Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Spin with Hyper-helicity.

Version 1 : Received: 16 January 2023 / Approved: 31 January 2023 / Online: 31 January 2023 (04:23:01 CET)
Version 2 : Received: 4 April 2023 / Approved: 4 April 2023 / Online: 4 April 2023 (04:32:30 CEST)

How to cite: Sanctuary, B. Spin with Hyper-helicity.. Preprints 2023, 2023010571. Sanctuary, B. Spin with Hyper-helicity.. Preprints 2023, 2023010571.


We present an analysis of the local singlet state and compare its correlation to that of a separated pair of spins devoid of entanglement. In addition to polarization, we include its hyper-helicity, and this quantum coherence is shown to account for the quantum correlation that leads to the apparent violation of Bell's inequalities. Upon separation, particles conserve linear momentum, angular momentum, helicity and correlation. In order to agree with experimental coincidence data, both polarization and coherence, incompatible elements of reality, must simultaneously exist.


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


Physical Sciences, Quantum Science and Technology

Comments (2)

Comment 1
Received: 2 March 2023
Commenter: Mark Hadley
The commenter has declared there is no conflict of interests.
Comment: The main result of this paper is eq 17. It is wrong. That is not how you combine distributions.
The preceding equations 9 and 15 and are also most peculiar. The correlation functions depend on the absolute value of the angles not their differences. If both arms are at zero degrees (eq 9) the correlation is - 1, but if both are still perfectly aligned but at 60 degrees the correlation is 0.25. Considering that this change could be just a relabeling of the axis, it is not a physically sensible equation. One must conclude that the equation is wrong, the source is not isotropic or both.
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Response 1 to Comment 1
Received: 3 March 2023
The commenter has declared there is no conflict of interests.
Comment: By stating Eq.(17) is wrong, Hadley is rejecting on of the most well established formulas of Geometric Algebra which is that a dyadic of Pauli spin matrices has a symmetric, (i=j) and and antisymmetric part (i not equal j). This is given in Eq,(10) which he cannot assail. His statement that Eq.(17) is wrong and unsupportable.

He also fails to grasp that the two contributions of that equation are complementary properties of spin that combine to give the observed results. He states combining them is wrong, but fails to say how the seminal Eq.(10) is also wrong.

Stating that Eq.(9) and (15) are peculiar is subjective, unclear and unsupported. He should realize that Eq.(9) uses the same mathematics commonly found in well-know papers, such as (Greenberger, D. M., Horne, M. A., Shimony, A., & Zeilinger, A. (1990). Bell’s theorem without inequalities. American Journal of Physics, 58(12), 1131-1143.) If I am wrong, then so are they. The results are the same too. The difference is the inclusion of coherence which makes the difference.

Hadley appears not to understand how to work out the step-by-step evaluation of coherence given in Eq.(15). His comments appear contrived and of no real relevance to the work.

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