Bell's inequality refuted via elementary algebra

[gill1109]

BTW. Bell was wrong, in one respect. He wrote “Moreover, the signal involved must propagate instantaneously, so that such a theory could not be Lorentz invariant,” Bell (1964:199)”. But we now know this is not true. Please read my swan song for references.

[Joy Christian]

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.

The evidence is already here:

https://arxiv.org/abs/1704.02876

https://arxiv.org/abs/1211.0784

https://arxiv.org/abs/1405.2355

https://arxiv.org/abs/1806.02392

And some funerals have already happened: John S. Bell is no more; my former Ph.D. mentor Abner Shimony is no more; Asher Peres is no more. Other followers of Bell too are getting old.

The younger generation is increasingly familiar with my ideas and quietly following them. While their voices are frequently drowned out by the noises of today, their minds are not closed to the criticisms of Bell. In the long run, neither Nature nor Physics remains a monopoly of the dominant generation. Perhaps after I am gone, but my time is sure to come; for I am the future!

***

[gill1109]

I plan to live a long, long time Joy! I think we can probably go on fighting one another for another 30 years (my cardiologist is very happy with his work). Ever seen Bertolucci's Novecento?

[Gordon Watson]

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.

You write: "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."

In reply:

1. Bell (1964:195) sets out a clear intention: to provide a "more complete specification" of the EPRB experiment.

2. Elementary algebra shows that his move from his first equation on p.198 to the second restricts his analysis to experiments less correlated than EPRB.

3. Thus, insurprisingly: In 1990 he expressed his dilemma -- admitting to possible silliness -- by insisting that "you cannot get away with locality."

4. Alas, in 1990 he was still advocating his "Bell locality" formula:

[sic]!

5. My formulation addresses Bell's intention -- as in # 1 above -- while you are left trying to get around "Bell locality".

6. Yet we agree: In your words, "It's obviously, physically, a much too strong assumption."

7. Which, unfortunately leaves you avoiding some elementary algebra that proves a certain Bellian silliness.

8. Now it is heartening to see you apologising to Joy: which I appreciate. Yet you maintain the claim that Joy is astray.

9. Interesting then that you don't fix my half-page of elementary algebra:

but, instead, attempt to edit Bell's clear (and, for Bell, a problematic dilemma-producing) intention!?

10. Since I take math to be the best logic, I suggest you best stick to the math with me.

Thanks.

PS: Correspondence with Bertlmann -- Bell's good friend -- suggests that Bell might have liked my formulation.
.

[gill1109]

Gordon, I have earlier tried hard to convince you of the naivety and the hopeless lack of transparency of your arguments. I respect your opinion but I don't see any point in trying to convince you that you are wrong. You are at least as obstinate as me, if not more so.

Come by some time and drink some beer with me, at a blackboard. Or single malt. Or: why don't you rise to *my* challenge and write some computer programs which definitely prove you are right and moreover which will win you the Nobel prize? Classical computers are classical physical objects so that would be worth the Nobel prize. My 10 000 Euro says you can't.

Similarly, I like and respect Joy, but there is no point in my trying to convince him that he's wrong. Here I have to yield to his superior obstinacy. I should have given up my hopeless quest, for the greater benefit of the human race, to get him to see reason, long, long ago.

Over the years, Bell's arguments became more refined, less ambiguous, and more powerful. His language also became both more precise and more subtle at the same time ... as the complexity of the matter actually does demand. It demands very careful mathematical thinking and very careful distinction between on the one hand, physical reality, and on the other hand, mathematical reality - mathematical models which are supposed to mirror certain aspects of reality. Physicists and engineers are not well qualified for this task.

[Gordon Watson]

Gordon, I have earlier tried hard to convince you of the naivety and the hopeless lack of transparency of your arguments. I respect your opinion but I don't see any point in trying to convince you that you are wrong. You are at least as obstinate as me, if not more so.

Come by some time and drink some beer with me, at a blackboard. Or single malt. Or: why don't you rise to *my* challenge and write some computer programs which definitely prove you are right and moreover which will win you the Nobel prize? Classical computers are classical physical objects so that would be worth the Nobel prize. My 10 000 Euro says you can't.

