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# Simulated Local EPR Correlation: CHSH = 3

Version 1
: Received: 16 January 2023 / Approved: 31 January 2023 / Online: 31 January 2023 (04:19:48 CET)

Version 2 : Received: 3 February 2023 / Approved: 6 February 2023 / Online: 6 February 2023 (02:04:35 CET)

Version 3 : Received: 31 March 2023 / Approved: 3 April 2023 / Online: 3 April 2023 (04:12:41 CEST)

Version 4 : Received: 3 April 2023 / Approved: 4 April 2023 / Online: 4 April 2023 (03:54:28 CEST)

Version 5 : Received: 29 July 2023 / Approved: 31 July 2023 / Online: 1 August 2023 (10:03:11 CEST)

Version 6 : Received: 17 October 2023 / Approved: 18 October 2023 / Online: 18 October 2023 (10:08:48 CEST)

Version 7 : Received: 26 January 2024 / Approved: 28 January 2024 / Online: 29 January 2024 (04:18:41 CET)

Version 2 : Received: 3 February 2023 / Approved: 6 February 2023 / Online: 6 February 2023 (02:04:35 CET)

Version 3 : Received: 31 March 2023 / Approved: 3 April 2023 / Online: 3 April 2023 (04:12:41 CEST)

Version 4 : Received: 3 April 2023 / Approved: 4 April 2023 / Online: 4 April 2023 (03:54:28 CEST)

Version 5 : Received: 29 July 2023 / Approved: 31 July 2023 / Online: 1 August 2023 (10:03:11 CEST)

Version 6 : Received: 17 October 2023 / Approved: 18 October 2023 / Online: 18 October 2023 (10:08:48 CEST)

Version 7 : Received: 26 January 2024 / Approved: 28 January 2024 / Online: 29 January 2024 (04:18:41 CET)

How to cite:
Sanctuary, B. Simulated Local EPR Correlation: CHSH = 3. *Preprints* **2023**, 2023010570. https://doi.org/10.20944/preprints202301.0570.v2
Sanctuary, B. Simulated Local EPR Correlation: CHSH = 3. Preprints 2023, 2023010570. https://doi.org/10.20944/preprints202301.0570.v2

## Abstract

A statistical simulation is presented which reproduces the correlation obtained from EPR coincidence experiments without non-local connectivity. Defining spin under the quaternion group reveals hyper-helicity, a hitherto missed attribute of spin. Including this in the treatment, reveals two complementary properties: spin polarization and spin coherence. The former has a CHSH value of 2, and spin coherence has a CHSH = 1 giving CHSH = 3 for an EPR pair. The simulation here gives 2.995. We suggest that Nature has CHSH=3 being considerable more than predicted from quantum mechanics of $2\sqrt{2}$. There are no Local Hidden Variables. We suggest that quaternion spin is more fundamental than Dirac spin. A computer program which performs the simulation without non-local connectivity is described.

## Keywords

Foundations of physics; Dirac equation; Spin; Quantum Theory; non-locality; helicity

## Subject

Physical Sciences, Quantum Science and Technology

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

## Comments (5)

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Commenter: Bryan Sanctuary

Commenter's Conflict of Interests: Author

Commenter: Mark Hadley

The commenter has declared there is no conflict of interests.

If a parameter, such as theta, is introduced to calculate or explain the outcome of spin measurements and correlations then it is a hidden variable theory. BI apply. If BI does not apply then it hard to see what value this work has. What could it possibly be explaining?

To explain EPR type experiments, several basic steps are required. These are ALL either missing or wrong.

1) A formula is required to predict + or - outcomes at one arm of the apparatus. Missing

2) The formula should be tested against QM spin predictions at one arm.

3) 1) then needs to be used to predict correlations. Somehow correlations arise without any such calculation.

4) Correlation coefficients for any pair of a, b settings can only be between +1 and - 1. Getting a value outside this range shows a monumental error and to not realise it really undermines the credibility of the paper .

5) Note that QM already predicts correct correlation coefficients, but does so without any underlying explanation for individual results. So to go beyond QM requires an underlying explanation of the coefficients in terms of individual events.

6) Finally 3 needs to be used at different angles for A and B and added together in the CSCH equation. It is this equation that has a magnitude less than or equal to 2 for LHV theories.

7) The author repeatedly refers to CSCH correlations and makes claims to violate them, but does so without ever constructing the CSCH expression.

7) The author should be able to say clearly in principle how Bell's inequality is violated. This should be in the abstract, introduction and conclusion.

8) The author should state clearly if the predictions at each stage agree with QM. If they disagree, then there is an enormous credibility hurdle to surmount. Some effort should be made to justify it.

9) it is not appropriate in this type of paper to insert computer code. Just give the expression as an equation.

Commenter:

Commenter's Conflict of Interests: I am the author

The work is most definitely not about LHV. I do not introduce a new parameter. The only local variable used was first presented in the 1920’s and given in Eq.(2). No other variables are used, and its inclusion precludes the non-local conclusion of Bell’s Theorem. The paper is not about Bell's work but has consequences, showing that his theorem requiring non-locality to explain the observations is obviated.

The main points appear lost on Hadley: the changing of spin to quaternion symmetry; the prediction of the four spatial dimensions of quaternions that have no time; the properties of spin which extend the two observed polarization states to the fourth dimensional Dirac field; the need for a bivector to explain the observations; that particles emerge that have no parity. He fails to consider that Nature might extend beyond our spacetime and our ability to directly measure attributes, and that these, nonetheless, influence our observation.

