## The simplest illustration of Bell's error

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

### Re: The simplest illustration of Bell's error

minkwe wrote:From day 1, I've always stated that I disagree with the comparison of Bell's mathematical results with QM or experiments. You know this. I have no problem with Bell's mathematics as a purely mathematical exercise.

Yes, I know this. It’s good to hear you confirm it.

Now, what do you think of the comparison of Bell’s mathematical results with computer experiments?

I have a particular kind of experiment in mind. Suppose I dream up some functions A and B, taking values in {-1, 1}, which are functions of (1) a direction represented by an angle in the interval [0, 2 pi] and (2) of a number “u” in the interval [0, 1]. I write programs, in Python, say, which compute A and B for any given values of the two arguments. I now run a computer simulation in which I simply pick two angles “a” and “b” and use Python’s built in pseudo random number generator to generate a long sequence of N draws “u_i” of random numbers between 0 and 1. My simulation then averages the N numbers A(a, u_i) * B(b, u_i). Take N equal to say 1 million.

I am not taking about QM or about experiments in laboratories with lasers and photodetectors. I’m talking about simple Python computer programs run on an ordinary PC.

Do you think it is likely that the result could be close to - cos(a - b), whatever a and b I chose? What would you expect to be the result?
gill1109
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### Re: The simplest illustration of Bell's error

gill1109 wrote:Now, what do you think of the comparison of Bell’s mathematical results with computer experiments?

Same concerns. Just because it is done in a computer doesn't change anything. The only problem is that it is possible to do things in a computer that do not correspond to what happens in the real world thus leading to more confusion when things like that are done. Two examples:

- resetting random number seeds. There is no analog in the real world. While useful in some cases to get reproducible results, it can result in many delusions when trying to compare with real-world experiments
- access to complete information. There is no such thing in the real world.

I have a particular kind of experiment in mind. Suppose I dream up some functions A and B, taking values in {-1, 1}, which are functions of (1) a direction represented by an angle in the interval [0, 2 pi] and (2) of a number “u” in the interval [0, 1]. I write programs, in Python, say, which compute A and B for any given values of the two arguments. I now run a computer simulation in which I simply pick two angles “a” and “b” and use Python’s built in pseudo random number generator to generate a long sequence of N draws “u_i” of random numbers between 0 and 1. My simulation then averages the N numbers A(a, u_i) * B(b, u_i). Take N equal to say 1 million.

I am not taking about QM or about experiments in laboratories with lasers and photodetectors. I’m talking about simple Python computer programs run on an ordinary PC.

Do you think it is likely that the result could be close to - cos(a - b), whatever a and b I chose? What would you expect to be the result?

Yes it is likely. I'm surprised you asked me this when I already have two computer programs that do just that. You see, you are missing an important detail in your "mind" experiment. The domain of A(.)B(.) is only defined for regions where the domains of both functions are defined. In pure mathematical terms, the functions in EPR-simple and EPR-clocked are just functions that are undefined for non-trivial regions of the 2-dimensional domain of (a,u). And when you multiply the two together, you get an even more restricted domain but you do get close to -cos(a,b). Have some imagination Richard.
minkwe

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### Re: The simplest illustration of Bell's error

minkwe wrote:
gill1109 wrote:Now, what do you think of the comparison of Bell’s mathematical results with computer experiments?

Same concerns. Just because it is done in a computer doesn't change anything. The only problem is that it is possible to do things in a computer that do not correspond to what happens in the real world thus leading to more confusion when things like that are done. Two examples:

- resetting random number seeds. There is no analog in the real world. While useful in some cases to get reproducible results, it can result in many delusions when trying to compare with real-world experiments
- access to complete information. There is no such thing in the real world.

I have a particular kind of experiment in mind. Suppose I dream up some functions A and B, taking values in {-1, 1}, which are functions of (1) a direction represented by an angle in the interval [0, 2 pi] and (2) of a number “u” in the interval [0, 1]. I write programs, in Python, say, which compute A and B for any given values of the two arguments. I now run a computer simulation in which I simply pick two angles “a” and “b” and use Python’s built in pseudo random number generator to generate a long sequence of N draws “u_i” of random numbers between 0 and 1. My simulation then averages the N numbers A(a, u_i) * B(b, u_i). Take N equal to say 1 million.