Similarly, I like and respect Joy, but there is no point in my trying to convince him that he's wrong. Here I have to yield to his superior obstinacy. I should have given up my hopeless quest, for the greater benefit of the human race, to get him to see reason, long, long ago.

Over the years, Bell's arguments became more refined, less ambiguous, and more powerful. His language also became both more precise and more subtle at the same time ... as the complexity of the matter actually does demand. It demands very careful mathematical thinking and very careful distinction between on the one hand, physical reality, and on the other hand, mathematical reality - mathematical models which are supposed to mirror certain aspects of reality. Physicists and engineers are not well qualified for this task.

Please, despite your words, Bell died on the horns of a dilemma.

Please: just refute my elementary algebra!

[Heinera]

This was an excellent reply, Richard.

[gill1109]

Thanks, Heinera! Interested in a trip to Sweden in two weeks?

Please: just refute my elementary algebra!

Gordon, NO, because I will not be able to convince you that you are wrong. My paper on Anna Karenina and the Two Envelopes Problem explains why. The psychology *and the logic* (or - meta-logic) is obvious. Dunning and Kruger gives us the psychology. But there is more to it. Namely, the inadequacy of language. Wittgenstein, the Buddha...they've all explained it at great depth and with better words than I can easily command. Then we also have "extraordinary claims require extraordinary evidence". Your claim is now an extraordinary claim.

You've published it and the whole world can take a look. If your claim is well supported, a few people here and there will notice it and pick it up and they will become world famous, even if you don't.

I've offered you 10 000 Euro, easily earned if you are right. And I have access to really good single malt as well. And as a bonus I also offer to publicly eat my hat if *you* prove me wrong.

Anyone else can pick up the ideas in your paper and is welcome to pick up the challenge and the 10 000 Euro too.

I've looked at your elementary algebra and it makes me laugh. I've told you what's wrong with it but you prefer not to try to understand me. I can understand why, no problem. I would rather we stay friends. And I would like to enjoy today's afternoon sunshine in my garden in other ways. Life is short.

And I want to organise an interesting workshop and symposium. One thing we certainly *should* talk about there is the sense and/or non-sense of quantum Randi challenges and the like. How can such a challenge be made acceptable to both sides of the argument? It's a serious scientific question! I hope that Joy, Jay and Fred will give us their thoughts on that issue. I recall that Joy also came up with a counter-challenge. Unfortunately, it was so formulated that he and he only was the adjudicator. We need a challenge which independent third parties can adjudicate.

I guess his squidgy balls experiment is what really is needed... Gordon: my challenge to you is to use your mathematical analysis to design a real life applied physics lab experiment which proves the world you are right. Throw down your pen. Put on your overalls and get into the lab.

[gill1109]

The mistake in your algebra is that you think that your (9) is not justified. Which you say is Bell’s famous 1964:(15). You think that Bell here needs what you call "SIR" (single instant realisation?) and I've explained that he doesn't need SIR "in reality (i.e. as a physical assumption)". His more realistic assumptions in his much later works allow him to assume without loss of generality that SIR *can* hold in *a mathematical model which reproduces the same predictions*.

I have said this so many times before! I recommend some good books where this way of thinking is expanded and justified and put to powerful use in law, morality, history, science... Or try and find someone else who can explain it to you, if you are actually interested in learning that the world is more complex than you thought.

[Joy Christian]

Similarly, I like and respect Joy, but there is no point in my trying to convince him that he's wrong. Here I have to yield to his superior obstinacy. I should have given up my hopeless quest, for the greater benefit of the human race, to get him to see reason, long, long ago.

I don't really care what the Tweedledum or Tweedledee thinks of me or my work on the quantum correlations.

***

[gill1109]

Similarly, I like and respect Joy, but there is no point in my trying to convince him that he's wrong. Here I have to yield to his superior obstinacy. I should have given up my hopeless quest, for the greater benefit of the human race, to get him to see reason, long, long ago.

I don't really care what the Tweedledum or Tweedledee thinks of me or my work on the quantum correlations.

