Bell's theorem refuted via elementary probability theory

[Gordon Watson]

With less need for explanation, how about this:



where is the space of twins, , pairwise correlated via the same-instance conservation of total angular momentum.
The above reduces to the Bell formulation. But makes it clear that our work begins with TLR [distinct local arguments] and the common detector-function .

No, it doesn’t reduce to the Bell formulation. And you are wasting space defining +beta = beta, and -beta = -(beta). Try:



Bell starts right there, and shows that the second equality leads to a contradiction (the first is a definition).

TO GILL, FROM WATSON, RE NO.
HAVE MONEY. WILL BET.
AGAINST YOU. ON ME.
HOW MUCH? WHAT ODDS?
A.S.A.P.

What exactly do you want to bet on?

It’s important to fix how and when the winner will be determined.

For instance, I have 64 000 Euro says that you can’t reproduce the singlet correlations in a networked computer simulation. As I see it, Bell’s theorem says I’ll win. There are however stringent rules on the protocol of the simulation experiment. No cheating, no experimental loopholes.

According to my calculations the odds in that bet are overwhelmingly in my favour. But anyway, if I should happen to *lose*, the impact of the experiment on science will be so huge that I’ll quickly get the money back by appearing on talk shows. Moreover, the winner will get the Nobel prize, and won’t be interested in the cash he or she gets from the bet. A graceful winner will be happy that I just give 5000 Euro to “Medecins sans Frontieres”.

If you can come up with A, B and rho which do the job, then program them, and win the bet.

I thought you claim that Bell’s theorem is wrong. Come up with proof! I bet you have none!

My note "RE NO" refers to the "NO" in your claim.
.

[gill1109]

No, it doesn’t reduce to the Bell formulation. And you are wasting space defining +beta = beta, and -beta = -(beta). Try:



Bell starts right there, and shows that the second equality leads to a contradiction (the first is a definition).

TO GILL, FROM WATSON, RE NO.
HAVE MONEY. WILL BET.
AGAINST YOU. ON ME.
HOW MUCH? WHAT ODDS?
A.S.A.P.

What exactly do you want to bet on?

It’s important to fix how and when the winner will be determined.

For instance, I have 64 000 Euro says that you can’t reproduce the singlet correlations in a networked computer simulation. As I see it, Bell’s theorem says I’ll win. There are however stringent rules on the protocol of the simulation experiment. No cheating, no experimental loopholes.

According to my calculations the odds in that bet are overwhelmingly in my favour. But anyway, if I should happen to *lose*, the impact of the experiment on science will be so huge that I’ll quickly get the money back by appearing on talk shows. Moreover, the winner will get the Nobel prize, and won’t be interested in the cash he or she gets from the bet. A graceful winner will be happy that I just give 5000 Euro to “Medecins sans Frontieres”.

If you can come up with A, B and rho which do the job, then program them, and win the bet.

I thought you claim that Bell’s theorem is wrong. Come up with proof! I bet you have none!

My note "RE NO" refers to the "NO" in your claim.
.

OK! So you agree that you do not have an A, B and rho which disprove Bell's claim. In short, you have no proof that Bell is wrong.

[Gordon Watson]

I take probability theory (PT) to be the logic of science. (And I like the related math to do much of my talking.) PT allows me to encode incomplete information, en route to establishing more complete information.

That's not what the phrase "Logic of Science" is supposed to mean when referring to PT. It doesn't mean non-probabilistic answers are illogical.

You object to what PT means to me?? So what is the phrase "Logic of Science" supposed to mean when referring to PT? (I find no clue in your provision of a non sequitur from who-knows-where.)

In like fashion, you objected to my use of to denote a particle with properties . So I sent you an email (10 days ago), asking: "How would you sketch a particle schematically in a simple flow-chart?"

Given your response: I'll provide a revised draft in the light of it and ideas already in this thread.

So I am not saying that I don't know how the transformation happens. In my view, under EPRB, particle-polariser interactions expose the equivalence class (EC) to which each incoming (pristine) particle belonged.

How? Either you know how and don't want to tell us, or you don't know how and don't want to tell us.