I am not taking about QM or about experiments in laboratories with lasers and photodetectors. I’m talking about simple Python computer programs run on an ordinary PC.

Do you think it is likely that the result could be close to - cos(a - b), whatever a and b I chose? What would you expect to be the result?

Yes it is likely. I'm surprised you asked me this when I already have two computer programs that do just that. You see, you are missing an important detail in your "mind" experiment. The domain of A(.)B(.) is only defined for regions where the domains of both functions are defined. In pure mathematical terms, the functions in EPR-simple and EPR-clocked are just functions that are undefined for non-trivial regions of the 2-dimensional domain of (a,u). And when you multiply the two together, you get an even more restricted domain but you do get close to -cos(a,b). Have some imagination Richard.

Sorry Michel, you are now saying that you can get the negative cosine when you do something different from what I described. I told you the domains of the functions A and B. You ignored what I said. You moreover added an ad hoc procedure to deal with the situation that (a, u_i) or (b, u_i) is not in the domain of A or B, respectively. Your first trick was described by Pearle (1970) https://journals.aps.org/prd/abstract/10.1103/PhysRevD.2.1418 and your second by Pascazio (1986) http://www.ba.infn.it/~pascazio/publications/pla86.pdf. So: both of them, long ago. But I am very impressed that you discovered them yourself. You certainly do have a creative imagination.
gill1109
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### Re: The simplest illustration of Bell's error

gill1109 wrote:Your first trick was described by Pearle (1970) https://journals.aps.org/prd/abstract/1 ... evD.2.1418 and your second by Pascazio (1986) http://www.ba.infn.it/~pascazio/publications/pla86.pdf.

Gill again engages in disingenuous scholarship. Gill harbors a grudge against Arthur Fine and that is why he fails to properly credit Fine for the coincidence "loophole", even though Fine's priority (1980) was communicated to him several times. And don't forget that Gill originally claimed priority for it but changed his tune when the Fine and Pascazio references were brought to his attention. Now he conveniently forgets about Fine. There are no suitable references in his joint paper with Larsson on the coincidence mechanism.

Some Local Models for Correlation Experiments. Synthese 50 (1982), pp 279-94
Arthur Fine
See section 4.

Correlations and Physical Locality. In P. Asquith & R. Giere (eds.) PSA 1980, Volume 2. E. Lansing, MI: Philosophy of Science Association, 1981, pp. 535-56.
Arthur Fine
Jump to the section on synchronization models.
local

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### Re: The simplest illustration of Bell's error

@local Well..., we have come to expect that kind of behavior by Bell fanatics. Thanks for pointing it out.
.
FrediFizzx
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### Re: The simplest illustration of Bell's error

gill1109 wrote:Sorry Michel, you are now saying that you can get the negative cosine when you do something different from what I described.

Absolutely not, I'm doing exactly what you described. Perhaps now that I've told you want to do, you plan to change the goal posts.

I told you the domains of the functions A and B.

You did not. You told me the range of values that a, b, and u can lie in. You did not specify the domain which is 2-dimensional.

You ignored what I said.

Absolutely not. I read what you said carefully. Now you want to change the goal post.

You moreover added an ad hoc procedure to deal with the situation that (a, u_i) or (b, u_i) is not in the domain of A or B, respectively.

Absolutely not, I did no such thing. My functions take $a,b \in [0,2\pi]$ and $u \in [0, 1]$ just like you specified in your "computer experiment". Produce outcomes $\{ \pm 1 \}$ just like you specified. Now you want to change the rules.

Your first trick was described by Pearle (1970) https://journals.aps.org/prd/abstract/10.1103/PhysRevD.2.1418 and your second by Pascazio (1986) http://www.ba.infn.it/~pascazio/publications/pla86.pdf. So: both of them, long ago. But I am very impressed that you discovered them yourself. You certainly do have a creative imagination.

This is irrelevant. BTW it's not a trick, it simply shows that Bell did not have enough imagination of what was possible. That is why he made some very silly mistakes. But that's okay, some very smart people have also made silly mistakes before.

