The triangle wave versus the cosine: How classical systems can optimally approximate EPR-B correlations

[Richard Gill]

Dear friends

A paper I first wrote in 2013 finally got published as Entropy 2020, 22(3), 287. It's about simulating quantum correlations (specifically, the EPR-B correlations) using classical physics (local realism, local hidden variables, ...). For this final, published, version I wrote some passages especially for Tim Palmer, and others especially for Tony Crofts. The paper also points out open mathematical problems. It's about the spinning bi-coloured disk model. Imagine a big wheel whose rim is coloured black and white, in such a way that white and black are always exactly opposite one another.  A fairground Wheel of Fortune or Rota Fortunae https://en.wikipedia.org/wiki/Rota_Fortunae. So the total amounts of black and white are equal. Alice and Bob now each choose a measurement *setting*: they are little pointers just outside the wheel. Each can freely select any position they like. The wheel is spun really hard, and after a while it slowly comes to rest. Alice's pointer and Bob's pointer now each point to a colour, and that colour determines their *outcome*. If Alice's colour is black she says "spin up", if it is white she says "spin down". Bob does exactly the *reverse*. If Bob's colour is black he says "spin down", if it is white he says "spin up".

If Alice and Bob choose the same setting, they get the same colour, and their outcomes will obviously be equal and opposite. Perfect anti-correlation. If they choose opposite settings, their colours will be different, and their outcomes with be the same. Perfect correlation. If they choose settings at right angles to one another, their outcomes will be independent. Each outcome on its own is a fair coin-toss.

The simplest colouring - two semi-circles - generates the zig-zag curve called the triangle-wave. 

It turns out that there exist bi-coloured disks which generate correlations which are stronger than then EPR-B correlations for whole intervals of values! But you can never create the negative cosine.

https://arxiv.org/abs/1312.6403v7

https://www.mdpi.com/1099-4300/22/3/287

https://doi.org/10.3390/e22030287

One can generalise to a tri-coloured disk where the third colour, grey, stands for "no detection". One can replace the wheel with a ball, and one gets Caroline Thompson's (RIP) chaotic ball model. So: those are tricks to get the full amplitude quantum correlations by post-selection (detection loophole) or, without post-selection, with lower than maximum amplitude.

I have been quiet in recent weeks first of all because of a tragedy in my close family, the death of a grandchild at age one month, and now a week ago, the unexpected death of a half-brother-in-law at age 69. I have to get to work fast getting our workshop and symposium plans moving again. We aim to submit a proposal to the Lorentz Center on May 30.

Tomorrow there will also be a new paper on arXiv on something completely different, the Two Envelopes Problem. It's entitled *Anna Karenina and The Two Envelopes Problem*. But there is a challenge there: to invent a challenging Quantum Two Envelopes Problem. There is another connection to quantum foundations, namely the Anna Karenina principle also plays an important role in discussions with people who have shown by a complicated counter-example that Bell was wrong. Here's a link to the paper on my university webpage.

https://www.math.leidenuniv.nl/~gill/tep.pdf

Richard

[Алексей Никулов]

Dear Richard,

I offer my condolences for your grief.

No model in which colors exist before the first observation can reproduce the prediction of the EPR-B correlations because the EPR-B correlations is based on the postulate of quantum mechanics that colors (or eigenstates) do not exist before the first observation and created by the mind of the observer at this observation. The creators of quantum mechanics postulated this absurd in order to describe the Stern - Gerlach paradoxical effect observed almost a hundred years ago, in 1922.

Alexey

пн, 9 мар. 2020 г. в 11:15, Richard Gill <gill...@gmail.com>:

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[Richard Gill]

Dear Alexei

Thanks for your condoleances.

I still do not understand how you explain the fact that the EPR-B correlations are seen in reality.

Are you saying that *no* model can explain what we see in experiments? Or are you saying that the experimental results are an illusion?

Richard

[Алексей Никулов]

Dear Richard,

Experimental results cannot be an illusion if they are repeated many times. I say that no model can explain, for example, the results of the Stern - Gerlach experiment made firstly almost a hundred years ago [1] and repeated many times. The results of this experiment are at the heart of the Bell's inequality controversy, since it was Stern and Gerlach who first observed only binary responses at the measurement the projections of the magnetic moment of atoms: spin up and spin down.