If I say , I've provided exactly how is transformed together with the setting to generate the outcomes . Then I've also shown that there are just two equivalence classes of lambda, as there must be because we already know that the outcomes can only be one of by definition. The important point about specifying the mechanism of transformation is to show how the universe of vectors are divided into the two equivalence classes.

However, if I refuse to provide the mechanism (aka details of the function) and just insist that there are equivalence classes, I would have added zero content to the Bell discussion.

The mechanism that I propose is based on latent properties of each . I define these properties via ECs. ECs determine the related results. Via ECs, I can predict, with certainty: the outcome of a specific test and the distribution of results over a long run of tests.

When the ECs are unknown, I use PT to confirm the QM results under TLR.

Now, turning to these ECs that you say must be: where do I find them in the Bell lit? Further, who else uses them (in conjunction with the application of Malus' Law to local beables) to confirm the QM results under TLR?

The function Bell specifies is . So, as a factual starting point, I provide the two relevant ECs that deliver .

Do I go on provide lower level functions and the dynamics of spin, torque, precession? Here, I do not. I expect such functions to emerge from QM and GA; and I hope these are the functions that JC and others are also working on.

Instead, here, for me: Having shown that BT is false, I go on to show that his claimed proof (Bell's famous inequality) is false under EPRB and high-school math. (In my view: "naive-realism", aka CFD, is not forced upon us under EPRB.)

So I say that EPRB particle-pairs are such that and and that the direct application of the related Malusian Law leads us to the QM result.

In other words: under EPRB, via this particle/analyser interaction -- eg: -- this particle's spin will emerge re-oriented in one and only one way: spin-up in the direction.

So, here, QM says and I say the same via Malus' Law under TLR.

E&OE! To be continued.
.

[Gordon Watson]

I don't see that my focus on ECs is excessive. As for the Bell literature, please show me a tested that did not reveal an EC. It seems to me that it would not be EPRB if a produced other than a specific outcome?

I think you miss the point. It is not that ECs are lacking, but that they are so obvious as to be uninteresting for the analysis. Bell introduces equivalence classes by definition. The interesting part is not the presence of ECs but in specifying which belong to the same equivalence class in the context of a setting . And you show that by presenting the functions, otherwise talking about ECs is uninteresting.

So obvious, and Bell introduces ECs by definition? Yet his inequality (the proof of his theorem) is false under EPRB?

I do not recall much use of ECs in the earliest Bellian-literature; say, up to 2000. Could you point me to a few, please? The subject is indeed interesting.

Does this next help you understand my difficulty here? Suppose, under the conservation of charge, you split a neutral particle into two. Are you then asking me which is positive and which is negative?

Yes, I struggle with , superscripted or otherwise! Reason: I believe, (i) we advance teaching and understanding when we expose symmetries; (ii) we clarify Bell's ideas when we use the licence given by Bell at the end of II. Formulation; (iii) it seems that my shorthand needs to be clearer.

Who is it are you trying to teach? Have you figured that these purported students need to learn about symmetry at the same time as trying to understand a topic for which symmetry so obvious as to not be interesting? A good teacher shows focus and restraint when conveying information. Just because you are thinking about it doesn't mean it needs to be written down. What exactly is the main point you want to make. Focus on that. If your brain is overflowing with great ideas, write many different papers, each one focused on one key idea.

As for my shorthand and the use of . Believing that I define its use precisely, I struggle to see the claimed difficulties (but am working to eliminate any such)!

Relatedly, I asked you (via email): What you would use in place of my "confusing" in a brief flowchart. That might help?

As for symmetries. I prefer the option that Bell provides at the end of II.—Formulation. To me, it is more physically significant: and more-clearly compatible with TLR.

Thus I prefer to learn via such symmetries as , , etc.

HTH; Gordon

[gill1109]

I take probability theory (PT) to be the logic of science. (And I like the related math to do much of my talking.) PT allows me to encode incomplete information, en route to establishing more complete information.

That's not what the phrase "Logic of Science" is supposed to mean when referring to PT. It doesn't mean non-probabilistic answers are illogical.

You object to what PT means to me?? So what is the phrase "Logic of Science" supposed to mean when referring to PT? (I find no clue in your provision of a non sequitur from who-knows-where.)