I beat your challenge and now you want to change the rules. Let me remind you what you said:

Suppose I dream up some functions A and B, taking values in {-1, 1}, which are functions of (1) a direction represented by an angle in the interval [0, 2 pi] and (2) of a number “u” in the interval [0, 1].

That's exactly what my functions do.
minkwe

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### Re: The simplest illustration of Bell's error

He even denies the existence of the CHSH urn experiment, because this of course disproves everything he believes in.
Last edited by FrediFizzx on Sat Sep 04, 2021 1:10 pm, edited 1 time in total.
Reason: Personal comment deleted
Heinera

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### Re: The simplest illustration of Bell's error

local wrote:
gill1109 wrote:Your first trick was described by Pearle (1970) https://journals.aps.org/prd/abstract/1 ... evD.2.1418 and your second by Pascazio (1986) http://www.ba.infn.it/~pascazio/publications/pla86.pdf.

Gill again engages in disingenuous scholarship. Gill harbors a grudge against Arthur Fine and that is why he fails to properly credit Fine for the coincidence "loophole", even though Fine's priority (1980) was communicated to him several times. And don't forget that Gill originally claimed priority for it but changed his tune when the Fine and Pascazio references were brought to his attention. Now he conveniently forgets about Fine. There are no suitable references in his joint paper with Larsson on the coincidence mechanism.

Some Local Models for Correlation Experiments. Synthese 50 (1982), pp 279-94
Arthur Fine
See section 4.

Correlations and Physical Locality. In P. Asquith & R. Giere (eds.) PSA 1980, Volume 2. E. Lansing, MI: Philosophy of Science Association, 1981, pp. 535-56.
Arthur Fine
Jump to the section on synchronization models.

Excellent papers on the subject. I hadn't read any of these before. Thanks for mentioning them. Fine's paper lays out the reasons why I believe any experiment in which synchronization of pairs is done, whether through coincidence matching, real-time matching(aka "heralding") etc cannot claim to have "closed the coincidence loophole". A great many experimenters have been deceived by Larsson and Gill (perhaps unknowingly) into believing pre-agreed timeslots eliminates the "loophole". Not so at all. Any type of Matching introduces a Probability of matching a pair that depends on both sides. Fine's $C_{ij}(\lambda)$

In any case, I don't like to use the term "loophole" because each one simply reveals a flaw in Bell's theorem. Bell's theorem becomes. No local hidden variable theory can reproduce the results of quantum mechanics, except for ... and ... and ... and ... and ...
minkwe

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### Re: The simplest illustration of Bell's error

minkwe wrote:
gill1109 wrote:Sorry Michel, you are now saying that you can get the negative cosine when you do something different from what I described.

Absolutely not, I'm doing exactly what you described. Perhaps now that I've told you want to do, you plan to change the goal posts.

I told you the domains of the functions A and B.

You did not. You told me the range of values that a, b, and u can lie in. You did not specify the domain which is 2-dimensional.

You ignored what I said.

Absolutely not. I read what you said carefully. Now you want to change the goal post.

You moreover added an ad hoc procedure to deal with the situation that (a, u_i) or (b, u_i) is not in the domain of A or B, respectively.

Absolutely not, I did no such thing. My functions take $a,b \in [0,2\pi]$ and $u \in [0, 1]$ just like you specified in your "computer experiment". Produce outcomes $\{ \pm 1 \}$ just like you specified. Now you want to change the rules.

Your first trick was described by Pearle (1970) https://journals.aps.org/prd/abstract/10.1103/PhysRevD.2.1418 and your second by Pascazio (1986) http://www.ba.infn.it/~pascazio/publications/pla86.pdf. So: both of them, long ago. But I am very impressed that you discovered them yourself. You certainly do have a creative imagination.

This is irrelevant. BTW it's not a trick, it simply shows that Bell did not have enough imagination of what was possible. That is why he made some very silly mistakes. But that's okay, some very smart people have also made silly mistakes before.

I beat your challenge and now you want to change the rules. Let me remind you what you said:

Suppose I dream up some functions A and B, taking values in {-1, 1}, which are functions of (1) a direction represented by an angle in the interval [0, 2 pi] and (2) of a number “u” in the interval [0, 1].

That's exactly what my functions do.

