BCS-ALV Debate: Physical Meaning of Bivectors

[anton vrba]

Here we discuss the physical meaning of Bryan C. Sanctuary's (BCS) bivectors. BCS claims them as physical, and Anton L. Vrba (ALV) claims that they are non physical, insofar as how BCS uses geometry to argue against Bell's theorem.

BCS states  "[B]ut where does the bivector miserably fail? My bivector contains the SU(2) to SO(3) homology, and is much more physical than fermions.  Do you understand this "fermions are not fundamental, but the polarized blades of a spin 1 boson"  It requires some thought.  Have you seen the classical origin of spin?  You do not  have that with fermions.  I am consistent with all experiments, except the hype around neutrinos.  They have never been detected, and I say they do not exist."

Here is the list of BCS publications

[1] B. Sanctuary, Quaternion-Spin and Some Consequences, Preprints 2023, 202312.1277. 

https://www.preprints.org/manuscript/202312.1277/v1
[2] B. Sanctuary, Spin Helicity, Preprints 2024, 202301.0571. 

https://www.preprints.org/manuscript/202301.0571
[3] B. Sanctuary, Beta Decay with No Neutrinos and Parity Conservation, Preprints 2024, 202401.0118, version 3. 

https://www.preprints.org/manuscript/202401.0118/v3
[4] B. Sanctuary, Quaternion Spin, Mathematics 2024, 12(13), 1962. 

https://www.mdpi.com/2227-7390/12/13/1962
[5] B. Sanctuary, EPR Correlations Using Quaternion Spin, Quantum Rep. 2024, 6(3), 409–425.
https://www.mdpi.com/2624-960X/6/3/26
[6] B. Sanctuary, Spin Helicity and the Disproof of Bell’s Theorem, Quantum Rep. 2024, 6(3), 436–441.
https://www.mdpi.com/2624-960X/6/3/28
[7] B. Sanctuary, The Classical Origin of Spin: Vectors Versus Bivectors, Axioms 2025, 14(9), 668.
https://www.mdpi.com/2075-1680/14/9/668

References [1-3] were found as self-references in [4-7]

I, ALV, claim that the bivector as BCS describes is not a physical description of spin or reality. I do not criticise BCS's geometric analysis. However, I do criticise BCS's interpretation with respect to natural philosophy.

My first critique is from [5], BCS writes

Which implies a flight path to Alice and Bob to be exactly the same for each sample. If one is slightly longer than the other, does not matter in above equations as randomley set filters are specified, a delta-time of flight is just a constant angular offset to the random set filters.

But, this is not what is observed in nature, here I refer to to J. Yin et al. 

[8] J. Yin (2017) “Satellite-based entanglement distribution over 1200 kilometers,” Science, 356, pp. 1140–1144.

Copy attached. I specifically refer to Figure 3 in [8]

Which depicts the flight path evolution over a near 300 second period. During this time period entangled of a photon pairs was demonstrated

I rewrite BCS's equation 10 in such a satellite based system: 

Introducing flight times t_a and t_b. The phase term omega t_ab is now equivalent to a random phase between 0 and 2 pi.

Summing and averaging over many samples we have Sum_i E(a,b)_i ---> 0 , thus no entanglement.

Conclusion:  The bivector as employed by BCS with properties of helical spin and quaternion spin is not a physical object, because it does not conform to experience.

Regards

Anton

[Bryan Sanctuary]

Is ALV you?  I am happy to discuss. In the correlations that you say have identical paths, no, they can differ by $2n\pi$.  In the product of quaternions, \theta is set at the source, and then, later A and B choose a polarizer, and so the only parameters are (\theta_a  - \theta}.

So in short, I hope I have answered you.  BTW, when Alice measures her spin then Bob's is decided. So does that mean his spin collapsed in mid-flight?  Same question as you raised.

Second, more importantly, you question spin is not a bivector. So since this is a debate, can I recall in QM we have position-momentum, two complementary variables. What, I ask you, are the complementary variables of spin?  I really want to know your views on this, so wait to hear from you.

Bryan

[Mark Hadley]

Bryan. It is well known what the complimentary variables of spin are. It's spin in different directions. So x, y, z directions form a basis for the system. That is theoretically proven. Experimentally it is supported by the fact that you cannot do an ideal measurement in two different directions.

You use the word complimentary to describe two disjoint distributions. It works as an English phrase, but it's not what the word means in QM. Like choosing  a person at random and measuring their height. It might be a man's height or a woman's height but not both. The total height distribution is made up of two disjoint distributions. The averages can be combined in a well known way.