In like fashion, you objected to my use of to denote a particle with properties . So I sent you an email (10 days ago), asking: "How would you sketch a particle schematically in a simple flow-chart?"

Given your response: I'll provide a revised draft in the light of it and ideas already in this thread.

So I am not saying that I don't know how the transformation happens. In my view, under EPRB, particle-polariser interactions expose the equivalence class (EC) to which each incoming (pristine) particle belonged.

How? Either you know how and don't want to tell us, or you don't know how and don't want to tell us.

If I say , I've provided exactly how is transformed together with the setting to generate the outcomes . Then I've also shown that there are just two equivalence classes of lambda, as there must be because we already know that the outcomes can only be one of by definition. The important point about specifying the mechanism of transformation is to show how the universe of vectors are divided into the two equivalence classes.

However, if I refuse to provide the mechanism (aka details of the function) and just insist that there are equivalence classes, I would have added zero content to the Bell discussion.

The mechanism that I propose is based on latent properties of each . I define these properties via ECs. ECs determine the related results. Via ECs, I can predict, with certainty: the outcome of a specific test and the distribution of results over a long run of tests.

When the ECs are unknown, I use PT to confirm the QM results under TLR.

Now, turning to these ECs that you say must be: where do I find them in the Bell lit? Further, who else uses them (in conjunction with the application of Malus' Law to local beables) to confirm the QM results under TLR?

The function Bell specifies is . So, as a factual starting point, I provide the two relevant ECs that deliver .

Do I go on provide lower level functions and the dynamics of spin, torque, precession? Here, I do not. I expect such functions to emerge from QM and GA; and I hope these are the functions that JC and others are also working on.

Instead, here, for me: Having shown that BT is false, I go on to show that his claimed proof (Bell's famous inequality) is false under EPRB and high-school math. (In my view: "naive-realism", aka CFD, is not forced upon us under EPRB.)

So I say that EPRB particle-pairs are such that and and that the direct application of the related Malusian Law leads us to the QM result.

In other words: under EPRB, via this particle/analyser interaction -- eg: -- this particle's spin will emerge re-oriented in one and only one way: spin-up in the direction.

So, here, QM says and I say the same via Malus' Law under TLR.

E&OE! To be continued.
.

So naïeve realism is CFD (Counterfactual definiteness). TLR, “true local realism”, is just the singlet correlations viewed as a plain surface-level description of the measurement outcome statistics predicted by QM in the EPR-B experiment (the collection of probabilities of each possible outcome pair given any setting pair).

Gordon, you have no disproof of Bell’s theorem. Bell’s theorem states that those statistics can’t be generated by functions A, B, rho with the usual properties. Seems you agree with that statement.

All the chit-chat about equivalence classes is empty. You can define an equivalence relation on Lambda by using A(a, .) to split Lambda into two subsets, depending on whether A is +1 or -1, but the equivalence relation drogende on “a”. Your notation hides dependence on important parameters. But adds superfluous decorations. It merely makes your maths impenetrable. A smoke screen.

Finally, all you are saying is: if you don’t believe in local realism then Bell’s theorem has no interest for you. This is exactly what Bohr would have thought. Bell already pointed out that Bohr would simply have said “I told you so”.

[minkwe]

So obvious, and Bell introduces ECs by definition? Yet his inequality (the proof of his theorem) is false under EPRB?

Bell's inequality is not false for the EPRB experiment due to the lack of equivalence classes. It is false for reasons you have mentioned previously but not emphasized enough in your recent paper. It is false for reasons Richard has mentioned in his 2004 EPL paper (though he would disagree with my characterization).

I do not recall much use of ECs in the earliest Bellian-literature; say, up to 2000. Could you point me to a few, please? The subject is indeed interesting.

I don't think anybody emphasized the phrase "equivalence classes" simply because it is too obvious to be interesting. The equation present in Bell's original paper, implies immediately that where is the equivalence class of all that produce the outcome together with the setting , and is the equivalence class of all that produce the outcome together with the setting .

Unless you are using EC with a different definition that you have not explained yet, the above is uninteresting.