Rather he focuses on rather banal points, for example, stating the well-known CHSH formula is missing when it is clearly stated in Eq.(12) and appears in Figure (9). Not only that, but the fundamental origin of the violation of the CHSH is shown to be rationalized by quaternion spin that these papers are about. No one has ever come close to explaining this, rather attributing it to “quantum weirdness”. In my view, revelation has no place in physics.

There are parts of this draft, v2, however, which require clarification, and these will follow in v3. These changes are minor in the global framework of the papers.

I accept that the ideas used here may be too heretical for some, and their significance appears to be lost on Hadley. HIs remarks are quite banal and seem based upon a cursory reading and a result of his own bias towards the foundations of physics. To his points:

1. The treatment deals with pure states which give definite outcomes and are not probabilistic. However, probabilities do arise and are in the computer code as coincidences. With a little work, individual + and - clicks are easily extracted. Moreover, they agree with the experimental results.

2. It is unnecessary to encumber the paper with well-established expressions and data. Despite this, the treatment discusses one spin and how spin coherence, a totally new point, has been overlooked.

3. Totally wrong: my Eq.(1), which is derived in the Appendix, does just that.

4. I show that there are two complementary properties of spin. One has correlation that lies between -1 and +1; the other between -1/4 and +1/4. His comment is nonsense.

5. QM does not predict the correct correlation coefficients, otherwise all the work on the violation of Bell’s Inequalities would be moot. As he says, QM predictions do “so without any underlying explanation”. I provide that explanation, click by click in the simulation.

6. Indeed, I do just that. For each value of the filter settings, the results are obtained one coincidence at a time and added together. The magnitude of each attribute, polarization and coherence, have CHSH values of respectively 2 and 1, neither of which violates CHSH. These are discussed and illustrated in Fig.(6).

7. Please see Eq.(12) and Figure (9). The CHSH value is calculated in the usual manner in the computer code. Hadley misses this. A review of the background and formulation of CHSH is unnecessary for the audience of this paper.

8. I show that the CHSH is apparently violated by the distribution of two complementary properties, neither of which violate the CHSH. Therefore, there is no “enormous credibility to surmount”. The alternative explanation for the violation requires the use of instantaneous-action-at-a-distance, a notion both Newton and Einstein rejected. I stand on their shoulders.

9. The code snippets are included to show how elementary it is to generate the symmetric and antisymmetric properties of spin simply by knowing which way a spin spins. If offensive, I can remove them. Please see Eq.(1) and the appendix.

Commenter:

Commenter's Conflict of Interests: I am the author

The main points appear lost on him: the changing of spin to quaternion symmetry; the prediction of the four spatial dimensions of quaternions that have no time; the properties of spin which extend the two observed polarization states to the fourth dimensional Dirac field; the need for a bivector to explain the observations; that particles emerge that have no parity. He fails to consider that Nature might extend beyond our spacetime and our ability to directly measure attributes, and that these, nonetheless, influence our observation.

The work is most definitely not about LHV. The only local variable used was first presented in the 1920’s and given in Eq.(2). No other variables are used, and its inclusion obviates the non-local conclusion of Bell’s Theorem. Bell’s Inequalities, however, are used as a useful tool and a quantitative measure of correlation.

Rather Hadley focuses on rather banal points, for example, stating the well-known CHSH formula is missing when it is clearly stated in Eq.(12) and appears in Figure (9). Not only that, but the fundamental origin of the violation of the CHSH is shown to be rationalized by quaternion spin that these papers are about. No one has ever come close to explaining this, rather attributing it to “quantum weirdness”. In my view, revelation has no place in physics.

There are parts of this draft, version 2, however, which require clarification, and these will follow in v3. These changes are minor in the global framework of the papers.

I accept that the ideas used here may be too heretical for some, and their significance appears to be lost on Hadley. His remarks are quite banal and seem based upon a cursory reading and a result of his own bias towards the foundations of physics. To his points:

1. The treatment deals with pure states which give definite outcomes and are not probabilistic. However, probabilities do arise and are in the computer code as coincidences. With a little work, individual + and - clicks are easily extracted. Moreover, they agree with the experimental results.

2. It is unnecessary to encumber the paper with well-established expressions and data. Despite this, the treatment discusses one spin and how spin coherence, a totally new point, has been overlooked.

3. Totally wrong: my Eq.(1), which is derived in the Appendix, does just that.

4. I show that there are two complementary properties of spin. One has correlation that lies between -1 and +1; the other between -1/4 and +1/4. His comment is wrong.

5. QM does not predict the correct correlation coefficients, otherwise all the work on the violation of Bell’s Inequalities would be moot. As he says, QM predictions do “so without any underlying explanation”. I provide that explanation, click by click in the simulation.

6. Indeed, I do just that. For each value of the filter settings, the results are obtained one coincidence at a time and added together. The magnitude of each attribute, polarization and coherence, have CHSH values of respectively 2 and 1, neither of which violates CHSH. These are discussed and illustrated in Fig.(6).

7. Please see Eq.(12) and Figure (9). The CHSH value is calculated in the usual manner in the computer code. Hadley misses this. A review of the background and formulation of CHSH is unnecessary for the audience of this paper.

8. I show that the CHSH is apparently violated by the distribution of two complementary properties, neither of which violate the CHSH. Therefore, there is no “enormous credibility to surmount”. The alternative explanation for the violation requires the use of instantaneous-action-at-a-distance, a notion both Newton and Einstein rejected. I stand on their shoulders.

9. The code snippets are included to show how elementary it is to generate the symmetric and antisymmetric properties of spin, simply by knowing which way a spin spins. Please see Eq.(1) and the appendix.

Commenter:

The commenter has declared there is no conflict of interests.