I said:
I dream up some functions A and B, taking values in {-1, 1}, which are functions of (1) a direction represented by an angle in the interval [0, 2 pi] and (2) of a number “u” in the interval [0, 1]. I write programs, in Python, say, which compute A and B for any given values of the two arguments.

Michel, you ignored a crucial sentence. *You* are talking about functions which take values in {-1, +1, “undefined”}.

By the way, there is some difference in use of the words “domain” and “range” in different mathematical traditions. England in the 70’s of the last century was different from mainland Europe at that time. Fashions change. Maybe that explains Michel’s misunderstanding?

From my maths it is evident that I do not allow ‘undefined’ as a possible value of the functions A and B. If you work through my derivation you can see exactly what I assume, if you had any doubts.

By the way, Michel’s model generates data such that the chance of accepting a data point depends on the difference between “a” and “b”. You will notice this when you plot the number of counted outcome pairs as a function of “a - b”. Please try it! Any physicist looking at your data will see that it is nonlocal in an unacceptable way.

Sorry I forgot about Fine’s work. I remember him more for his proof that the 8 one-sided Bell-CHSH inequalities are necessary and sufficient for LHV to describe the data, as long as you have no-signalling (on each side, individual outcome probabilities, given individual setting, do not depend on setting on other side). Maybe “local” is now arguing that Fine stole from Boole, 1850’s? Boole did the necessary and sufficient version of Bell’s original 3 correlation inequality.

I was inspired to think see coincidence counting as a loophole by Hess and Philip’s claims that Bell had not taken account of time. He had done, explicitly. Hess first said that I had plagiarised them, which is not true, so we wrote where we had got the idea from. Later Hess changed his tune: Pascazio had found it. I don’t recall Hess mentioning Fine, nor apologising that he had (though unknowingly) plagiarised Pascazio. It is true that Hess and Philip’s mathematical model which depended on probability densities of rho which did not integrate to 1 could actually be rewritten, on normalisation, as a detection loophole model. Hans de Raedt from Groningen (Netherlands) and his wife teamed up with Hess and did detection-loophole simulations based on it.
gill1109
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### Re: The simplest illustration of Bell's error

minkwe wrote:
In any case, I don't like to use the term "loophole" because each one simply reveals a flaw in Bell's theorem. Bell's theorem becomes. No local hidden variable theory can reproduce the results of quantum mechanics, except for ... and ... and ... and ... and ...

In one of my recent papers I have written something similar (which Gill keeps misquoting so put the record straight here): https://ieeexplore.ieee.org/document/9418997.

Joy Christian wrote:
Much is made in the critique [1] of the so-called "theorem" of Bell that claims that the models such as the one presented in [2 -- 6] are impossible. But mathematically a theorem with loopholes [13] is an oxymoron, while physically we know that the bounds on Bell inequalities are not respected by Nature. The consequent conclusion that therefore Nature must be non-local, non-realistic, or conspiratorial is not justified. For Bell's theorem depends on a number of assumptions [4], in addition to those of locality and realism. And, in fact, Bell inequalities can be derived without assuming either locality or realism, as shown, for example, in Section 4.2 of [4].

.
Joy Christian
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### Re: The simplest illustration of Bell's error

Joy Christian wrote:
minkwe wrote:
In any case, I don't like to use the term "loophole" because each one simply reveals a flaw in Bell's theorem. Bell's theorem becomes. No local hidden variable theory can reproduce the results of quantum mechanics, except for ... and ... and ... and ... and ...

In one of my recent papers I have written something similar (which Gill keeps misquoting so put the record straight here): https://ieeexplore.ieee.org/document/9418997.

Joy Christian wrote:
Much is made in the critique [1] of the so-called "theorem" of Bell that claims that the models such as the one presented in [2 -- 6] are impossible. But mathematically a theorem with loopholes [13] is an oxymoron, while physically we know that the bounds on Bell inequalities are not respected by Nature. The consequent conclusion that therefore Nature must be non-local, non-realistic, or conspiratorial is not justified. For Bell's theorem depends on a number of assumptions [4], in addition to those of locality and realism. And, in fact, Bell inequalities can be derived without assuming either locality or realism, as shown, for example, in Section 4.2 of [4].

.

