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Link: http://vixra.org/pdf/1812.0437v7.pdf (5 pages.)

Abstract: Bell’s inequality is widely regarded as a profound impediment to any intuitive understanding of physical reality. We disagree: for elementary algebra allows us to refute Bell's inequality, identify his errors, dismiss his work generally. We thus begin reiterating the anti-Bellian ideas that we’ve advanced since 1989: ie, we seek to restore commonsense/intuitive ideas to physics and make physical reality intelligible—like Einstein argued, according to Bell—‘by completing the quantum mechanical account in a classical way'.

Request: I look forward to critical comments, suggestions, etc -- by Bellians and anti-Bellians alike -- especially by gill1109 and Heinera in view of their recent confusing/false claims in http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=373

eg, claims to the effect that nonlocality is OK, or that a six-sided dice showing a number greater that 6 is somehow OK to a Bellian.

Let me add that many "anti-Bellian" arguments and claims are also challenged; eg, even Fred's claim (his emphasis) makes me wonder: "Once more... IT IS MATHEMATICALLY IMPOSSIBLE FOR ANYTHING TO VIOLATE BELL'S INEQUALITIES!"

For [as shown in the above essay] Bell's inequalities -- supposedly derived in the context of EPRB -- are mathematically AND experimentally false under EPRB: imho, to the point that Bell inequalities are nonsense!

I therefore support Jay's suggestion

So while I know it is vogue, why don't we set aside all of the "inequalities" discussion and focus directly on the theoretical physics of the mechanisms which bring about the strong correlations?

And especially, why don't we see if we are overlooking something in quantum mechanics itself, which actually reveals QM to be an LRHV theory which to date has simply not been understood as such?So while I know it is vogue, why don't we set aside all of the "inequalities" discussion and focus directly on the theoretical physics of the mechanisms which bring about the strong correlations?

For [coincidentally] I'm rewriting an old essay that explains EPRB in classical terms: thereby making the point that reality can be understood via a a truly LRHV theory.

Also making the point that QM is an advanced probability theory -- based on a theorem known to mathematicians since 1915: see the Fröhner (1988) reference in the above essay.
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Gordon Watson wrote:.
Let me add that many "anti-Bellian" arguments and claims are also challenged; eg, even Fred's claim (his emphasis) makes me wonder: "Once more... IT IS MATHEMATICALLY IMPOSSIBLE FOR ANYTHING TO VIOLATE BELL'S INEQUALITIES!"

Hello Gordon,
Let me say I agree with Fred's claim. Often when people talk of "violation" of a mathematical rule such as inequality, they are being very sloppy with language often resulting in self-delusions. Take the mathematical rule 1 + 1 = 2. It cannot be violated. But some may argue that they've found a violation where 1 + 1 = 1, only for it to be revealed, when fully specified, what they've actually found is 1 hemisphere + 1 hemisphere = 1 sphere. That is hardly a violation. Rather, the *apparent violation* forces us to conclude that we have not achieved a one to one correspondence of our variables to the variables of the original relationship and that we need further “coordinates” to complete the specification.

In every single case where a "violation" of Bell's inequalities is claimed, there is a lack of one-to-one correspondence between the variables being measured, and the variables in the original inequality. This is precisely what Boole established a century before Bell.

minkwe wrote:

Gordon Watson wrote:.
Let me add that many "anti-Bellian" arguments and claims are also challenged; eg, even Fred's claim (his emphasis) makes me wonder: "Once more... IT IS MATHEMATICALLY IMPOSSIBLE FOR ANYTHING TO VIOLATE BELL'S INEQUALITIES!"

Hello Gordon,
Let me say I agree with Fred's claim. Often when people talk of "violation" of a mathematical rule such as inequality, they are being very sloppy with language often resulting in self-delusions. Take the mathematical rule 1 + 1 = 2. It cannot be violated. But some may argue that they've found a violation where 1 + 1 = 1, only for it to be revealed, when fully specified, what they've actually found is 1 hemisphere + 1 hemisphere = 1 sphere. That is hardly a violation. Rather, the *apparent violation* forces us to conclude that we have not achieved a one to one correspondence of our variables to the variables of the original relationship and that we need further “coordinates” to complete the specification.

In every single case where a "violation" of Bell's inequalities is claimed, there is a lack of one-to-one correspondence between the variables being measured, and the variables in the original inequality. This is precisely what Boole established a century before Bell.

Hi minkwe, and thanks: but I disagree. Maybe I'm missing your point, but I suspect that you are missing mine. Let's see:

Eqn (9) in my essay is Bell's inequality for EPRB: its upper-bound is 1.

Eqn (10) is my inequality for EPRB: its upper-bound is 3/2.

Now (10) provides -- precisely -- a one-to-one correspondence of "my variables to the variables of the original relationship".

(i): So what do you mean 'we need further “coordinates” to complete the specification'?

(ii) WRT this from you, talking about what is measured:

In every single case where a "violation" of Bell's inequalities is claimed, there is a lack of one-to-one correspondence between the variables being measured, and the variables in the original inequality. This is precisely what Boole established a century before Bell.

