joint prediction. It cannot be recovered in an experiment with separated measurements, and reduced density matrices must be used instead of the joint distribution. Refer to http://arxiv.org/abs/1309.1153 and the Conclusion of http://arxiv.org/abs/1409.5158 for a full account of this important distinction." These are the links you need to understand my position. Let me know if anything is unclear or you find it wrong in any way. This error of thinking that a joint distribution can be sampled via marginal measurements is the root of the whole befuddlement over EPRB.

Don, I agree with many of your statements and sentiments -- and I want to encourage your in your work -- but I find your use of standard Probability Theory (PT) to be wrong. For example, in your 2013 essay (where A and B are taken to be "up" results), we have in your first equation:

(1) QM(AB)_J = P(AB|α,β) = 1/2 cos^2 (θ) = 1/2 cos^2 (α,β).

So, from PT and given (1), we can insert two new intermediate terms (the 2nd and 3rd) which can never be false:

(2) P(AB|α,β) = P(A|α,β)P(B|α,β,A) = P(B|α,β)P(A|α,β,B) = 1/2 cos^2 (θ) = 1/2 cos^2 (α,β).

Then, from our agreement re locality:

(3) P(AB|α,β) = P(A|α)P(B|α,β,A) = P(B|β)P(A|α,β,B) = 1/2 cos^2 (α,β) = the joint probability.

Then, since the input particle-variables to the detectors are pairwise random:

(4) P(A|α) = P(B|β) = 1/2 = the marginal probabilities; so

(5) P(B|α,β,A) = P(A|α,β,B) = cos^2 (α,β) = the conditional probabilities.

Equations (3)-(5) are predicted by QM and experimentally confirmed; as is the expectation <AB>. (4) is confirmed via assessment of Alice's data, independent of Bob's; and vice-versa. (3) and (5) and <AB> are confirmed via the pair-wise matching of their data; ie, we are not limited to the marginals!

Turning now to your second equation and your interpretation of it:

(6) QM(AB)_M = P(A|α)P(B|β). "The expression QM(AB)_M represents the predicted probability using the marginals P(A|α) and P(B|β)."

However, under PT, this would hold if A and B were uncorrelated, and not otherwise. So it cannot (and does not) hold in Bell-test experiments (which, as you know, are highly correlated). Thus (3) and (5) defeat Bell's inequalities without any reference to nonlocality. To see this, note this: The detector-settings are correlated by cos2s(α,β) where s = spin: So (α,β) = 0 or π, cos2(α,β) = +1 and the detectors are effectively parallel; (α,β) = π/2 or 3π/2, cos2(α,β) = -1 and the detectors are orthogonal; etc. NB: though Alice and Bob set their detectors randomly, this underlying correlation always holds sway. The particles are also highly correlated, quite independently; etc.

So, given that their is no mechanism here for action at a distance, nor any need for nonlocality or signalling, we see that highly correlated Bell-test results arise from highly correlated particle-pairs interacting locally with highly correlated (and space-like separated) detectors.

Much more can be said but HTH for now; Gordon

[Don]

You claim "highly-correlated Bell test results" as a fact, and claim that I must know that, but that is exactly what I challenge. So there is little point in discussing it further.

Also, you have seized upon this aspect without commenting upon my arguments about joint distributions, marginal sampling, copulas, and why one cannot expect a joint distribution to be recoverable from marginal sampling. I also developed a theory and model of separated sampling that clearly shows that the joint distribution cannot be sampled in an EPRB experiment, but you ignore it.

I'm so tempted to say "HTH".

[Gordon Watson]

Don, sorry for any misunderstandings. I was responding to your invitation, highlighted below:

Hi Gordon,

Nice to meet you and thanks for the welcome.

I had written above: "Regarding the quantum prediction, -a.b is the quantum joint prediction. It cannot be recovered in an experiment with separated measurements, and reduced density matrices must be used instead of the joint distribution. Refer to http://arxiv.org/abs/1309.1153 and the Conclusion of http://arxiv.org/abs/1409.5158 for a full account of this important distinction." These are the links you need to understand my position. Let me know if anything is unclear or you find it wrong in any way. This error of thinking that a joint distribution can be sampled via marginal measurements is the root of the whole befuddlement over EPRB.

So, given my focus,* I let you know that I found your use of classical Probability Theory (PT) wrong.

* My focus was on: "Letting you know if anything was unclear or I found it wrong in any way."

Turning now to a matter that was unclear to me: Could you spell out your understanding of the term marginal as in "marginal probabilities" and compare it with your use of the term marginal as in "marginal sampling" and "marginal (separated) measurements". That would help.

Thanks.

[Don]

No time to give you remedial lessons in probability theory.

[Gordon Watson]

No time to give you remedial lessons in probability theory.

OK. But how about explaining the term: "marginal (separated) measurements"? I've not seen it before.
.

[Don]

The whole point of the paper is to explicate that very concept. I suggest that you read it beyond the introduction.

[FrediFizzx]

No time to give you remedial lessons in probability theory.

OK. But how about explaining the term: "marginal (separated) measurements"? I've not seen it before.
.

Hi Gordon,

I suspect it has something to do with the fact that neither QM nor local HV models can get the joint prediction of -a.b using +/- 1 outcomes in R^3. Only non-local hidden variable models can do it for R^3. As Joy has shown, his LHV model can do it in S^3. Don's papers are so wordy, it would be nice if we could just get a simple definition of exactly what he means by "marginal measurements" here.

[FrediFizzx]

No time to give you remedial lessons in probability theory.

OK. But how about explaining the term: "marginal (separated) measurements"? I've not seen it before.
.

Hi Gordon,

I suspect it has something to do with the fact that neither QM nor local HV models can get the joint prediction of -a.b using +/- 1 outcomes in R^3. Only non-local hidden variable models can do it for R^3. As Joy has shown, his LHV model can do it in S^3. Don's papers are so wordy, it would be nice if we could just get a simple definition of exactly what he means by "marginal measurements" here.

There is not all that much significance to the term "marginal". It is just a probability term as opposed to "joint" probability.