***

That’s right. Our work won’t be of much use to us in our graves. I also doubt that the Good Lord will be particularly interested in it. Carpe Diem. Let’s see if we can do something about Climate Armageddon, and about Inequality. And generally try to increase happiness and decrease suffering right now. Maybe add some footnotes to physics and help others better evaluate all that quantum hype and obscurantism.

[FrediFizzx]

Yep, we are just at the beginning of finally getting physics straightened out.

[Mikko]

1. Bell (1964:195) sets out a clear intention: to provide a "more complete specification" of the EPRB experiment.

What makes you think so? In Bell's 1964 article there is no statement of intention nor any other support for this claim.

[Gordon Watson]

1. Bell (1964:195) sets out a clear intention: to provide a "more complete specification" of the EPRB experiment.

What makes you think so? In Bell's 1964 article there is no statement of intention nor any other support for this claim.

Here's what makes me know so:

1. Bell (1964:195) sets out a clear intention: "Let this more complete specification be effected by means of parameters λ."

Then due to his early error, the whole of his essay -- indeed, via the self-confessed dilemma [which you seem to overlook?], the rest of his life -- is consumed by his inability to deliver.

[Mikko]

1. Bell (1964:195) sets out a clear intention: to provide a "more complete specification" of the EPRB experiment.

What makes you think so? In Bell's 1964 article there is no statement of intention nor any other support for this claim.

Here's what makes me know so:

1. Bell (1964:195) sets out a clear intention: "Let this more complete specification be effected by means of parameters λ."

That does not declare or imply any intent. It is merely the introduction of the symbol λ (for the "more complete specification" of the EPR argument).

[gill1109]

1. Bell (1964:195) sets out a clear intention: to provide a "more complete specification" of the EPRB experiment.

What makes you think so? In Bell's 1964 article there is no statement of intention nor any other support for this claim.

Here's what makes me know so:

1. Bell (1964:195) sets out a clear intention: "Let this more complete specification be effected by means of parameters λ."

Then due to his early error, the whole of his essay -- indeed, via the self-confessed dilemma [which you seem to overlook?], the rest of his life -- is consumed by his inability to deliver.

Mikko tells it exactly as it is. Brevity is the soul of wit.

Gordon, permit me to just repeat *my* analysis of where I believe you are wrong, which you are ignoring too. It's a bit longer but still fairly short. I can do longer versions too, if you would like me to.

The mistake in your algebra is that you think that your (9) is not justified. Which you say is Bell’s famous 1964:(15). You think that Bell here needs what you call "SIR" (single instant realisation?) and I've explained that he doesn't need SIR "in reality (i.e. as a physical assumption)". His more realistic assumptions in his much later works allow him to assume without loss of generality that SIR *can* hold in *a mathematical model which reproduces the same predictions*.

I've explained what we could do to resolve a breakdown in communication. Permit me, please, to repeat some options:

1) We could stand together at a blackboard with a beer and go through some basic ideas from probability theory and from causality theory. I want to teach you about the mathematical (probability theory) concept called "coupling" and I need to show you how one can and does frequently draw conclusions about "counterfactual experiments" (what would have happened if ...) from experimental data from the experiments which can be done. Of course, one needs to make assumptions about reality, in order to do this. Bell gives his arguments, just a refinement of EPR's, and over the years they have been improved and sharpened, first by Bell and later by other people in quantum information. Interestingly, there has been a parallel development by computer scientists and people working in AI, machine learning, and data science, as well as by epidemiologists and biostatisticians and medical statisticians, as well as by econometrists and economists, leading to standard works like that of Pearle and like that of Peters et al. An army of imitators and popularisers is hard at work, too. This is going to be the foundation of AI for many decennia to come.

2) You could rise to one of my computer challenges or to Sasha Vongehr's quantum Randi challenge, put on your overalls, and write some computer programs which will *prove* beyond a shadow of doubt that you are right. You can even try to interest some young ambitious computer minded person to do the programming for you.

3) You could try hard to understand the, on the whole fairly elementary, math in some of my papers, and you can try to tell me where I am making a mistake. You couldn't make any sense of Bell. Take a look at that of another "Bell supporter" then. I think Tim Maudlin's book is a masterpiece, which has influenced now several generations of philosophers and historians of science.