In an EPR type experiment, the outcomes in your model can be described by a LHV function A ( lambda) where lambda is a hidden variable spanning both distributions. Hence CSHS applies.

When are you going to pay up the bet that you lost and that you used this group to promote.

Mark

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[Bryan Sanctuary]

Mark,

No, you are wrong: spin components, S_x, S_y, S_z are not complementary, they are only incompatible.  To be complementary, they must belong to different spaces, like position and momentum has inverse fourier spaces.  The spin components are all expressed within the same 2D vector space, so cannot be complementary.

The complementary variables of spin are \sigma  and i\sigma. They are in different spaces, they are orthogonal, and the bivector is a bivector because  i\sigma_2 = \sigma_3\sigma_1.  

So who is in this debate, Anton or Mark or you both.  Happy to have you both.

What, then Mark or Anton, is a spin?

Bryan

[Richard Gill]

Bryan, I think you asked a mathematical question: “What are the complementary variables of spin?”

The complementarity of position and momentum is a mathematical property within the mathematical framework called quantum mechanics.

In QM there is a family of observables called “spin”. Spin has a direction. [Like position and momentum]. 

My Question 1: Why should spin in a particular direction have a complementary variable?

It seems you are proposing an extension of conventional QM.  You’ll need to extend the conventional rules to include measurement. Born. Von Neumann-Lüders. …

My Question 2: What is ‘’measurement” in BCS-QM?

Richard

Sent from my iPad

On 29 Jan 2026, at 01:29, Bryan Sanctuary <bryancs...@gmail.com> wrote:



<v4x3nuso.png>

Which implies a flight path to Alice and Bob to be exactly the same for each sample. If one is slightly longer than the other, does not matter in above equations as randomley set filters are specified, a delta-time of flight is just a constant angular offset to the random set filters.

But, this is not what is observed in nature, here I refer to to J. Yin et al. 

[8] J. Yin (2017) “Satellite-based entanglement distribution over 1200 kilometers,” Science, 356, pp. 1140–1144.

Copy attached. I specifically refer to Figure 3 in [8]

<njciqmjy.png>

Which depicts the flight path evolution over a near 300 second period. During this time period entangled of a photon pairs was demonstrated

I rewrite BCS's equation 10 in such a satellite based system: 

<ndxohfqh.png>

Introducing flight times t_a and t_b. The phase term omega t_ab is now equivalent to a random phase between 0 and 2 pi.

Summing and averaging over many samples we have Sum_i E(a,b)_i ---> 0 , thus no entanglement.

Conclusion:  The bivector as employed by BCS with properties of helical spin and quaternion spin is not a physical object, because it does not conform to experience.

Regards

Anton

[Richard Gill]

The “inverse spaces” of Fourier theory are the same space. The word “inverse” comes from the operations between these spaces, ie mappings from one to another. Fourier transform and inverse Fourier transform.

\sigma and \i sigma lie in the same space: they are operators *on* the same Hilbert space.

“Spin components are all expressed within the same 2D vector space”. What 2D vector space? Are you talking about classical mechanics?

You ask one very good question, Bryan! What is a spin?

Sent from my iPad

On 29 Jan 2026, at 04:30, Bryan Sanctuary <bryancs...@gmail.com> wrote:



<v4x3nuso.png>

Which implies a flight path to Alice and Bob to be exactly the same for each sample. If one is slightly longer than the other, does not matter in above equations as randomley set filters are specified, a delta-time of flight is just a constant angular offset to the random set filters.

But, this is not what is observed in nature, here I refer to to J. Yin et al. 

[8] J. Yin (2017) “Satellite-based entanglement distribution over 1200 kilometers,” Science, 356, pp. 1140–1144.

Copy attached. I specifically refer to Figure 3 in [8]

<njciqmjy.png>

Which depicts the flight path evolution over a near 300 second period. During this time period entangled of a photon pairs was demonstrated

I rewrite BCS's equation 10 in such a satellite based system: 

<ndxohfqh.png>

Introducing flight times t_a and t_b. The phase term omega t_ab is now equivalent to a random phase between 0 and 2 pi.

Summing and averaging over many samples we have Sum_i E(a,b)_i ---> 0 , thus no entanglement.

Conclusion:  The bivector as employed by BCS with properties of helical spin and quaternion spin is not a physical object, because it does not conform to experience.

Regards

Anton

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[Richard Gill]

I just came across this insightful 1949 quote by Dirac (published in 1951, the year I was born).