Does this next help you understand my difficulty here? Suppose, under the conservation of charge, you split a neutral particle into two. Are you then asking me which is positive and which is negative?

No. I'm saying if you present the details of the functions, it will reveal how a specific is transformed to the outcome and thus how is split into either , or . That would be interesting. Then when you purport to provide a function, it should clearly show that instead of something like .

Relatedly, I asked you (via email): What you would use in place of my "confusing" in a brief flowchart. That might help?

Let's keep this discussion here rather than spread it around in many places. I believe I explained already why is not a good notation for particles. I don't have anything else to add to that.

[minkwe]

You object to what PT means to me?? So what is the phrase "Logic of Science" supposed to mean when referring to PT? (I find no clue in your provision of a non sequitur from who-knows-where.)

When you are asked to provide a function showing the mechanism of how is transformed to , invoking PT as the "Logic of Science" to justify relying on probabilities as an excuse for not providing any dynamics is the non sequitur. That was the whole point of my retort. But let's not go there.

In like fashion, you objected to my use of to denote a particle with properties . So I sent you an email (10 days ago), asking: "How would you sketch a particle schematically in a simple flow-chart?"

I wouldn't. Another non-sequitur . Whether it's a good idea to sketch a particle on a simple flow chart or not, it is still my opinion that using the notation to represent something that is not a function, is a bad use of notation. I made a suggestion of something else, which you rejected. It is up to you what you want to do about it since it's your paper after all.

The mechanism that I propose is based on latent properties of each . I define these properties via ECs. ECs determine the related results. Via ECs, I can predict, with certainty: the outcome of a specific test and the distribution of results over a long run of tests.

Where is the mechanism? You haven't provided any. I'm still waiting. I have the feeling we are speaking different languages as concerns physics.

The function Bell specifies is . So, as a factual starting point, I provide the two relevant ECs that deliver .

That's a definition, not a specification of the dynamics of the function. What you have provided is a definition, not a specification. It doesn't deliver anything. At best it is a promise that the specification to be provided later will deliver . And Bell goes on to provide such a specification

Do I go on provide lower level functions and the dynamics of spin, torque, precession? Here, I do not. I expect such functions to emerge from QM and GA; and I hope these are the functions that JC and others are also working on.

Yes, if you claim to have functions that deliver dynamics, you must. If you don't have that yet, then don't claim to have functions that deliver anything.

[Gordon Watson]

So obvious, and Bell introduces ECs by definition? Yet his inequality (the proof of his theorem) is false under EPRB?

Bell's inequality is not false for the EPRB experiment due to the lack of equivalence classes. It is false for reasons you have mentioned previously but not emphasized enough in your recent paper. It is false for reasons Richard has mentioned in his 2004 EPL paper (though he would disagree with my characterization).

Thanks minkwe; more soon. For now: Please remind me of these reasons; G

EDIT: Are you referring to Europhysics Letters: "Bell’s inequality and the coincidence-time loophole" https://arxiv.org/pdf/quant-ph/0312035.pdf

I'd welcome your identification of the Gillian reasons you refer to. Tks, G
.

[gill1109]

So obvious, and Bell introduces ECs by definition? Yet his inequality (the proof of his theorem) is false under EPRB?

Bell's inequality is not false for the EPRB experiment due to the lack of equivalence classes. It is false for reasons you have mentioned previously but not emphasized enough in your recent paper. It is false for reasons Richard has mentioned in his 2004 EPL paper (though he would disagree with my characterization).

Thanks minkwe; more soon. For now: Please remind me of these reasons; G

EDIT: Are you referring to Europhysics Letters: "Bell’s inequality and the coincidence-time loophole" https://arxiv.org/pdf/quant-ph/0312035.pdf

I'd welcome your identification of the Gillian reasons you refer to. Tks, G
.