Well Aspect (2004) -- see the link in my essay -- is a real experiment with real measurements. And my generalized inequality -- see fn.5 and my eqn (10a) there that covers Aspect (2004) as well-- again has a one-to-one correspondence of "my variables to the variables of the original relationship".

PS: WRT your hemisphere analogy, I suggest Bell's claim is akin to this: all spherical triangles have an upper-bound of angles summing to 180º. And his first [and inappropriate] assumption confines his inequality to 2D planes. Which, as with his EPRB/Aspect inequalities, means his spherical claim is sometimes valid. BUT false in general!
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Gordon Watson wrote:Eqn (9) in my essay is Bell's inequality for EPRB: its upper-bound is 1.

Eqn (10) is my inequality for EPRB: its upper-bound is 3/2.

Now (10) provides -- precisely -- a one-to-one correspondence of "my variables to the variables of the original relationship".

It should be obvious from the contradiction between (9) and (10) in your paper that there is no one-to-one correspondence. E(a,b) is incompletely specified. What exactly is E(a,b) in equation (9)? What you have done is to claim that there is one-to-one correspondence, and therefore Bell must have made an error. In other words, you are assuming one-to-one correspondence and then concluding that there is an error in Bell's mathematics. That may very well be the case, but if that is granted, the effect of the error is to break the one-to-one correspondence.

What I see in fact is that Bell's mathematics is correct, but his error is in failing to preserve the one-to-one correspondence between his mathematics and the induction made by comparing the mathematics with QM. Although the results are the same, I believe this analysis is more accurate than yours because Bell's assumptions in Bell 1964 implies an assumption of counterfactual definiteness that will not be meaningful were he following the logical steps you impute to him. Thus, Bell starts out with paired relationships drawn from a set of triples and ends up making comparisons with paired relationships drawn from three disjoint sets of pairs. Whereas his mathematics and resulting inequalities are valid for paired relationships drawn from a set of triples, the variables from paired relationships drawn from three disjoint sets of pairs (like from QM and experiments) do not have one-to-one correspondence to those representing paired relationships drawn from a set of triples.

(i): So what do you mean 'we need further “coordinates” to complete the specification'?

This means you need to label each E(a,b) with coordinates fully specifying all relevant facts of how they are obtained. For example your equation (9) will become.



And your equation (10) will become



See https://iopscience.iop.org/article/10.1 ... 60007/meta

Well Aspect (2004) -- see the link in my essay -- is a real experiment with real measurements. And my generalized inequality -- see fn.5 and my eqn (10a) there that covers Aspect (2004) as well-- again has a one-to-one correspondence of "my variables to the variables of the original relationship".

Precisely, equation (10) is meaningful for actual measurements, whereas, equation (9) is meaningless as far as measurements are concerned. The variables in (9) can never be measured.

PS: WRT your hemisphere analogy, I suggest Bell's claim is akin to this: all spherical triangles have an upper-bound of angles summing to 180º. And his first [and inappropriate] assumption confines his inequality to 2D planes. Which, as with his EPRB/Aspect inequalities, means his spherical claim is sometimes valid. BUT false in general!...

It means simply that there is no violation, just lack of correspondence of the terms.

The most devastating criticism of Bell was delivered by Bell himself before Bell 1964 was ever published.

John S. Bell wrote:Thus the formal proof of von Neumann does not justify his informal conclusion. ....... It was not the objective measurable predictions of quantum mechanics which ruled out hidden variables. It was the arbitrary assumption of a particular (and impossible) relation between the results of incompatible measurements either of which might be made on a given occasion but only one of which can in fact be made.

minkwe wrote:The most devastating criticism of Bell was delivered by Bell himself before Bell 1964 was ever published.

John S. Bell wrote:Thus the formal proof of von Neumann does not justify his informal conclusion. ....... It was not the objective measurable predictions of quantum mechanics which ruled out hidden variables. It was the arbitrary assumption of a particular (and impossible) relation between the results of incompatible measurements either of which might be made on a given occasion but only one of which can in fact be made.

This is indeed the key mistake in Bell's theorem. And one does not have to be Einstein to appreciate it. One does not even have to be Bell to appreciate it. Even I, with my limited intellect, am able to appreciate it. I have tried to bring it out in all its glory in this paper, which includes the above quote from Bell's paper published in 1966: https://arxiv.org/abs/1704.02876.

But you are quite right to say that the above quote, even though from Bell's paper that was officially published in 1966, was actually written ``before Bell 1964 was ever published." That is quite true. Bell wrote his 1966 paper (which is also the first chapter of his book) and submitted it to Reviews of Modern Physics several years before 1966, and had conceived his 1964 paper only after having submitted his 1966 paper to Reviews of Modern Physics. The dealy by several years in the publication of his 1966 paper was due to an editorial mixup or error. I heard this story only orally from my former Ph.D. mentor Abner Shimony in the mid-1980s (Shimony, of course, knew Bell personally). I do not have written evidence to back it up.

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minkwe wrote:

Gordon Watson wrote:Eqn (9) in my essay is Bell's inequality for EPRB: its upper-bound is 1.

Eqn (10) is my inequality for EPRB: its upper-bound is 3/2.

Now (10) provides -- precisely -- a one-to-one correspondence of "my variables to the variables of the original relationship".