A. Einstein and P. Ehrenfest [2] drew attention in the same 1922 year on the difficulty to explain why only discrete values of projections the atom magnetic moment can be observed.  Bell perfectly explained almost sixty years later what this difficulty is in the article “Bertlmann’s socks and the nature of reality” [3]. Bell's inequalities came into being and became popular only because of the illusion that quantum mechanics was able to explain the paradox of the Stern- Gerlach effect prevailed and still prevail among most physicists.

Most physicists do not want to know up to now that quantum mechanics did not solve the problem of the Stern - Gerlach paradoxical effect. The creators of quantum mechanics created the illusion of solving the problem limiting themselves to the description of the probability to observe, for example, spin up or spin down of particles with spin 1/2. The desire of the creators of quantum mechanics to describe paradoxical quantum phenomena at any cost has misled several generations of physicists. To describe the Stern - Gerlach effect, they had to postulate that the observed does not exist before the observation and is created by the mind of the observer during the observation. I clearly explain this logical fact of quantum mechanics with the help of the comparison of two examples binary responses: two balls, red and blue and projections of spin 1/2, see my preprint Logical proof of the absurdity of the EPR correlation . The prediction of violation of Bell's inequalities is direct logical consequence of the illusion of the description of the Stern - Gerlach effect: the mind of the observer creates spin eigenstates of the both particles of the EPR pair regardless of distance.

Most scientists do not want to admit that already in the Stern - Gerlach effect, and even more so in the violation of Bell inequalities, we may have faced with the unknowability of Nature. Einstein said that the most amazing thing about Nature is its cognizability. But Nature may not be as amazing as Einstein thought. In any case we have no reason to think all objects of Nature must conform to our cognitive ability.

The illusion of understanding is worse than the misunderstanding, because it is misleading. The illusion of understanding quantum phenomena led to the illusion of the reality of a quantum computer. This illusion became possible because of the dogmatic belief of the majority in quantum mechanics and the ridiculous mistake made by Richard Feynman and others. Feynman drew attention to the complexity of computing quantum systems and proposed to carry out such calculations using quantum systems. He did not take into account that the complexity of computing increases exponentially with the number of elements, not because the system is quantum, but because the probability of observation is calculated. Feynman, like the majority, did not understand also that the complexity increases exponentially only in the knowledge of the observer rather than in reality. The mathematics of the probabilities of binary responses of observation should not depend on the subjects of observation, two balls or projections of spin 1/2.

[1] W. Gerlach, and O. Stern, Das magnetische Moment des Silberatoms. Zeitschrift fur Physik 9, 353-355 (1922).

[2] A. Einstein and P. Ehrenfest, Quantentheoretische Bemerkungen zum Experiment von Stern und Gerlach. Zs. Phys. 11, 31-34 (1922).

[3] J.S. Bell, Bertlmann’s socks and the nature of reality, Journal de Physique 42, 41 (1981).

Alexey

пн, 9 мар. 2020 г. в 13:21, Richard Gill <gill...@gmail.com>:

[Ilja Schmelzer]

Am Dienstag, 10. März 2020 02:31:55 UTC+6:30 schrieb nikulovalexey:

Most scientists do not want to admit that already in the Stern - Gerlach effect, and even more so in the violation of Bell inequalities, we may have faced with the unknowability of Nature.

Sorry, but there is no base for assuming that in these experiments we are faced with such a strange thing.  

In principle, one cannot exclude that such a thing happens at some point.  But actually, for these experiments, we have established theories which have realist and causal interpretations.  

 

... and the ridiculous mistake made by Richard Feynman ....

Feel free do disagree with Feynman, but this is simply bad style. 

 

and others. Feynman drew attention to the complexity of computing quantum systems and proposed to carry out such calculations using quantum systems. He did not take into account that the complexity of computing increases exponentially with the number of elements, not because the system is quantum, but because the probability of observation is calculated. Feynman, like the majority, did not understand also that the complexity increases exponentially only in the knowledge of the observer rather than in reality.

Even if there would be a point in this, it would not matter.  Because what matters is that finally we know the result.  So, if the computer gives us that knowledge, what's the problem? Similarly, if the quantum computer gives the correct result with some high enough probability, what's the problem?

 

The mathematics of the probabilities of binary responses of observation should not depend on the subjects of observation, two balls or projections of spin 1/2.