I wouldn’t say it is *false*. I would say that it was often unjustifiably applied. We (Jan-Åke Larsson and I) showed that it needed adjustment or modification, and gave one way in which it could be adjusted, when detection events are selected by comparing times of events in the two sides of the experiments. Pre 2015 most experiments suffered from this loophole. From 2015, many experiments have been performed and analysed in a rigorous way. See Larsson’s paper https://arxiv.org/abs/1407.0363 for a survey of experimental loopholes and how to avoid them. It was published here https://iopscience.iop.org/article/10.1088/1751-8113/47/42/424003, Jan-Åke Larsson 2014 J. Phys. A: Math. Theor. 47 424003

[Gordon Watson]

So naïeve realism is CFD (Counterfactual definiteness). TLR, “true local realism”, is just the singlet correlations viewed as a plain surface-level description of the measurement outcome statistics predicted by QM in the EPR-B experiment (the collection of probabilities of each possible outcome pair given any setting pair).

Gordon, you have no disproof of Bell’s theorem. Bell’s theorem states that those statistics can’t be generated by functions A, B, rho with the usual properties. Seems you agree with that statement.

All the chit-chat about equivalence classes is empty. You can define an equivalence relation on Lambda by using A(a, .) to split Lambda into two subsets, depending on whether A is +1 or -1, but the equivalence relation drogende on “a”. Your notation hides dependence on important parameters. But adds superfluous decorations. It merely makes your maths impenetrable. A smoke screen.

Finally, all you are saying is: if you don’t believe in local realism then Bell’s theorem has no interest for you. This is exactly what Bohr would have thought. Bell already pointed out that Bohr would simply have said “I told you so”.

Thanks Richard,

For, via your "Finally" note above, you seem to be understanding my position more clearly.

So, for now, let's set aside the supposed 'smoke-screen' re BT.

(I'll be discussing clarifications with minkwe; so it'd help if you identified the superfluous decorations.)

And let's see if I can as easily dismiss Bell as Bohr does!

1. Since I use Bell's references to Bohr to support my position, what is the source for:

Bell already pointed out that Bohr would simply have said “I told you so”?

2. I ask because the quotes I use are such "plain common sense" that I'd be surprised if Bell breached them.

3. Thus: What definitions of "realism" and "CFD" is Bell using?

4. Further: How do these definitions manifest in Bell's derivation of his 1964 inequality? Where are they?

5. FOR, unless he introduces fresh errors: Since I use high-school math to refute Bell's inequality — Bell 1964:(15) — Bell's definitions must be the source of his error here.***

*** An error confirmed experimentally.

Thanks again; Gordon
.

[Gordon Watson]

So obvious, and Bell introduces ECs by definition? Yet his inequality (the proof of his theorem) is false under EPRB?

Bell's inequality is not false for the EPRB experiment due to the lack of equivalence classes. It is false for reasons you have mentioned previously but not emphasized enough in your recent paper. It is false for reasons Richard has mentioned in his 2004 EPL paper (though he would disagree with my characterization).

I do not recall much use of ECs in the earliest Bellian-literature; say, up to 2000. Could you point me to a few, please? The subject is indeed interesting.

I don't think anybody emphasized the phrase "equivalence classes" simply because it is too obvious to be interesting. The equation present in Bell's original paper, implies immediately that where is the equivalence class of all that produce the outcome together with the setting , and is the equivalence class of all that produce the outcome together with the setting .

Unless you are using EC with a different definition that you have not explained yet, the above is uninteresting.

Does this next help you understand my difficulty here? Suppose, under the conservation of charge, you split a neutral particle into two. Are you then asking me which is positive and which is negative?

No. I'm saying if you present the details of the functions, it will reveal how a specific is transformed to the outcome and thus how is split into either , or . That would be interesting. Then when you purport to provide a function, it should clearly show that instead of something like .

Relatedly, I asked you (via email): What you would use in place of my "confusing" in a brief flowchart. That might help?

Let's keep this discussion here rather than spread it around in many places. I believe I explained already why is not a good notation for particles. I don't have anything else to add to that.

Thanks for all of the above. And re this: "Unless you are using EC with a different definition that you have not explained yet, the above is uninteresting."

Footnote #2 of my draft is intended to make this point: I regard my ECs as latent elements of physical reality. (For I can predict them with certainty without disturbing the related system.)

So it seems OK to me to call upon them, as I do. Gordon [hastily; battery fading]
.

[gill1109]

1. Since I use Bell's references to Bohr to support my position, what is the source for:

Bell already pointed out that Bohr would simply have said “I told you so”?