Gordon Watson wrote:
It should be obvious from the contradiction between (9) and (10) in your paper that there is no one-to-one correspondence. E(a,b) is incompletely specified. What exactly is E(a,b) in equation (9)?

E(a,b) is defined in ¶2.1 of my essay. It is Bell's P(a,b) and is intended by him to be under EPRB.

minkwe wrote:What you have done is to claim that there is one-to-one correspondence, and therefore Bell must have made an error. In other words, you are assuming one-to-one correspondence and then concluding that there is an error in Bell's mathematics. That may very well be the case, but if that is granted, the effect of the error is to break the one-to-one correspondence.

I am comparing apples with apples. The 3 terms in my (9) are the 3 terms in Bell's (15). The grub in Bell's apple does not change the one-to-one correspondence; it simply means that no one -- who understands apples --- buys it!

minkwe wrote:What I see in fact is that Bell's mathematics is correct, but his error is in failing to preserve the one-to-one correspondence between his mathematics and the induction made by comparing the mathematics with QM.

Bell is offering his math under the auspices of EPRB. He fails under EPRB without any reference to QM; the more so since the correct EPRB result can be derived without reference to QM.

minkwe wrote:Although the results are the same, I believe this analysis is more accurate than yours because Bell's assumptions in Bell 1964 implies an assumption of counterfactual definiteness that will not be meaningful were he following the logical steps you impute to him.

Since when is counterfactual definiteness allowable under EPRB? You are making my point here: Bell's erroneous assumption takes him to settings less-correlated than EPRB. So his critique of Einstein, etc., under EPRB is based on an experiment that is NOT EPRB.

minkwe wrote: Thus, Bell starts out with paired relationships drawn from a set of triples and ends up making comparisons with paired relationships drawn from three disjoint sets of pairs. Whereas his mathematics and resulting inequalities are valid for paired relationships drawn from a set of triples, the variables from paired relationships drawn from three disjoint sets of pairs (like from QM and experiments) do not have one-to-one correspondence to those representing paired relationships drawn from a set of triples.

Whatever Bell starts with, he finishes up BEYOND the EPRB BOUNDARY-CONDITIONS. You are describing the EPRB experiment -- disjoint pairs -- which Bell claims to critique.

minkwe wrote:Although the results are the same, I believe this analysis is more accurate than yours because Bell's assumptions in Bell 1964

(i): So what do you mean 'we need further “coordinates” to complete the specification'?

This means you need to label each E(a,b) with coordinates fully specifying all relevant facts of how they are obtained. For example your equation (9) will become.



And your equation (10) will become



See https://iopscience.iop.org/article/10.1 ... 60007/meta

E(a,b) is perfectly clear under EPRB; the experimenters know exactly what to measure. NB: Bell's nominated context is EPRB; his erroneous analysis is NOT relevant to EPRB. That is the point of my essay. Whose analysis under EPRB is valid: mine (agreeing with elementary algebra and experiment) or Bell's which fails both tests?

Well Aspect (2004) -- see the link in my essay -- is a real experiment with real measurements. And my generalized inequality -- see fn.5 and my eqn (10a) there that covers Aspect (2004) as well-- again has a one-to-one correspondence of "my variables to the variables of the original relationship".

minkwe wrote:Precisely, equation (10) is meaningful for actual measurements, whereas, equation (9) is meaningless as far as measurements are concerned. The variables in (9) can never be measured.

Of course (9) can be measured under EPRB-basics; eg, when adjusted and tested via Aspect's experiments. You seem to be saying that the experimenters are saying that they did not test (9) or its equivalent. But they routinely take the EPRB expectations, they show that Bell erred, AND they confirm my results!

minkwe wrote:

PS: WRT your hemisphere analogy, I suggest Bell's claim is akin to this: all spherical triangles have an upper-bound of angles summing to 180º. And his first [and inappropriate] assumption confines his inequality to 2D planes. Which, as with his EPRB/Aspect inequalities, means his spherical claim is sometimes valid. BUT false in general!...

It means simply that there is no violation, just lack of correspondence of the terms.

So Bell's analysis has terms that lack correspondence with the underlying EPRB physical reality. You again appear to be making my point; which will soon be reinforced via Bell's critique of von Neumann.

minkwe wrote:The most devastating criticism of Bell was delivered by Bell himself before Bell 1964 was ever published.

John S. Bell wrote:Thus the formal proof of von Neumann does not justify his informal conclusion. ....... It was not the objective measurable predictions of quantum mechanics which ruled out hidden variables. It was the arbitrary assumption of a particular (and impossible) relation between the results of incompatible measurements either of which might be made on a given occasion but only one of which can in fact be made.

This is well known. But you are giving it a new twist -- it seems to me -- and one that helps make my case.

Bell knew of this defect before he published his 1964 essay. So you are confirming that he published his EPRB-based essay with the same defect.

So we agree: He did repeat von Neumann's mistake, but only because he did not recognize his own errors under EPRB-- as my essay is intended to make clear.
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Gordon Watson wrote:E(a,b) is defined in ¶2.1 of my essay. It is Bell's P(a,b) and is intended by him to be under EPRB.
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You've missed the point completely. I tried to be very clear in my explanation. You really should read https://iopscience.iop.org/article/10.1 ... 60007/meta

minkwe wrote:

Gordon Watson wrote:E(a,b) is defined in ¶2.1 of my essay. It is Bell's P(a,b) and is intended by him to be under EPRB.
...