The word “loophole” in this context does not refer to a loophole in a theorem, but to a loophole in an attempt to apply a logical argument to a practical situation.
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### Re: The simplest illustration of Bell's error

gill1109 wrote:Maybe “local” is now arguing that Fine stole from Boole, 1850’s? Boole did the necessary and sufficient version of Bell’s original 3 correlation inequality.
Bullcrap. First, stop trying to speak for me! Second, this is a total non-sequitur; Bell's inequality and/or Boole's work has nothing to do with the coincidence "loophole". Your desperation to excuse your poor scholarship is disgusting and typical. Leave me out of your nonsense!

And isn't it interesting that an amateur such as myself could find the cited references with ease when you as a professional academic could find no relevant citations for your paper with Larsson? Disgusting duplicity.
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### Re: The simplest illustration of Bell's error

local wrote:
gill1109 wrote:Maybe “local” is now arguing that Fine stole from Boole, 1850’s? Boole did the necessary and sufficient version of Bell’s original 3 correlation inequality.
Bullcrap. First, stop trying to speak for me! Second, this is a total non-sequitur; Bell's inequality and/or Boole's work has nothing to do with the coincidence "loophole". Your desperation to excuse your poor scholarship is disgusting and typical. Leave me out of your nonsense!

And isn't it interesting that an amateur such as myself could find the cited references with ease when you as a professional academic could find no relevant citations for your paper with Larsson? Disgusting duplicity.

I agree, Bell and Boole’s work has nothing to do with the so-called coincidence loophole. Larsson and I were not the only ones who overlooked Fine’s paper. Thanks for the reference to that particular contribution by him. I have been corresponding with him recently. For the rest, see http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=481&p=14402#p14402
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### Re: The simplest illustration of Bell's error

gill1109 wrote:Larsson and I were not the only ones who overlooked Fine’s paper.
Here's what you sound like: "I'm not the only poor scholar. They did it too. Wah!"

I have been corresponding with him recently.
Hopefully to apologize.
local

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### Re: The simplest illustration of Bell's error

local wrote:
gill1109 wrote:Larsson and I were not the only ones who overlooked Fine’s paper.
Here's what you sound like: "I'm not the only poor scholar. They did it too. Wah!"

I have been corresponding with him recently.
Hopefully to apologize.

Actually, he congratulated me on my recent work. And he pointed out the paper by him which I had missed.
gill1109
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### Re: The simplest illustration of Bell's error

gill1109 wrote:And he pointed out the paper by him which I had missed.
When will the errata for your paper with Larsson be forthcoming?
local

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### Re: The simplest illustration of Bell's error

gill1109 wrote:
local wrote:
gill1109 wrote:Larsson and I were not the only ones who overlooked Fine’s paper.
Here's what you sound like: "I'm not the only poor scholar. They did it too. Wah!"

I have been corresponding with him recently.
Hopefully to apologize.

Actually, he congratulated me on my recent work. And he pointed out the paper by him which I had missed.

Anyone congratulating Gill on his "work" is laughable. It reflects badly on the person "congratulating." He or she is only saved by the fact that I never believe a word Gill ever says.
.
Joy Christian
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### Re: The simplest illustration of Bell's error

Joy, Arthur Fine is a traditional gentleman and would respond politely to any correspondent. I wouldn't take that against him. I do agree with your assessment of Gill as there is ample evidence.
local

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### Re: The simplest illustration of Bell's error

Joy Christian wrote:
gill1109 wrote:
local wrote:
gill1109 wrote:Larsson and I were not the only ones who overlooked Fine’s paper.
Here's what you sound like: "I'm not the only poor scholar. They did it too. Wah!"

I have been corresponding with him recently.
Hopefully to apologize.

Actually, he congratulated me on my recent work. And he pointed out the paper by him which I had missed.

Anyone congratulating Gill on his "work" is laughable. It reflects badly on the person "congratulating." He or she is only saved by the fact that I never believe a word Gill ever says.
.

That’s your biggest mistake, Joy!
gill1109
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### Re: The simplest illustration of Bell's error

gill1109 wrote:Michel, you ignored a crucial sentence. *You* are talking about functions which take values in {-1, +1, “undefined”}.

Wow Richard, you are a mathematician don't make such stupid statements. Next you will tell me the range of tan(x) is $\{ \mathbb{R}, undefined \}$
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