But to present some artificial thought experiment based on images from classical theory, which behave differently in classical theory, is not helpful for understanding.  In particular if one uses the disagreement between quantum theory and classical theory in this case to name quantum theory absurd (instead of the particular choice of the images from classical theory).

[Justo Pastor Lambare]

Dear Alexei

You keep insisting on this view:

".... only because of the illusion that quantum mechanics was able to explain the paradox of the Stern- Gerlach effect prevailed and still prevail among most physicists."

This is not correct, QM does not explain anything, it only gives (ridicule and absurd?) rules so that scientists can predict the result of experiments

El lun., 9 mar. 2020 a las 17:01, Алексей Никулов (<nikulo...@gmail.com>) escribió:

Dear Richard,

Experimental results cannot be an illusion if they are repeated many times. I say that no model can explain, for example, the results of the Stern - Gerlach experiment made firstly almost a hundred years ago [1] and repeated many times. The results of this experiment are at the heart of the Bell's inequality controversy, since it was Stern and Gerlach who first observed only binary responses at the measurement the projections of the magnetic moment of atoms: spin up and spin down.

A. Einstein and P. Ehrenfest [2] drew attention in the same 1922 year on the difficulty to explain why only discrete values of projections the atom magnetic moment can be observed.  Bell perfectly explained almost sixty years later what this difficulty is in the article “Bertlmann’s socks and the nature of reality” [3]. Bell's inequalities came into being and became popularonly because of the illusion that quantum mechanics was able to explain the paradox of the Stern- Gerlach effect prevailed and still prevail among most physicists.

[Алексей Никулов]

Dear Ilja,

You claim that we have a realistic theory which can without any trick describe the Stern - Gerlach effect. Then tell us what this theory is and how it explains the observation of only discrete values of projections of the magnetic moment in any direction. Before writing, read carefully the beginning of Bell's article [1], in which he clearly explains why such a theory is impossible, or at least unlikely.

Do you think any disagreement with recognized scientists is bad style? I don't think so. I realized that in the beginning of the famous book [2] is written stupidity, due to the fact that John Bell also did not think so. Landau, the scientist no less famous than Feynman, wrote an obvious nonsense, but I didn't realize it until I read Bell's work [3], in which Bell analyzes the beginning of the book [2] and draws attention to the difference between the LL (Landau-Lifshitz) jump and the Dirac jump. Only then I realized that a fairy tale about a magic device (which the LL called ‘classical’) is told at the beginning of the book [2]. This magic device can jump by itself into eigenstate, and not its eigenstate, but the eigenstate of the quantum system which it measures.

Landau and Feynman were outstanding physicists. I draw attention on the Landau postulate proposed in 1941, which allows to describe macroscopic quantum phenomena, see the article “Bohm's quantum potential and quantum force in superconductor”, see https://arxiv.org/abs/0812.4118 and ResearchGate https://www.researchgate.net/profile/Alexey_Nikulov/research . The Ginzburg-Landau theory one of the most excellent theories of physics is based on the Landau postulate.

But Landau and Feynman did not understand the essence of the controversy between the creators of quantum theory. Bell noted that “Landau sat at the feet of Bohr” [3]. They adapted quantum mechanics to the level of their understanding and that of the majority, radically perverting it.

The problem with a quantum computer is that it can be created on any system with binary responses, such as Schrodinger's cats.

[1] J.S. Bell, Bertlmann’s socks and the nature of reality, Journal de Physique 42, 41 (1981).

[2] L. D. Landau, E. M. Lifshitz, Quantum Mechanics: Non Relativistic Theory (Volume 3, Third Edition, Elsevier Science, Oxford, 1977).

[3] J.S. Bell, Against Measurement. Phys. World 3, 33-40 (1990).

Alexey

вт, 10 мар. 2020 г. в 14:26, Justo Pastor Lambare <jup...@gmail.com>:

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[Antony Crofts]

Dear Alexey,

        I’ve been following your argument with Ilja, and thought you might be interested in the paper I have been discussing with Richard and Jan-Åke. In Part B, section 3, (  on p. 32) I provide a local realistic explanation for the Stern-Gerlach effect. Part A of the paper is about Bell’s own model, which seems to me mistaken, and Part B is on the Copenhagen Interpretation of QM, which I think is flawed. I realize that both these views are anathematic to the Bell’s theorem community, but am happy to argue my case.