You've missed the point completely. I tried to be very clear in my explanation. You really should read https://iopscience.iop.org/article/10.1 ... 60007/meta

I'd be pleased if you could be clearer re the point you are making.

For example, please make your point re this:

E(a,b) is defined in ¶2.1 of my essay. It is Bell's P(a,b) and is intended by him to be under EPRB.

PS: Please do not rely on your psychic abilities: they are not working. I studied that article long ago; and studied it again at your suggestion.
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Gordon Watson wrote:I'd be pleased if you could be clearer re the point you are making.

For example, please make your point re this:

E(a,b) is defined in ¶2.1 of my essay. It is Bell's P(a,b) and is intended by him to be under EPRB.

PS: Please do not rely on your psychic abilities: they are not working. I studied that article long ago; and studied it again at your suggestion.
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I was very clear when I said the following:

This means you need to label each E(a,b) with coordinates fully specifying all relevant facts of how they are obtained. For example your equation (9) will become.



And your equation (10) will become

If you disagree with this, state why. "I disagree, E(a,b) is very clear under EPRB ..." is not a response that's meaningful.

So you've studied the paper but none of your paper takes into consideration the relevant crucial points raised in it. Do you disagree with it or not? You didn't say. Again "I've studied it ..." Is not a meaningful response because I shouldn't have to explain again facts thoroughly explained and illustrated in the article.

minkwe wrote:

Gordon Watson wrote:I'd be pleased if you could be clearer re the point you are making.

For example, please make your point re this:

E(a,b) is defined in ¶2.1 of my essay. It is Bell's P(a,b) and is intended by him to be under EPRB.

PS: Please do not rely on your psychic abilities: they are not working. I studied that article long ago; and studied it again at your suggestion.
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I was very clear when I said the following:

This means you need to label each E(a,b) with coordinates fully specifying all relevant facts of how they are obtained. For example your equation (9) will become.



And your equation (10) will become

If you disagree with this, state why. "I disagree, E(a,b) is very clear under EPRB ..." is not a response that's meaningful.

So you've studied the paper but none of your paper takes into consideration the relevant crucial points raised in it. Do you disagree with it or not? You didn't say. Again "I've studied it ..." Is not a meaningful response because I shouldn't have to explain again facts thoroughly explained and illustrated in the article.

Please explain the physical significance of your labels.

PS: if you want to know why I ask, turn on PM and alert me.

Thanks.

The fascinating paper "Possible experience: From Boole to Bell" by Karl Hess, Kristel Michielsen and Hans De Raedt (9 October 2009 - Europhysics Letters Association - EPL (Europhysics Letters), Volume 87, Number 6) https://iopscience.iop.org/article/10.1209/0295-5075/87/60007/meta contains the words "The mistake here is that Bell and followers insist from the start that the same element of reality occurs for the three different experiments with three different setting pairs". This is simply not true. Bell and followers do not insist on this at all. I have no idea where this idea came from. Bell and his followers insist only that the "same element of reality" has the same probability distribution in each of the three different experiments. The "element of reality" is the name of a *variable* and the *variable* can take on many different *values*.

This allows the construction of a probability model in which the elements of reality are also identified value by value. In probability theory this is called a "coupling". It does not imply that one believes that in "reality", whatever that means, that the coupling is "true". One should distinguish mathematical models which attempt to reproduce some features of reality with reality itself. It is difficult since mathematics is the language of physics; while a mathematical model is generally thought of by mathematicians as a mathematical reality in itself. We could get into the millenia old philosophical discussions about that. Idealist or Platonist?

Anyway, back to the mistake: I think that the same "mistake" or misinterpretation is made by Gordon and by Michel.

For a modern take on causality and Bell-inequalities see the prize-winning "Causality" (2nd ed.) by Judea Pearl, http://bayes.cs.ucla.edu/BOOK-2K/, or the more recent but also prize-winning "Elements of Causal Inference", by Jonas Peters, Dominik Janzing and Bernhard Schölkopf, https://mitpress.mit.edu/books/elements-causal-inference. Free pdf available.

gill1109 wrote:The fascinating paper "Possible experience: From Boole to Bell" by Karl Hess, Kristel Michielsen and Hans De Raedt (9 October 2009 - Europhysics Letters Association - EPL (Europhysics Letters), Volume 87, Number 6) https://iopscience.iop.org/article/10.1209/0295-5075/87/60007/meta contains the words "The mistake here is that Bell and followers insist from the start that the same element of reality occurs for the three different experiments with three different setting pairs". This is simply not true. Bell and followers do not insist on this at all. I have no idea where this idea came from. Bell and his followers insist only that the "same element of reality" has the same probability distribution in each of the three different experiments. The "element of reality" is the name of a *variable* and the *variable* can take on many different *values*.

