The simplest illustration of Bell's error

[minkwe]

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.

Joy is 100% right. There is no such thing as a mathematical theorem with loopholes. Richard is wrong, the so-called "loopholes" in Bell's theorem are directly related to oversights in Bell's analysis. In other words, the "loopholes" disprove the theorem. Why else will Richard (and Larsson) try to create a new theorem if the original one was valid? Notwithstanding the fact that Fine first identified the time synchronization flaw in Bell's theorem.

It is not simply a problem with practical application.

[gill1109]

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

Yes. I will tell you that. It’s very convenient indeed to think of the function “tan” as a mapping from the real line to the union of the real line and a disjoint one-point set {“undefined”}.

The alternative is to define it as a function from the real line with an infinite series of points removed to the real line.

Wikipedia: “Modern definitions express trigonometric functions as infinite series or as solutions of differential equations. This allows extending the domain of sine and cosine functions to the whole complex plane, and the domain of the other trigonometric functions to the complex plane from which some isolated points are removed.”

The simple parts of the wikipedia page on trigonometric functions (the parts for school children) uses an old fashioned definition, making it “+infinity” on those points.

Joy is 100% right. There is no such thing as a mathematical theorem with loopholes. Richard is wrong, the so-called "loopholes" in Bell's theorem are directly related to oversights in Bell's analysis. In other words, the "loopholes" disprove the theorem. Why else will Richard (and Larsson) try to create a new theorem if the original one was valid? Notwithstanding the fact that Fine first identified the time synchronization flaw in Bell's theorem.

It is not simply a problem with practical application.

Joy is not 100% right. There can be a loophole in an attempt to apply a mathematical theorem to a practical matter.

Larsson and my theorem is a different theorem to the “Bell theorem seen as a math theorem”. The conditions are different, and the conclusion is different.

The theorem of Lasrsson and myself, for instance, applies to the computer simulation “epr-simple”.

Bell’s theorem doesn’t. See https://arxiv.org/abs/1507.00106

[Submitted on 1 Jul 2015 (v1), last revised 10 Apr 2021 (this version, v10)]
Event based simulation of an EPR-B experiment by local hidden variables: epr-simple and epr-clocked

Richard D. Gill
In this note, I analyze the data generated by M. Fodje's (2013, 2014) simulation programs "epr-simple" and "epr-clocked". They were written in Python and published on Github. Inspection of the program descriptions showed that they made use of the detection-loophole and the coincidence-loophole respectively. I evaluate them with appropriate modified Bell-CHSH type inequalities: the Larsson detection-loophole adjusted CHSH, and the Larsson-Gill coincidence-loophole adjusted CHSH (NB: its correctness is conjecture, we do not have proof). The experimental efficiencies turn out to be approximately eta = 81% (close to optimal) and gamma = 55% (far from optimal). The observed values of CHSH are, as they should be, within the appropriately adjusted bounds. Fodjes' detection-loophole model turns out to be very, very close to Pearle's famous 1970 model, so the efficiency is close to optimal. The model has the same defect as Pearle's: the joint detection rates exhibit signalling. His coincidence-loophole model is actually a clever modification of his detection-loophole model. Because of this, however, it cannot lead to optimal efficiency.
Comments: This is version 11 of this preprint. Earlier versions incorrectly stated that documentation of Michel Fodje's simulation was inexistent. This version also contains better explanation of my terminology. It is also posted on Researchers.one, article 2020-01-1. Another version on this http URL, preprints202001.0045, is being updated

[gill1109]

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.

Arthur approached me. Indeed, he is a traditional gentleman. I used to admire “local” for being much the same but he suddenly dramatically changed personality, as well as nickname. I suppose he prefers to be ungentlemanly anonymously. Clearly a case of a split personality.

[minkwe]

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

Yes. I will tell you that. It’s very convenient indeed to think of the function “tan” as a mapping from the real line to the union of the real line and a disjoint one-point set {“undefined”}.

Now I know it's just polemics to you. You are not serious at all.

[gill1109]

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

Yes. I will tell you that. It’s very convenient indeed to think of the function “tan” as a mapping from the real line to the union of the real line and a disjoint one-point set {“undefined”}.

Now I know it's just polemics to you. You are not serious at all.

I’m a very serious mathematician. We are talking about mathematics, and I mention its application to computer science (distributed computing). Did you read my paper on Gull’s theorem yet?

What do you think is the definition of the mathematical function “tan”? What is the definition of “function”?

[minkwe]

Sorry, Richard. That was the last straw, I'm done with you.

The domain of tan(x) is
The range of tan(x) is

[gill1109]

The domain of tan(x) is
The range of tan(x) is

That's indeed a common definition. Read the Wikipedia page on the trigonometric functions: it is not the only common definition.