        You will find the paper at:

http://www.life.illinois.edu/crofts/Bell_Ineq/Entanglement_paper_PDF_versions/

        Best wishes,

                Tony

 

Sent from Mail for Windows 10

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[Ilja Schmelzer]

Am Mittwoch, 11. März 2020 00:51:33 UTC+6:30 schrieb nikulovalexey:

You claim that we have a realistic theory which can without any trick describe the Stern - Gerlach effect. Then tell us what this theory is and how it explains the observation of only discrete values of projections of the magnetic moment in any direction. Before writing, read carefully the beginning of Bell's article [1], in which he clearly explains why such a theory is impossible, or at least unlikely.

Don't teach me what to read and how, this is simply yet another case of indecent behavior.  The realistic theories are the realist interpretations of quantum theory.  This includes dBB theory as well as other, stochastic interpretations, like Nelsonian stochastics and Caticha's entropic dynamics.  

 

Do you think any disagreement with recognized scientists is bad style? I don't think so.

Disagreement is unproblematic, I disagree with scientists like Einstein and Feynman too.  But disagreement is one thing, violations of the rules of courtesy another one. And the problem is not that the scientist is recognized, if you use such words in relation to usual people it is impolite too. 

Regarding LL, I disagree with their interpretation too, but would never use words like "stupidity" or "fairy tale". 

 

[Алексей Никулов]

Dear Tony,

I have read section 3 “Indeterminacy and superposition of the entangled state ”, (on p. 32) of Part B “MAYBE EINSTEIN GOT IT RIGHT” of your paper “Entanglement re-examined: If Bell got it wrong, then maybe Einstein had it right”. But I didn't find any explanation for the Stern-Gerlach effect. How are you explaining the Stern-Gerlach effect?

Alexey

ср, 11 мар. 2020 г. в 18:47, Ilja Schmelzer <ilja.sc...@gmail.com>:

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[Алексей Никулов]

Dear Justo,

You claim obvious nonsense because of your blind faith in quantum mechanics. A theory, which does not explain anything, is only no scientific theory, but even no trick. I must remind you of the titles of both the EPR [1] and the Bohr [2] papers “Can quantum-mechanical description of physical reality be considered complete?” According to the majority belief and yours, Einstein and Bohr argued about whether the description of quantum mechanics is complete and that Bell's inequalities allow this dispute to be resolved.

The quantum debate of Bohr with Einstein and Bell's inequalities would have no sense whether if quantum mechanics “only gives rules so that scientists can predict the result of experiments” as you claim.

Believers in quantum mechanics have always engaged in self -deception. On the one hand, they claimed that quantum mechanics perfectly describes the results of observations, but on the other hand, they were sure that quantum mechanics describes physical reality. This self-deception eventually led to the absurd idea to create a real device - a quantum computer, based on the principle - the EPR correlation, which contradicts realism. Alain Aspect states in his Viewpoint [3]: ”By closing two loopholes at once, three experimental tests of Bell’s inequalities remove the last doubts that we should renounce local realism. They also open the door to new quantum information technologies”. Alain Aspect a great experimenter, but he doesn't understand what he claims.

[1] A. Einstein, B. Podolsky, N. and Rosen, Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777-780 (1935).

[2] N. Bohr, Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 48, 696-702 (1935).

[3] A. Aspect, Viewpoint: Closing the Door on Einstein and Bohr’s Quantum Debate. Physics 8, 123 (2015)

вт, 10 мар. 2020 г. в 14:26, Justo Pastor Lambare <jup...@gmail.com>:

Dear Alexei

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[Richard Gill]

 Dear Tony

I wish you would read the paper which I talked about at the beginning of this thread. The triangle wave versus the cosine

About Bertlmann's socks and my Warsaw talk (which was broadcast from Krakow actually; I was in my home in Apeldoorn) - I would hope that you would be able to follow the mathematical argument presented there. I have added four more slides and will discuss them at the next meeting, next week. Anybody who'd like to be there can just email me and I'll forward the invite.

Richard

https://www.math.leidenuniv.nl/~gill/Warsaw.pdf

https://www.math.leidenuniv.nl/~gill/Warsaw2.pdf

On 9 Mar 2020, at 08:20, Richard Gill <gill...@gmail.com> wrote:

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[jupalam]

Richard

What would happen if your colored regions on the disk reduce to lines determining points on the limit circumference of the disk in a manner that the area of the color regions is zero? I do not even know if my question makes sense.

Justo