This allows the construction of a probability model in which the elements of reality are also identified value by value. In probability theory this is called a "coupling". It does not imply that one believes that in "reality", whatever that means, that the coupling is "true". One should distinguish mathematical models which attempt to reproduce some features of reality with reality itself. It is difficult since mathematics is the language of physics; while a mathematical model is generally thought of by mathematicians as a mathematical reality in itself. We could get into the millenia old philosophical discussions about that. Idealist or Platonist?

Anyway, back to the mistake: I think that the same "mistake" or misinterpretation is made by Gordon and by Michel.

For a modern take on causality and Bell-inequalities see the prize-winning "Causality" (2nd ed.) by Judea Pearl, http://bayes.cs.ucla.edu/BOOK-2K/, or the more recent but also prize-winning "Elements of Causal Inference", by Jonas Peters, Dominik Janzing and Bernhard Schölkopf, https://mitpress.mit.edu/books/elements-causal-inference. Free pdf available.

Richard,

Minkwe and I appear to be on opposite tacks. For one, I need no additional labels or identifiers; the identity of the experiment being well-known.

So what is this "same mistake" that you think you identify, please?

Since my elementary math take a few minutes to check, please also point to any mistake in my essay, by paragraph or eqn number.

Thanks; Gordon

gill1109 wrote: ... {SNIP} ...

Anyway, back to the mistake: I think that the same "mistake" or misinterpretation is made by Gordon and by Michel.

For a modern take on causality and Bell-inequalities see the prize-winning "Causality" (2nd ed.) by Judea Pearl, http://bayes.cs.ucla.edu/BOOK-2K/, or the more recent but also prize-winning "Elements of Causal Inference", by Jonas Peters, Dominik Janzing and Bernhard Schölkopf, https://mitpress.mit.edu/books/elements-causal-inference. Free pdf available.

RE : For a modern take on causality and Bell-inequalities ...

On p.187 of Peters++ (2017) I find what appears to be the only reference to Bell's work.

There they refer to the CHSH inequality: seemingly unaware that it is as irrelevant to "causal studies" as Bell's 1964 inequality is irrelevant to EPRB.

Does the Pearl book have references to Bell?

PS: Richard, I know you say that you are not a physicist, but my essay is based on elementary algebra. Thus I would like to see how your support for Bell's work meshes with "the mistake" you think I've made in producing its algebraic refutation. The more so since [rightly in my opinion] you do not require Minkwe's additional labels.

Thanks; Gordon

Exactly. They do the CHSH inequality. Pearle also does it. Just look up "Bell" in the index. Both books use it as illustration of the use of techniques from graphical models (Bayes nets) in order to bound probabilities involving counterfactual variables, in the situation that there are "hidden variables" which are not observed at all, and there is some knowledge about the underlying causal structure of both hidden and un-hidden (manifest) variables. It is amusing that a well-known inequality which epidemiologists use when studying non-compliance in clinical trials, and Bell-CHSH, are just two examples of a general methodology, which is also useful in litigation (probability of causation), in biostatistics, in knowledge discovery, data-mining ... The two books also have whole sections or whole chapters on the whole concept of causality. About the meaning of "independence", the relationship between causal independence, mathematical independence, and statistical independence.

You say that Peters et al are "seemingly unaware that it is as irrelevant to 'causal studies' as Bell's 1964 inequality is irrelevant to EPRB". You are reporting *your* opinion. They give in the rest of the book the argumentation, both mathematical and philosophical, why it is *not* irrelevant.

gill1109 wrote:Exactly. They do the CHSH inequality. Pearle also does it. Just look up "Bell" in the index. Both books use it as illustration of the use of techniques from graphical models (Bayes nets) in order to bound probabilities involving counterfactual variables, in the situation that there are "hidden variables" which are not observed at all, and there is some knowledge about the underlying causal structure of both hidden and un-hidden (manifest) variables. It is amusing that a well-known inequality which epidemiologists use when studying non-compliance in clinical trials, and Bell-CHSH, are just two examples of a general methodology, which is also useful in litigation (probability of causation), in biostatistics, in knowledge discovery, data-mining ... The two books also have whole sections or whole chapters on the whole concept of causality. About the meaning of "independence", the relationship between causal independence, mathematical independence, and statistical independence.

You say that Peters et al are "seemingly unaware that it is as irrelevant to 'causal studies' as Bell's 1964 inequality is irrelevant to EPRB". You are reporting *your* opinion. They give in the rest of the book the argumentation, both mathematical and philosophical, why it is *not* irrelevant.

1. My opinion is based on facts under EPRB: (i) derived via elementary algebra. (ii) no arbitrary assumptions (so easily audited). (iii) experimentally supported. (iv) QM-supported too (of course).

2. Bell-CHSH meets none of these criteria under EPRB.

.

Gordon Watson wrote:

gill1109 wrote:Exactly. They do the CHSH inequality. Pearle also does it. Just look up "Bell" in the index. Both books use it as illustration of the use of techniques from graphical models (Bayes nets) in order to bound probabilities involving counterfactual variables, in the situation that there are "hidden variables" which are not observed at all, and there is some knowledge about the underlying causal structure of both hidden and un-hidden (manifest) variables. It is amusing that a well-known inequality which epidemiologists use when studying non-compliance in clinical trials, and Bell-CHSH, are just two examples of a general methodology, which is also useful in litigation (probability of causation), in biostatistics, in knowledge discovery, data-mining ... The two books also have whole sections or whole chapters on the whole concept of causality. About the meaning of "independence", the relationship between causal independence, mathematical independence, and statistical independence.