It is also legitimate to define domain and range a bit differently. You are saying yourself that tan(x) is not defined for x = (n pi + pi/2), n an integer. I say the same thing in a different way. Wikipedia says it is equal to +infty for those values! That is also a common convention. You can find out yourself what Mathematica does, or Python, or R, or C. They too must all build in some convention. No doubt, IEEE has established some conventions. But different computer languages have different concept of "number". Some allow values "+infty", "-infty" or "not a number".

You are avoiding the issue which was about Bell's theorem as a mathematical theorem, and about Larsson and my theorems. Different mathematical theorems. Different mathematical assumptions. Different mathematical conclusions. One can sometimes apply them to computer simulation programs.

[minkwe]

You are avoiding the issue which was about Bell's theorem as a mathematical theorem, and about Larsson and my theorems. Different mathematical theorems. Different mathematical assumptions. Different mathematical conclusions. One can sometimes apply them to computer simulation programs.

I'm definitely not. The issue is that I provided two functions that beat your challenge and you start relying on word games to change the goalposts. It's very obvious what you are doing. I'm not surprised.

But this is all off-topic in anycase. I noticed you don't have anything to say on the actual topic of this thread.

[gill1109]

You are avoiding the issue which was about Bell's theorem as a mathematical theorem, and about Larsson and my theorems. Different mathematical theorems. Different mathematical assumptions. Different mathematical conclusions. One can sometimes apply them to computer simulation programs.

I'm definitely not. The issue is that I provided two functions that beat your challenge and you start relying on word games to change the goalposts. It's very obvious what you are doing. I'm not surprised.

Michel, you did not provide two functions which beat my challenge. You thought you did, but apparently you did not read the challenge carefully.

No problem!

So please do answer the following question. Suppose A and B are two functions programmed in some programming language such as R or Python, with range {-1, +1} and domain [0, 2 pi) x [0, 1]. We generate a long stream of pseudo-random numbers u_1, ..., u_N, supposed to behave like independent realisations of a random number uniformly distributed on [0, 1]. We compute the average of the N numbers A(a, u_n) * B(b, u_n). Is it possible that this will very well approximate -cos(a - b) for say all a, b, , for instance corresponding to half degree steps between 0 and 360 degrees. Take N equal to a million.
This is actually strongly related to the original question you asked in this thread, though perhaps you don't quite see how, at the moment.

[minkwe]

So please do answer the following question. Suppose A and B are two functions programmed in some programming language such as R or Python, with range {-1, +1} and domain [0, 2 pi) x [0, 1]. We generate a long stream of pseudo-random numbers u_1, ..., u_N, supposed to behave like independent realisations of a random number uniformly distributed on [0, 1]. We compute the average of the N numbers A(a, u_n) * B(b, u_n). Is it possible that this will very well approximate -cos(a - b) for say all a, b, , for instance corresponding to half degree steps between 0 and 360 degrees. Take N equal to a million.
This is actually strongly related to the original question you asked in this thread, though perhaps you don't quite see how, at the moment.

I answered your challenge already. It is off-topic and unrelated to this thread please start a new one since you want to kee changing the rules. Start a new thread and I will provide any additional answers I have there if I change my mind.

This thread is about the fact that Bell used the wrong QM prediction for the "franken-correlation" P(b,c). He used -b.c when he should have used 0.

[gill1109]

So please do answer the following question. Suppose A and B are two functions programmed in some programming language such as R or Python, with range {-1, +1} and domain [0, 2 pi) x [0, 1]. We generate a long stream of pseudo-random numbers u_1, ..., u_N, supposed to behave like independent realisations of a random number uniformly distributed on [0, 1]. We compute the average of the N numbers A(a, u_n) * B(b, u_n). Is it possible that this will very well approximate -cos(a - b) for say all a, b, , for instance corresponding to half degree steps between 0 and 360 degrees. Take N equal to a million.
This is actually strongly related to the original question you asked in this thread, though perhaps you don't quite see how, at the moment.

I answered your challenge already. It is off-topic and unrelated to this thread please start a new one since you want to kee changing the rules. Start a new thread and I will provide any additional answers I have there if I change my mind.

This thread is about the fact that Bell used the wrong QM prediction for the "franken-correlation" P(b,c). He used -b.c when he should have used 0.

Michel, I’ve started a new thread at http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=491&p=14467#p14467
Looking forward to your reaction. Please think about it carefully; take your time.

[FrediFizzx]

@gill1109 Irrelevant rubbish!
.

[gill1109]

By the way, here are links to the two Fine papers which were mentioned earlier, thanks to "local".

Some Local Models for Correlation Experiments. Synthese 50 (1982), pp 279-94
Arthur Fine
https://www.jstor.org/stable/20115716

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
https://www.jstor.org/stable/192609

I can send you pdf's by email if you can't get through the paywall or don't find them on SciHub.

[FrediFizzx]

@gill1109 More old irrelevant stuff!
.