Sent from my iPad

On 29 Jan 2026, at 04:30, Bryan Sanctuary <bryancs...@gmail.com> wrote:



<v4x3nuso.png>

Which implies a flight path to Alice and Bob to be exactly the same for each sample. If one is slightly longer than the other, does not matter in above equations as randomley set filters are specified, a delta-time of flight is just a constant angular offset to the random set filters.

But, this is not what is observed in nature, here I refer to to J. Yin et al. 

[8] J. Yin (2017) “Satellite-based entanglement distribution over 1200 kilometers,” Science, 356, pp. 1140–1144.

Copy attached. I specifically refer to Figure 3 in [8]

<njciqmjy.png>

Which depicts the flight path evolution over a near 300 second period. During this time period entangled of a photon pairs was demonstrated

I rewrite BCS's equation 10 in such a satellite based system: 

<ndxohfqh.png>

Introducing flight times t_a and t_b. The phase term omega t_ab is now equivalent to a random phase between 0 and 2 pi.

Summing and averaging over many samples we have Sum_i E(a,b)_i ---> 0 , thus no entanglement.

Conclusion:  The bivector as employed by BCS with properties of helical spin and quaternion spin is not a physical object, because it does not conform to experience.

Regards

Anton

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[anton vrba]

Dear Bryan, yes ALV is me, my middle name is Lorenz (German spelling).

You say, "BTW, when Alice measures her spin then Bob's is decided."  (1) 

on what physical grounds? It is a heuristic proposition to suit your model or you making geometric manipulation to reality. 

Most importantly, (1) is the clarifying statement to Bryan's work. It signals a shift in ontology, Bryan is moving away from probabilistic wavefunction collapse (Copenhagen interpretation) to a global hidden variable (GHV).  That does not disprove Bell.

Bryan, declare your work as a GHV, Bell is agnostic to probabilistic and GHV interpretations, it excludes LHV. By attacking a mathematical theorem you alienating yourself from a potential audience, because no mathematical theorem, a truth by logic reasoning, has ever been disproved, and you are not going to be the first one to do so.

Should you claim: "I have a geometric ansatz to a GHV theory"  then there are many physicists who may listen. The Copenhagen vs de Broglie-Bohm debate has following and is debated in mainstream physics.

To progress this BCS-ALV debate we have to separate the apples from the pears.  The actual debate that Bryan has ignited is actually an ontological  debate, probabilistic vs causal. A GHV theory is causal and cannot be attacked by probabilistic arguments, and vice versa. So for the past years, criticisers and Bryan, were talking past each other.

The problem now is how to progress the debate, a couple of pages of geometric reasoning will not shift anything, it needs something more fundamental like attaching  bivectors to Maxwell's work.

You ask: "we have position-momentum, two complementary variables. What, I ask you, are the complementary variables of spin? "

The answer is simple position-momentum are physical in the classical sense, spin what ever it is sits in Hilbert.  Hilbert space is a nice word for "I do not know so I create a another dimension in Hilbert space"  so the complementary variable for spin if you need one define it and push it into another dimension in Hilbert space.  

Regards

Anton

[GeraldoAlexandreBarbosa]

Bryan proposes a new mathematical model (an extension over Dirac’s analysis) that intrinsically challenges many experimental facts. For the moment, let’s delay Bell’s discussion: it is first important to examine the compatibility of his model against “realistic measurements”. Reality here refers to repeated measurements which under similar conditions produce statistically repeatable results.

Compatibility with experimental results should be the first focus of this discussion. Model validity should first be tested against evidence from the Universe. 

Geraldo A. Barbosa, PhD

KeyBITS Encryption Technologies LLC

https://www.keybits.tech/

1540 Moorings Drive #2B, Reston VA 20190

E-Mail: GeraldoABarbosa@keybits.tech 

Cellphone: 1-443-891-7138 (US) - with WhatsApp

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[Bryan Sanctuary]

Richard

You do not answer and pose other questions to confuse.  Please stay focused. 

Can you define spin?   You are saying something about direction, but very unclear. Be mathematical.  What is complementarity, and what is spin?

I need no more rules and I have answered all your questions: Done measurement, done all the rules, done the Lagrangian, Done, so I do not repeat.  I am doing applications.  You are confused I think because you are grasping at ideas without reading what I said. See below

Bryan

It seems you are proposing an extension of conventional QM.  DONE  You’ll need to extend the conventional rules to include measurement. Born. Von Neumann-Lüders. …DONE DONE DONE

My Question 2: What is ‘’measurement” in BCS-QM?  DONE

[Mark Hadley]

I take the opposite, and more economical, approach to any models of QM or particles.