You say that Peters et al are "seemingly unaware that it is as irrelevant to 'causal studies' as Bell's 1964 inequality is irrelevant to EPRB". You are reporting *your* opinion. They give in the rest of the book the argumentation, both mathematical and philosophical, why it is *not* irrelevant.

1. My opinion is based on facts under EPRB: (i) derived via elementary algebra. (ii) no arbitrary assumptions (so easily audited). (iii) experimentally supported. (iv) QM-supported too (of course).

2. Bell-CHSH meets none of these criteria under EPRB.

.

The work of Judea Pearl, and also that of Jonas Peters et al, is based on known and easy to derive facts, there are no arbitrary assumptions, and it is experimentally supported. It is widely applied to much more complicated situations in law (both civil law and criminal law), biostatistics, epidemiology, engineering, and so on. The methodology (both in general, and in such "baby" examples as the CHSH case) has been published in what are generally considered the best peer reviewed journals. Software companies are selling apps which derive the inequalities using computer algebra and combinatorial optimization. Bell contrarians are forced to argue that there are establishment conspiracies to suppress the actual truth of the matter. Of course, there is a lot of money and power involved in quantum mysticism these days, so there certainly are powerful forces aligned against publication of work like yours.

I am afraid that you will only be able to convince *me* when you have operationalized your approach to such an extent that you can write computer programs which can be verified to satisfy the constraints of local realism and which manage to win my computer challenges to Luigi Accardi and to Joy Christian, or Sasha Vongehr's similar challenge. I already tried unsuccessfully several times to decode your mathematics. Maybe you can convince someone else that you are onto something important and valid.

gill1109 wrote:

Gordon Watson wrote:

gill1109 wrote:Exactly. They do the CHSH inequality. Pearle also does it. Just look up "Bell" in the index. Both books use it as illustration of the use of techniques from graphical models (Bayes nets) in order to bound probabilities involving counterfactual variables, in the situation that there are "hidden variables" which are not observed at all, and there is some knowledge about the underlying causal structure of both hidden and un-hidden (manifest) variables. It is amusing that a well-known inequality which epidemiologists use when studying non-compliance in clinical trials, and Bell-CHSH, are just two examples of a general methodology, which is also useful in litigation (probability of causation), in biostatistics, in knowledge discovery, data-mining ... The two books also have whole sections or whole chapters on the whole concept of causality. About the meaning of "independence", the relationship between causal independence, mathematical independence, and statistical independence.

You say that Peters et al are "seemingly unaware that it is as irrelevant to 'causal studies' as Bell's 1964 inequality is irrelevant to EPRB". You are reporting *your* opinion. They give in the rest of the book the argumentation, both mathematical and philosophical, why it is *not* irrelevant.

1. My opinion is based on facts under EPRB: (i) derived via elementary algebra. (ii) no arbitrary assumptions (so easily audited). (iii) experimentally supported. (iv) QM-supported too (of course).

2. Bell-CHSH meets none of these criteria under EPRB.

.

The work of Judea Pearl, and also that of Jonas Peters et al, is based on known and easy to derive facts, there are no arbitrary assumptions, and it is experimentally supported. It is widely applied to much more complicated situations in law (both civil law and criminal law), biostatistics, epidemiology, engineering, and so on. The methodology (both in general, and in such "baby" examples as the CHSH case) has been published in what are generally considered the best peer reviewed journals. Software companies are selling apps which derive the inequalities using computer algebra and combinatorial optimization. Bell contrarians are forced to argue that there are establishment conspiracies to suppress the actual truth of the matter. Of course, there is a lot of money and power involved in quantum mysticism these days, so there certainly are powerful forces aligned against publication of work like yours.

I am afraid that you will only be able to convince *me* when you have operationalized your approach to such an extent that you can write computer programs which can be verified to satisfy the constraints of local realism and which manage to win my computer challenges to Luigi Accardi and to Joy Christian, or Sasha Vongehr's similar challenge. I already tried unsuccessfully several times to decode your mathematics. Maybe you can convince someone else that you are onto something important and valid.

Thanks Richard,

1. Clarification: Since minkwe has not yet clarified the physical significance of his labels, let me be clear: a boundary condition on ALL of my Bell-analysis is this,

VALID paired-results arise, both theoretically and physically, from outcomes generated in the SAME instance; and not otherwise. This condition is explicit in Bell (1964) in the sentence that introduces his eqn (1). So, when I need to make this point, I use "instance-trackers" to show where Bell/CHSH -- erroneously breaching instances -- deliver theoretical and experimental nonsense.

2. Re Bell-CHSH errors: They arise solely from their neglect of the above boundary-condition.

3. Re your past difficulties decoding my math: I now use elementary algebra. So please try again with the current essay; Bell's 1964 inequality is refuted in less than a page.** "Bell-locality" can be refuted similarly!

4. Re those computer challenges: Do you allow me to invoke the following law [1]? It's a law of Nature in EPRB settings; a corollary of my refutation of "Bell-locality".