[jreed]

Gordon,

I looked through your paper, and in equation (8), which is from a quantum mechanical calculation, you come up with some expectations for E(a,b)..., then plug these into Bell's formula, and guess what - Bell's inequality is violated. Isn't that the result you would expect?

[Gordon Watson]

Gordon,

I looked through your paper, and in equation (8), which is from a quantum mechanical calculation, you come up with some expectations for E(a,b)..., then plug these into Bell's formula, and guess what - Bell's inequality is violated. Isn't that the result you would expect?

Thanks for the question. Please note:

1. Eqn (8) agrees with QM but it is not from QM, nor from a QM calculation: it is from WM (Wholistic Mechanics).

2. WM, my extended classical theory, derives Malus' Law extended [MLX] from first principles.

3. That is -- if we combine EPRB and Aspect's 2004 experiment under a unified experiment with spin = 1/2 or 1 respectively -- we have:

MLX: etc. [X]

4. Which, in turn leads to the eqn (8).

5. [X] is already included in an extended Appendix of the next version [in preparation] of this paper.

6. Since WM and QM are compatible, WM also simplifies calculation of the related expectations under QM (and GA).

Thanks again. Hoping the above helps; Gordon
.

[Gordon Watson]

1. Bell (1964:195) sets out a clear intention: to provide a "more complete specification" of the EPRB experiment.

What makes you think so? In Bell's 1964 article there is no statement of intention nor any other support for this claim.

Here's what makes me know so:

1. Bell (1964:195) sets out a clear intention: "Let this more complete specification be effected by means of parameters λ."

Then due to his early error, the whole of his essay -- indeed, via the self-confessed dilemma [which you seem to overlook?], the rest of his life -- is consumed by his inability to deliver.

Mikko tells it exactly as it is. Brevity is the soul of wit.

Gordon, permit me to just repeat *my* analysis of where I believe you are wrong, which you are ignoring too. It's a bit longer but still fairly short. I can do longer versions too, if you would like me to.

The mistake in your algebra is that you think that your (9) is not justified. Which you say is Bell’s famous 1964:(15). You think that Bell here needs what you call "SIR" (single instant realisation?) and I've explained that he doesn't need SIR "in reality (i.e. as a physical assumption)". His more realistic assumptions in his much later works allow him to assume without loss of generality that SIR *can* hold in *a mathematical model which reproduces the same predictions*.

I've explained what we could do to resolve a breakdown in communication. Permit me, please, to repeat some options:

1) We could stand together at a blackboard with a beer and go through some basic ideas from probability theory and from causality theory. I want to teach you about the mathematical (probability theory) concept called "coupling" and I need to show you how one can and does frequently draw conclusions about "counterfactual experiments" (what would have happened if ...) from experimental data from the experiments which can be done. Of course, one needs to make assumptions about reality, in order to do this. Bell gives his arguments, just a refinement of EPR's, and over the years they have been improved and sharpened, first by Bell and later by other people in quantum information. Interestingly, there has been a parallel development by computer scientists and people working in AI, machine learning, and data science, as well as by epidemiologists and biostatisticians and medical statisticians, as well as by econometrists and economists, leading to standard works like that of Pearle and like that of Peters et al. An army of imitators and popularisers is hard at work, too. This is going to be the foundation of AI for many decennia to come.

2) You could rise to one of my computer challenges or to Sasha Vongehr's quantum Randi challenge, put on your overalls, and write some computer programs which will *prove* beyond a shadow of doubt that you are right. You can even try to interest some young ambitious computer minded person to do the programming for you.

3) You could try hard to understand the, on the whole fairly elementary, math in some of my papers, and you can try to tell me where I am making a mistake. You couldn't make any sense of Bell. Take a look at that of another "Bell supporter" then. I think Tim Maudlin's book is a masterpiece, which has influenced now several generations of philosophers and historians of science.

1. I'm happy to include you in Maudlin's and Norsen's class.

2.

The mistake in your algebra is that you think that your (9) is not justified. Which you say is Bell’s famous 1964:(15). You think that Bell here needs what you call "SIR" (single instant realisation?) and I've explained that he doesn't need SIR "in reality (i.e. as a physical assumption)". His more realistic assumptions in his much later works allow him to assume without loss of generality that SIR *can* hold in *a mathematical model which reproduces the same predictions*.