BI is pretty much a theoretical and experimental distinction between the classical and quantum worlds. So I look at the top level: How does it get round BI?

If it does not then I'm probably not interested, it can't be a model of QM or even consistent with it.

If it claims to violate BI,that's interesting so I look to see which assumptions it bypasses and how. It so fundamental that expect the model to articulate that clearly and unambiguously. Then I decide if that interests me.

In Bryan's case: he claims the model violates BI, so that's one hurdle. But he can't give any meaningful explanation of the assumptions it violates - just a bit of poetry.

I would not normally spend time in such a paper, but because if the Bet with Richard, I did study it. The conclusion is clear to anyone who reads it: The model is consistent with Bells assumptions, and therefore cannot violate BI and cannot be a model for the quantum world. The allusion that the paper is significant comes only from a mathematics error.

Cheers

Mark

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[Bryan Sanctuary]

Thanks Gealdo

I have published all you ask.  The change from spin a vector to a bivector agrees with ALL experiments I have seen, except neutrinos that have never been measured.  More applications are needed, but it all works and replaces QFT with Geometric Algebra.

All you must do is change the algebra of Dirac from Cl(1,3) to Cl(2,2)  That is in good company because that is what Penrose did with Twistor Theory

Bryan

[Bryan Sanctuary]

Mark said:  "But he can't give any meaningful explanation of the assumptions it violates - just a bit of poetry."  

It violates no assumptions.  I get the classical origin of spin which is a bivector:  do you not think that is relevant?  Here is the start of a list which gives meaningful explanations:

Bryan

Consequences of the Bivector Standard Model (BiSM)

Nature is local, real, and deterministic.

• Apparent quantum randomness arises from incomplete access to internal degrees of freedom, not intrinsic indeterminacy or nonlocality.

Dirac’s nearly 100-year-old matter–antimatter interpretation is replaced.

• The conventional interpretation of the Dirac equation as requiring particle–antiparticle doubling is superseded by a bivector solution with internal rotational structure.

The Standard Model of particle physics is replaced by the Bivector Standard Model (BiSM).

• The BiSM provides a structural, geometric foundation based on real bivectors rather than abstract internal symmetries.

Spin has a classical origin as a bivector.

• Spin is not a postulated quantum property but a real, extended, two-dimensional rotational structure.

Spin is not a chiral vector in a 2D Hilbert space.

• It is a real 2D object—a classical rotor—embedded in spacetime.

Fermions are not fundamental.

• What are called fermions are polarized blades of bivectors, not elementary point particles.

Spin as a classical rotor has a well-defined quantum limit.

• This limit appears as a double-helical confinement of energy (Zitterbewegung-like structure), not as a postulated quantum degree of freedom.

Spin need not be postulated.

• In isotropy, the bivector is massless and electromagnetically inert.
• In a polarizing field, its blades separate, and polarization, chirality, and electric charge emerge naturally.

Pauli matrices do not define quantum spin.

• They describe the classical chirality of bivector blades.

The point-particle electron is replaced by a structured bivector object.

• Structure determines function: the bivector hosts energy that can be quantized.

Quantum Field Theory is replaced by Geometric Algebra.

• Fields and particles arise from real geometric structure rather than operator-valued distributions.

Particles are not excitations of a ubiquitous chiral field.

• Local symmetry maintained by hypothetical gauge bosons—represented by internal lines in Feynman diagrams—has no ontological basis; none of these objects have ever been directly observed.

Neutrinos do not exist.

• Billions of dollars spent on neutrino detection experiments have been misdirected.

Parity is not violated.

• Apparent parity violation arises from misidentification of internal bivector degrees of freedom.

Quantum superposition of spin states is replaced.

• What is called superposition is the rotation and projection of real objects in spacetime.

Teleportation and quantum information theory must reject Bell’s theorem.

• Bell’s theorem does not apply to systems with internal geometric structure.

Quantum computing cannot use qubits as usually conceived.

• Qubits do not physically exist.
• Teleportation is replaced by internal clock correlations originating from Zitterbewegung

• Billions in past research funding devoted to nonlocality have been misdirected.
• Companies based on Bell-theorem–dependent quantum information technologies will fail.
• Tens of thousands of research papers relying on Bell’s theorem are ill-founded.
• Thousands of ongoing research projects must be terminated.
• No new public research funds should be committed to nonlocal phenomena.
• The 2022 Nobel Prize in Physics was awarded for the wrong reason.
• The EPR paradox is resolved, and quantum “weirdness” is explained.
• The ontology of the foundations of physics is fundamentally changed.