2. I ask because the quotes I use are such "plain common sense" that I'd be surprised if Bell breached them.

3. Thus: What definitions of "realism" and "CFD" is Bell using?

4. Further: How do these definitions manifest in Bell's derivation of his 1964 inequality? Where are they?

5. FOR, unless he introduces fresh errors: Since I use high-school math to refute Bell's inequality — Bell 1964:(15) — Bell's definitions must be the source of his error here.***

*** An error confirmed experimentally.

Thanks again; Gordon
.

Read “Bertlmann’s socks”, especially the last section. I wrote a long time ago in https://arxiv.org/abs/quant-ph/0301059, “Time, Finite Statistics, and Bell’s Fifth Position”:

“In fact, in Bell (1981), the final section of the paper on Bertlmann’s famous socks (chapter 16 of Bell (1987)), he gave a list of four quite different positions one could take, each one logically consistent with his mathematical results. One of them is simply not to care: go with Bohr, don’t look for anything behind the scenes, for if you do you will get stuck in meaningless paradoxes, meaningless because there no necessity for anything behind the scenes. If, however, like Bell himself, you have a personal preference for imagining a realistic world behind the scenes, accept with Bell that it must be non-local. You will be in excellent company: with Bohm-Riley, with Girardi-Rimini-Weber (the continuous spontaneous localization model), and no doubt with others. Alternatively, accept even worse consequences—on which more, later.”

Read “Bertlmann’s socks” to find Bell’s most mature thinking. He always worked with CHSH from the moment it was invented, for very good reasons. As far as I know he never talked about CFD (counterfactual definiteness).

You do not refute Bell’s inequality. It only takes high school math to derive them. Apparently you have issues with the physical reasoning behind the mathematical assumptions which lead to Bell’s inequalities.

[minkwe]

Thanks minkwe; more soon. For now: Please remind me of these reasons; G

https://arxiv.org/abs/quant-ph/0312035

“The problem here is that the ensemble on which the correlations are evaluated changes with the settings, while the original Bell inequality requires that they stay the same. In effect, the Bell inequality only holds on the common part of the four different ensembles ΛAB , ΛAB′ , ΛA′B , and ΛA′B′”

Richard says above:

I wouldn’t say it is *false*. I would say that it was often unjustifiably applied. We (Jan-Åke Larsson and I) showed that it needed adjustment or modification, and gave one way in which it could be adjusted, when detection events are selected by comparing times of events in the two sides of the experiments.

I don't necessarily agree that their modification makes any difference but that's for a separate discussion.

[Gordon Watson]

So obvious, and Bell introduces ECs by definition? Yet his inequality (the proof of his theorem) is false under EPRB?

Bell's inequality is not false for the EPRB experiment due to the lack of equivalence classes. It is false for reasons you have mentioned previously but not emphasized enough in your recent paper. It is false for reasons Richard has mentioned in his 2004 EPL paper (though he would disagree with my characterization).

SOS: Let me try again: What are the reasons that I [GW] have mentioned previously [that Bell's inequality is false] but have not emphasised enough in my recent draft?

For, as I see it [perhaps mistakenly] this, below, has no relevance to my position.

https://arxiv.org/abs/quant-ph/0312035

“The problem here is that the ensemble on which the correlations are evaluated changes with the settings, while the original Bell inequality requires that they stay the same. In effect, the Bell inequality only holds on the common part of the four different ensembles ΛAB , ΛAB′ , ΛA′B , and ΛA′B′”

Here's one reason for it having no relevance for me: The solution is to ensure that, in each of the four runs, the ensemble size is adequately large. Thereby ensuring that the average over each ensemble approaches the related Bellian idealisation adequately.

SOS: Gordon

[gill1109]

Richard says above:

I wouldn’t say it is *false*. I would say that it was often unjustifiably applied. We (Jan-Åke Larsson and I) showed that it needed adjustment or modification, and gave one way in which it could be adjusted, when detection events are selected by comparing times of events in the two sides of the experiments.

I don't necessarily agree that their modification makes any difference but that's for a separate discussion.