Under my true-locality [AKA Einstein-locality], via common-cause correlation in the same instance; ie, Alice receives Bob receives :



Under false "Bell-locality":

[sic]!

PS: Please advise your position on "Bell-locality".

** EDIT: Out soon: I am now combining my two elementary essays under this title: "Bell's inequality refuted, his errors corrected, via elementary algebra."

Thanks again; Gordon

Gordon Watson wrote:1. Clarification: Since minkwe has not yet clarified the physical significance of his labels, let me be clear: a boundary condition on ALL of my Bell-analysis is this,

VALID paired-results arise, both theoretically and physically, from outcomes generated in the SAME instance; and not otherwise. This condition is explicit in Bell (1964) in the sentence that introduces his eqn (1). So, when I need to make this point, I use "instance-trackers" to show where Bell/CHSH -- erroneously breaching instances -- deliver theoretical and experimental nonsense.

2. Re Bell-CHSH errors: They arise solely from their neglect of the above boundary-condition.

3. Re your past difficulties decoding my math: I now use elementary algebra. So please try again with the current essay; Bell's 1964 inequality is refuted in less than a page.** "Bell-locality" can be refuted similarly!

4. Re those computer challenges: Do you allow me to invoke the following law [1]? It's a law of Nature in EPRB settings; a corollary of my refutation of "Bell-locality".

Under my true-locality [AKA Einstein-locality], via common-cause correlation in the same instance; ie, Alice receives Bob receives :



Under false "Bell-locality":

[sic]!

PS: Please advise your position on "Bell-locality".

The sentence of Bell preceding (1), with my underlining of a couple of key words, is:

The result of measuring is then determined by and , and the result of measuring in the same instance is determined by and .

It's clear to me that what he actually meant was something more like:

The result of measuring would then be determined by and , and the result of measuring in the same instance would then be determined by and .

He is talking about counterfactuals - what would have happened if - and he is working under the assumptions made in the previous sentences.

For the rest: your equation [1] is a triviality. You can call it Bayes' theorem if you like. You can also take it as the definition of conditional probability.

Your equation [2] comes out of the blue. Nobody is assuming that.

Regarding computer challenges, such as Vongehr's quantum Randi challenge, you can use whatever you like in the black-box part of your code. You just have to impose the time and spatial constraints, i.e. the basic causality rules, in such a way that someone who does not want to check your code or your formulas can still verify that you are not cheating. For this it is essential that there are separate "shots" in one "run" of shots, that settings are chosen outside of your programs, and delivered by the person who is challenging you, and that if you use (pesudop?) random number generators, there are facilities for saving the random seed, and resetting a random seed, so that the computer code can be forced to give identical results when run several times.

In other words, the computer experiment testing your computer implementation of your theory follows strictly the same rules as are nowadays adopted in so-called "loophole free" experiments. The whole point is that you cannot win the challenge since Bell's theorem is a simple and definitely true theorem of distributed computing, i.e., it is a theorem in computer science. It is not necessarily about physics or about electrons or photons or even about real computers. It is about idealised, abstract, deterministic Turing machines.

gill1109 wrote:

Gordon Watson wrote:1. Clarification: Since minkwe has not yet clarified the physical significance of his labels, let me be clear: a boundary condition on ALL of my Bell-analysis is this,

VALID paired-results arise, both theoretically and physically, from outcomes generated in the SAME instance; and not otherwise. This condition is explicit in Bell (1964) in the sentence that introduces his eqn (1). So, when I need to make this point, I use "instance-trackers" to show where Bell/CHSH -- erroneously breaching instances -- deliver theoretical and experimental nonsense.

2. Re Bell-CHSH errors: They arise solely from their neglect of the above boundary-condition.

3. Re your past difficulties decoding my math: I now use elementary algebra. So please try again with the current essay; Bell's 1964 inequality is refuted in less than a page.** "Bell-locality" can be refuted similarly!

4. Re those computer challenges: Do you allow me to invoke the following law [1]? It's a law of Nature in EPRB settings; a corollary of my refutation of "Bell-locality".

Under my true-locality [AKA Einstein-locality], via common-cause correlation in the same instance; ie, Alice receives Bob receives :



Under false "Bell-locality":

[sic]!

PS: Please advise your position on "Bell-locality".

The sentence of Bell preceding (1), with my underlining of a couple of key words, is:

The result of measuring is then determined by and , and the result of measuring in the same instance is determined by and .

It's clear to me that what he actually meant was something more like:

The result of measuring would then be determined by and , and the result of measuring in the same instance would then be determined by and .

He is talking about counterfactuals - what would have happened if - and he is working under the assumptions made in the previous sentences.

For the rest: your equation [1] is a triviality. You can call it Bayes' theorem if you like. You can also take it as the definition of conditional probability.

Your equation [2] comes out of the blue. Nobody is assuming that.

Regarding computer challenges, such as Vongehr's quantum Randi challenge, you can use whatever you like in the black-box part of your code. You just have to impose the time and spatial constraints, i.e. the basic causality rules, in such a way that someone who does not want to check your code or your formulas can still verify that you are not cheating. For this it is essential that there are separate "shots" in one "run" of shots, that settings are chosen outside of your programs, and delivered by the person who is challenging you, and that if you use (pesudop?) random number generators, there are facilities for saving the random seed, and resetting a random seed, so that the computer code can be forced to give identical results when run several times.