BUT what you call "Bell's more realistic assumptions" led him to his formulation of "Bell locality." Which you reject!?

3. Indeed, why did he bother with *a mathematical model which reproduces the same [DEFECTIVE, non-EPRB] predictions* when his AIM was to model EPRB!?

4. So, please, when you reply to my earlier question on that matter -- and perhaps more in keeping with you recent psycho-analytic writings [no offence meant]:

WHY did Bell or his associates (even you) not resolve -- so easily [and presumably without any loss of integrity] -- his self-confessed DILEMMA in the way that you propose!?
.

[gill1109]

1. I'm happy to include you in Maudlin's and Norsen's class.

2.

The mistake in your algebra is that you think that your (9) is not justified. Which you say is Bell’s famous 1964:(15). You think that Bell here needs what you call "SIR" (single instant realisation?) and I've explained that he doesn't need SIR "in reality (i.e. as a physical assumption)". His more realistic assumptions in his much later works allow him to assume without loss of generality that SIR *can* hold in *a mathematical model which reproduces the same predictions*.

BUT what you call "Bell's more realistic assumptions" led him to his formulation of "Bell locality." Which you reject!?

3. Indeed, why did he bother with *a mathematical model which reproduces the same [DEFECTIVE, non-EPRB] predictions* when his AIM was to model EPRB!?

4. So, please, when you reply to my earlier question on that matter -- and perhaps more in keeping with you recent psycho-analytic writings [no offence meant]:

WHY did Bell or his associates (even you) not resolve -- so easily [and presumably without any loss of integrity] -- his self-confessed DILEMMA in the way that you propose!?
.

Dear Gordon
Here are my replies

1. OK
2. Yes I reject "Bell locality". Nowadays I plump for what is often called "quantum non-locality". I prefer to call it "martingale-like or disciplined passion at a distance"
3. Bell's aim was to explore the boundaries of physics by adding new twists to the EPR-B saga. You could say he turned it completely on its head, in ways which EPR would not have liked at all
4. Bell wrote out four alternative logical consequences of his analysis in the famous Bertlmann's socks paper. Four possible positions to take. He did not say they were exclusive or exhaustive. Later in private correspondence with E. Santos, quoted by Santos himself, he admitted that there was another, fifth possible position. I didn't know Santos' paper at the time and invented the "fifth position" myself, writing a paper entitled "Time, Finite Statistics, and Bell's Fifth Position" https://arxiv.org/abs/quant-ph/0301059

Abstract: In this contribution to the 2002 Vaxjo conference on the foundations of quantum mechanics and probability, I discuss three issues connected to Bell’s theorem and Bell-CHSH-type experiments: time and the memory loophole, finite statistics (how wide are the error bars, under local realism?), and the question of whether a loophole-free experiment is feasible, a surprising omission on Bell’s list of four positions to hold in the light his results. Lévy’s (1935) theory of martingales, and Fisher’s (1935) theory of randomization in experimental design, take care of time and of finite statistics. I exploit a (classical) computer network metaphor for local realism to argue that Bell’s conclusions are independent of how one likes to interpret probability. I give a critique of some recent anti-Bellist literature.

Emilio Santos wrote https://arxiv.org/abs/quant-ph/0410193
"Bell's theorem and the experiments: Increasing empirical support to local realism"
Emilio Santos
(Submitted on 25 Oct 2004)
It is argued that local realism is a fundamental principle, which might be rejected only if experiments clearly show that it is untenable. A critical review is presented of the derivations of Bell's inequalities and the performed experiments, with the conclusion that no valid, loophole-free, test exists of local realism vs. quantum mechanics. It is pointed out that, without any essential modification, quantum mechanics might be compatible with local realism. This suggests that the principle may be respected by nature.
Comments: 28 pages
Subjects: Quantum Physics (quant-ph)
Cite as: arXiv:quant-ph/0410193
(or arXiv:quant-ph/0410193v1 for this version)
Submission history
From: Emilio Santos Corchero [view email]
[v1] Mon, 25 Oct 2004 15:12:26 UTC (23 KB)