Michel, it made the difference, in your simulations, between violating the inequality and not violating the inequality. See my paper https://arxiv.org/abs/1507.00106 “ Event based simulation of an EPR-B experiment by local hidden variables: epr-simple and epr-clocked”.

Gordon:

“The problem here is that the ensemble on which the correlations are evaluated changes with the settings, while the original Bell inequality requires that they stay the same. In effect, the Bell inequality only holds on the common part of the four different ensembles ΛAB , ΛAB′ , ΛA′B , and ΛA′B′”

Here's one reason for it having no relevance for me: The solution is to ensure that, in each of the four runs, the ensemble size is adequately large. Thereby ensuring that the average over each ensemble approaches the related Bellian idealisation adequately.
[/quote]
The sizes of the samples are irrelevant. The question is whether or not you are sampling from the same ensembles. With the detection loophole, and even worse with the coincidence loophole, you effectively sample from subpopulations of values of lambda determined by the settings on both sides simultaneously.

[Gordon Watson]

Richard says above:

I wouldn’t say it is *false*. I would say that it was often unjustifiably applied. We (Jan-Åke Larsson and I) showed that it needed adjustment or modification, and gave one way in which it could be adjusted, when detection events are selected by comparing times of events in the two sides of the experiments.

I don't necessarily agree that their modification makes any difference but that's for a separate discussion.

Michel, it made the difference, in your simulations, between violating the inequality and not violating the inequality. See my paper https://arxiv.org/abs/1507.00106 “ Event based simulation of an EPR-B experiment by local hidden variables: epr-simple and epr-clocked”.

Gordon:

“The problem here is that the ensemble on which the correlations are evaluated changes with the settings, while the original Bell inequality requires that they stay the same. In effect, the Bell inequality only holds on the common part of the four different ensembles ΛAB , ΛAB′ , ΛA′B , and ΛA′B′”

Here's one reason for it having no relevance for me: The solution is to ensure that, in each of the four runs, the ensemble size is adequately large. Thereby ensuring that the average over each ensemble approaches the related Bellian idealisation adequately.

The sizes of the samples are irrelevant. The question is whether or not you are sampling from the same ensembles. With the detection loophole, and even worse with the coincidence loophole, you effectively sample from subpopulations of values of lambda determined by the settings on both sides simultaneously.

1. In my terms: The sample sizes need to be adequate. By which I mean: each of the four runs leads to an adequate approximation of the related QM expectation.

2. "... subpopulations of values of lambda determined by the settings on both sides simultaneously." What does this mean?

3. I suspect that minkwe has in mind my claim (against Bell) that Bell's results do NOT commute.** That is, correcting Bell's first error— ie, his erroneous move from Bell 1964:(14a) to Bell 1964:(14b) — we have:

.

4. This Bellian error is confirmed and corrected in my refutation of BI — Bell 1964:(15) — via high-school math. So it would be helpful if you could show me, via my high-school math, what Bellian assumption I have overlooked.

5. I suspect it must be his naive-realism. But, in 1964, even I was old enough to reject such a silly belief! So surely my suspicion is false and you have better explanation?

** Edit: Remember, EPRB is a quantum experiment and quantum observables do NOT necessarily commute. ME HERE trusting that "non-commuting" is an OK wording for what Bell neglects. Some might prefer, with me, to say that the EPRB results are pairwise-bound?

Thanks; Gordon
.

[gill1109]

Richard says above:

I wouldn’t say it is *false*. I would say that it was often unjustifiably applied. We (Jan-Åke Larsson and I) showed that it needed adjustment or modification, and gave one way in which it could be adjusted, when detection events are selected by comparing times of events in the two sides of the experiments.

I don't necessarily agree that their modification makes any difference but that's for a separate discussion.

Michel, it made the difference, in your simulations, between violating the inequality and not violating the inequality. See my paper https://arxiv.org/abs/1507.00106 “ Event based simulation of an EPR-B experiment by local hidden variables: epr-simple and epr-clocked”.

Gordon:

“The problem here is that the ensemble on which the correlations are evaluated changes with the settings, while the original Bell inequality requires that they stay the same. In effect, the Bell inequality only holds on the common part of the four different ensembles ΛAB , ΛAB′ , ΛA′B , and ΛA′B′”

Here's one reason for it having no relevance for me: The solution is to ensure that, in each of the four runs, the ensemble size is adequately large. Thereby ensuring that the average over each ensemble approaches the related Bellian idealisation adequately.