In other words, the computer experiment testing your computer implementation of your theory follows strictly the same rules as are nowadays adopted in so-called "loophole free" experiments. The whole point is that you cannot win the challenge since Bell's theorem is a simple and definitely true theorem of distributed computing, i.e., it is a theorem in computer science. It is not necessarily about physics or about electrons or photons or even about real computers. It is about idealised, abstract, deterministic Turing machines.

Richard,

1. Your interpretation of [via additions to] the sentence that introduces Bell 1964:(1) makes no sense to me: it makes good sense as Bell has written. Further, I'm not aware of any other Bellian making your strange call: so I conclude that the sentence makes good sense to many others!

2. You say: "Your [ie, my, GW's] equation [2] comes out of the blue. Nobody is assuming that."

I trust you understood that it was a short-form representation of:

[sic]!

Which is eqn (10) in Bell's "La nouvelle cuisine".

It is known to Bellians as "Bell locality" :- some Bellians, agreeing with me, admit that is false; which it clearly is, both theoretically and experimentally and under QM.

See, for example, Norsen, eqn (18): https://arxiv.org/pdf/quant-ph/0408105.pdf

3. Richard, this all leaves my half-page of elementary algebra untouched.

Please, start with my eqn (1) and follow the elementary math.

For, seriously, if you cannot make sense of my half-page, there is little hope that you'll make sense of Joy Christian's math in the coming symposium.

Thanks; Gordon

Gordon Watson wrote:Richard,

1. Your interpretation of [via additions to] the sentence that introduces Bell 1964:(1) makes no sense to me: it makes good sense as Bell has written. Further, I'm not aware of any other Bellian making your strange call: so I conclude that the sentence makes good sense to many others!

2. You say: "Your [ie, my, GW's] equation [2] comes out of the blue. Nobody is assuming that."

I trust you understood that it was a short-form representation of:

[sic]!

Which is eqn (10) in Bell's "La nouvelle cuisine".

It is known to Bellians as "Bell locality" :- some Bellians, agreeing with me, admit that is false; which it clearly is, both theoretically and experimentally and under QM.

See, for example, Norsen, eqn (18): https://arxiv.org/pdf/quant-ph/0408105.pdf

3. Richard, this all leaves my half-page of elementary algebra untouched.

Please, start with my eqn (1) and follow the elementary math.

For, seriously, if you cannot make sense of my half-page, there is little hope that you'll make sense of Joy Christian's math in the coming symposium.

Thanks; Gordon

Gordon

1. I don't speak for anybody else. I'm not trying to change Bell, I'm trying to make his intention, which is obvious to me but not to you, more explicit. He is using counterfactual reasoning; and he is building on the working assumptions which he had previously made. Those assumptions were provisional. His intention is to show that they must be false. It's called arguing by contradiction. I have noticed that a lot of people have difficulties with arguing by contradiction.

Counterfactual reasoning has moreover been the subject of great controversy in philosophy; but also many ordinary people have gut-feeling objections to counterfactual reasoning. However it is the basis of Law, and the basis of Morality, and can be cogently argued to be the basis of Science, and you could say, the basis of History. Does History merely recount what did happen, or is it an attempt to explain *why* certain things happened? In counterfactual reasoning we always use "were" not "is". If Napoleon had been a woman then he would never have tried to invade Russia.

I recommend Pearl's book. It has created quite a revolution in many fields. Nowadays the limitations but also the power and the necessity of counterfactual reasoning are widely accepted.

You think you have proven that Bell is wrong. I think you have completely misunderstood Bell. You think Bell's sentence makes good sense as it stands. I can tell you that you have not understood Bell's sentence, because if you had understood him properly, you wouldn't have arrived at your conclusions.

2. I did not understand what your [2] was short-hand for. I understand the long form of [2] which you give now. It's obviously, physically, a much too strong assumption. It combines two different (conditional) independence assumptions, which the philosophers of science have got fancy names for. Parameter independence and something else. If you want to call it Bell locality, feel free. It is mathematically equivalent to assumptions that would appear at first sight to be much weaker, and much more physically reasonable. Such mathematical equivalences are nowadays all part of the standard theory of causality as set out in Pearl, Peters et al, etc. They go back to Fine's papers of 1980 or thereabouts, in which it is shown that the set of all CHSH inequalities together are in a certain sense necessary and sufficient conditions for existence of a LHV model. Note: existence of a LHV model! Not existence of LHV's

3. I had long, long ago made perfect sense, to my own satisfaction, of Joy Christian's mathematics. I felt I had got to understand his way of thinking very well, and I think I know exactly how it led him astray. But so what? My criticisms are well documented. Joy believes he has refuted them all. I doubt any symposium is going to change my thinking on this, nor Joy's thinking. That is not the point.

I think Joy should aim at convincing others. The point of the symposium is to give Joy a podium on which to do so. I offered him this symposium in order to atone, as far as I can, for the anguish I caused him in the past. I should not have pursued him, like I did, to all far corners of the internet! It was an unhealthy obsession on my part, and it caused harm to Joy and to others, which I'm deeply sorry for.