On Thu, Jan 29, 2026 at 8:25 AM Mark Hadley <sunshine...@googlemail.com> wrote:

I take the opposite, and more economical, approach to any models of QM or particles.

BI is pretty much a theoretical and experimental distinction between the classical and quantum worlds. So I look at the top level: How does it get round BI?

If it does not then I'm probably not interested, it can't be a model of QM or even consistent with it.

If it claims to violate BI,that's interesting so I look to see which assumptions it bypasses and how. It so fundamental that expect the model to articulate that clearly and unambiguously. Then I decide if that interests me.

In Bryan's case: he claims the model violates BI, so that's one hurdle. But he can't give any meaningful explanation of the assumptions it violates - just a bit of poetry.  But he can't give any meaningful explanation of the assumptions it violates - just a bit of poetry.

[Mark Hadley]

Bryan.

Good, that's clear. If it does not violate BI assumptions then it does not violate BI or CHSH. You change with the wind on this aspect. 

So it disagrees with QM - unless you make a silly maths error somewhere.

I'm not interested in a classical particle model that cannot reproduce fundamental aspects of QM. Others may do but that's up to them.

Mark

[Bryan Sanctuary]

Mark,

Many others have NOT got classical models (Name them), and those few who tried, failed, because they use fermions and not bivectors.  The classical spin reproduces ALL the properties of spin and much clearer than the SM.  What is spin in the SM:  an excitation in a ubiquitous chiral field with local symmetry preserved by gauge bosons (never observed).  In the BiSM Spin is a real object in 3D space with a quantum limit.  QFT is replaced by GA

Bryan

 

[Mark Hadley]

I repeat, if your work obeys BI, as classical models do, then it is not consistent with QM and is of little interest or relevance.

The talk of fermions and bivectors only serves to confuse what is otherwise a simple evaluate dismissal.

That is what you have presented to the group.

[anton vrba]

Exactly Mark! 

That's why I called Bryan out with: Most importantly, ("BTW, when Alice measures her spin then Bob's is decided.") is the clarifying statement to Bryan's work. It signals a shift in ontology, Bryan is moving away from probabilistic wavefunction collapse (Copenhagen interpretation) to a global hidden variable (GHV).  That does not disprove Bell.

Now Bryan, we are all aware of your claims, repeating them here for a third time (close to spamming) does not help. None of us have the academic clout to help you in promoting recognition. The only way is: Get your work published in a reputable journal, nobody reads mdpi unless directed to it. Alternatively,  organise a centenary Copenhagen Solvay conference next year. Here, you are engaging the wrong guys.   

You will have to do a lot more than producing a couple of pages on your helical and quaternion spin theory, as I pointed out before you need to come up with something more substantial. Produce an ansatz to classical QM explaining some of the points below

1. Photons:

1. For photons explain polarisation not as a superposition of Diirac's opposing rotations.
2. Explain Spin and Orbital Angular Momentum SAM and OAM respectively.
3. Explain Berry phase rates under cyclic evolution in polarisation.

2. Neutrinos

1. Explain neutrinos and not reject them as a convenience
2. Explain family of three

3. Electrons

1. Explain charge quantisation
2. Explain information preservation for positron--electron annihilation
3. Explain family of three 

4. Nuclei 

1. As you are challenging QM ontology you need a better explanation here too.
2. Explain why iron has the highest binding energy

And if you want to be the emperor of physics unite all of above with gravity and explain why clocks tick as they do.. Only once you have done all of above only that can you publish your list and the world will applaud.

Now on page 1067 of the book: Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler. Gravitation. W. H. Freeman, 1973  we find 

That is food for thought

regards

Anton

[Richard Gill]

Don’t be rude and insulting, Bryan.

And don’t be stupid. You’re not extending conventional QM.

[anton vrba]

PS:  Now that it cleared that Bryan seeks an ontological change any discussion Bell or not Bell, Mathematical methods, is it physical, etc are all superfluous.

A discussion on ontological change does not rest on a geometric dissertation with claims like: this is a fermion, this is a boson, neutrinos do not exist, these are all BCS-claims without proof of integration to a field theory.

------ Original Message ------

From "anton vrba" <anto...@gmail.com>

To "Mark Hadley" <sunshine...@googlemail.com>; "Bryan Sanctuary" <bryancs...@gmail.com>

Cc "GeraldoAlexandreBarbosa" <geraldo...@gmail.com>; "Bell quantum foundations" <bell_quantum...@googlegroups.com>

Date 1/29/2026 2:50:11 PM

Subject Re: [Bell_quantum_foundations] Re: BCS-ALV Debate: Physical Meaning of Bivectors