The sizes of the samples are irrelevant. The question is whether or not you are sampling from the same ensembles. With the detection loophole, and even worse with the coincidence loophole, you effectively sample from subpopulations of values of lambda determined by the settings on both sides simultaneously.

1. In my terms: The sample sizes need to be adequate. By which I mean: each of the four runs leads to an adequate approximation of the related QM expectation.

2. "... subpopulations of values of lambda determined by the settings on both sides simultaneously." What does this mean?

3. I suspect that minkwe has in mind my claim (against Bell) that Bell's results do NOT commute.** That is, correcting Bell's first error— ie, his erroneous move from Bell 1964:(14a) to Bell 1964:(14b) — we have:

.

4. This Bellian error is confirmed and corrected in my refutation of BI — Bell 1964:(15) — via high-school math. So it would be helpful if you could show me, via my high-school math, what Bellian assumption I have overlooked.

5. I suspect it must be his naive-realism. But, in 1964, even I was old enough to reject such a silly belief! So surely my suspicion is false and you have better explanation?

** Edit: Remember, EPRB is a quantum experiment and quantum observables do NOT necessarily commute. ME HERE trusting that "non-commuting" is an OK wording for what Bell neglects. Some might prefer, with me, to say that the EPRB results are pairwise-bound?

Thanks; Gordon
.

Ah, the cat is out of the bag, Gordon. Your A(a, lambda) are not numbers +/-1. They do not commute. You are not looking for a classical description of what is going on *behind the scenes* in quantum measurement: the kind that Einstein spent his life searching for. You don’t believe there is one anyway.

You shouldn’t say that Bell was wrong or made a mistake. You are on Bohr’s side and you find Bell’s work irrelevant. You find “local realism” naïeve.

[minkwe]

2. "... subpopulations of values of lambda determined by the settings on both sides simultaneously." What does this mean?

3. I suspect that minkwe has in mind my claim (against Bell) that Bell's results do NOT commute.** That is, correcting Bell's first error— ie, his erroneous move from Bell 1964:(14a) to Bell 1964:(14b)

2. You should read Larsson & Gill it presents a very general result that the authors themselves did not recognize as very general. It is the second part of the paper concerning the "remedy" that I take issue with. The first part is solid.
3. Yes there is a hidden assumption in the move from 14a to 14b that may be true for naive realism but false for EPRB experiments and this is related to (2).

[gill1109]

2. "... subpopulations of values of lambda determined by the settings on both sides simultaneously." What does this mean?

3. I suspect that minkwe has in mind my claim (against Bell) that Bell's results do NOT commute.** That is, correcting Bell's first error— ie, his erroneous move from Bell 1964:(14a) to Bell 1964:(14b)

2. You should read Larsson & Gill it presents a very general result that the authors themselves did not recognize as very general. It is the second part of the paper concerning the "remedy" that I take issue with. The first part is solid.
3. Yes there is a hidden assumption in the move from 14a to 14b that may be true for naive realism but false for EPRB experiments and this is related to (2).

We present *a* remedy but it is not the only remedy. From 2015 the best experimenters - who know all about Larsson and Gill - avoid the coincidence loophole altogether by defining the experiment and the data analysis in terms of a predefined sequence of fixed small time windows. The experimental unit is not “pair of particles” but pair of time windows (Alice and Bob each have one), many times in succession. A random binary setting is inserted at the beginning of each time window. Detectors and electronics generate and register a binary outcome before the end of the time window.

See for instance my analysis of the Vienna data here: https://www2.slideshare.net/mobile/gill1109/yet-another-statistical-analysis-of-the-data-of-the-loophole-free-experiments-of-2015-revised

[minkwe]

We present *a* remedy but it is not the only remedy. From 2015 the best experimenters - who know all about Larsson and Gill - avoid the coincidence loophole altogether by defining the experiment and the data analysis in terms of a predefined sequence of fixed small time windows.

I agree with you that they believe they have solved the problem. That's enough for this thread.