Debate on Bell: Sanctuary versus Gill

[Bryan Sanctuary]

Debate on Bell:  Sanctuary versus Gill

The Topic

Disproof or not of Bell’s theorem, which Bell stated as:

 “If [a hidden-variable theory] is local it will not agree with quantum mechanics, and if it agrees with QM it will not be local.”

 

Clarification:

Sanctuary does not reject Bell’s Inequalities which are accepted here as correct.

CHSH is less than or equal to 2

 

Rules:

Sanctuary first leads Gill through an objective process to show that spin has two channels that can produce EPR coincidences. Bell used only one channel. The second channel disproves Bell’s theorem thereby restoring local reality to physics.

At that initial stage, Gill responds only to the objective steps and does not go out of scope with subjective or ontological arguments. He only agrees or not with the mathematical steps which are not subjective and can only be either right or wrong, so yes or no.

When Sanctuary has finished, Gill will lead, giving his arguments that counter the two channels. Sanctuary responds. The debate continues as to whether Bell’s theorem stands or not.

We assume that the audience knows the topic, so pedagogy is avoided.

I ask that others not interject in this thread.  I have started a second thread, Debate of Bell: comments.  This will keep the debate focused between us.

 

The debaters from Sanctuary’s perspective

Gill is a well-known and respected mathematician in probability theory with considerable credibility.  Gill is the gatekeeper of Bell. He argues against anyone who questions Bell’s work. He is prone to discrediting and dismissing Bell dissenters without substance, rather than engaging.

Sanctuary is a theoretical chemist with a background in spin theory, with little credibility. Richard characterizes him as a quantum crackpot.  Sanctuary’s main interest is not Bell’s work but rather developing the Bivector SM to replace the SM.

 

Motivation and Background

On this forum bell_quantum...@googlegroups.com recent acrimonious exchanges were initiated by Fred Diether III, who presented a disproof of Bell’s theorem based upon the past 20 years of Joy Christian’s work. Diether relentlessly asserted “Bell was wrong bigtime” and bullied, with ad hominem remarks, anyone who attempted to engage. This led to loss in membership and threatened the existence of the group. Sanctuary responded with a short paper showing that Diether and Christian’s method is fundamentally flawed, and that Diether had tacitly included non-locality.

In that three-page paper, the two-channel mechanism was clearly identified, to which Gill did not counter objectively. While this silenced Diether, Gill remarked that Sanctuary’s math was substandard and ridiculed his approach to add the two channels.  Gill asserted without concrete arguments that the two channels are already in Bell’s work, saying it is “obvious” the correlations should be averaged not added.

Sanctuary used Bell’s 64 paper to explicitly show the second channel was missed by Bell and including it disproves his theorem.  

These are attached as pdfs: 

·        Diether’s paper (jqis_1300492);

·        Diether’s errors;

·        Bell’s 64 paper

·        Two-channel paper.

The last paper forms the basis that supports my view for the Debate.

Additionally, Sanctuary asserts that the bivector approach is consistent with experiment. At this stage the arguments are theoretical. Experimental conformities are reserved for future debates.

The Outcome

If Sanctuary’s two channel theory is accepted, then Gill concedes publicly that Bell’s theorem is disproven.

If Gill’s assertion that only one channel exists is accepted, Sanctuary concedes publicly that Bell’s theorem is not disproven.

If the topic is not resolved and ends in a stalemate, then each will write a paragraph that defends their position and reasons to reject the other’s arguments.  Subjective conclusions should be supported by logic, rather than relying on institutional bias.

 

The Stakes and some consequences

With Bell’s theorem repudiated, from Sanctuary’s perspective, the stakes are enormous, far reaching and paradigm shifting.

·        Nature becomes local, real and deterministic

·        Dirac’s near 100-year-old antimatter-matter solution is replaced by the bivector solution.

·        The SM of physics is replaced by the Bivector Standard Model, BiSM.

·        Spin has a classical origin as a bivector. 

·        Spin is not a chiral vector in a 2D Hilbert space, it is a real 2D structure, a classical rotor, embedded in spacetime.

·        Fermions are not fundamental.  Fermions are the polarized blades of bivectors.

·        Spin, as a classical rotor, has a well-defined quantum limit of a double helix of mass.

·        Spin need not be postulated. In isotropy, it is massless and EM inert. In a polarizing field, its blades are forced apart, the polarization, chirality and charge emerge naturally.

·        Pauli matrices do not define quantum spin but rather describe the classical chirality of bivector blades.

·        Point particle electron is replaced by a bivector structure. Structure determines function. The bivector structure hosts energy that can be quantized.

·        QFT is replaced by Geometric Algebra.

·        Particles are not excitations on a ubiquitous chiral field with local symmetry maintained gauge bosons

·        Neutrinos do not exist and billions spent on their detection was wasted.

·        Parity is not violated.

·        Superposition of spin states is replaced by rotation and projection of real objects in spacetime.

·        Teleportation, and Quantum information must henceforth reject the premise of Bell’s theorem.

·        Quantum Computing cannot use qubits since they cannot physically exist. Teleportation is replaced by the internal clock of the bivector with origin from the ZBW.

·        Billions of past research funds into non-locality will have been misdirected.

·        Companies involved in applications of quantum information based on Bell’s theorem, will fail.

·        Tens of thousands of research papers that use Bell’s Theorem are ill based.

·        Thousands of research projects must end.

·        No new research funds should henceforth be committed to non-local phenomena.

·        The 2022 Nobel prize in physics was given for the wrong reason

·        The EPR paradox is resolved and quantum weirdness explained.

·        The ontology of the foundations is changed.

In short, disproof of Bell’s theorem will usher in a paradigm shift. It changes the ontology established in 1925 and persisted until now.

 

Some persons copied

For academic transparency, I copy this to some people who are impacted and I invite them to follow the debate. These include members not in this group: 

·        Sabine Hossenfelder: who may wish to report on the debate from her YouTube channel

·        The 2022 Nobel Prize winners

·        The current chair of the Nobel Prize committee on physics

·        Lee Smolin influential in the Perimeter Institute dedicated to the foundations of physics

·        Charles Bennett, lead author of the 1993 paper on teleportation

·        Nicolas Gisin, advocate of teleportation and quantum cryptography

·        Other members of the academic community involved in the foundations.        

            

Invitation to Gill

I invite Gill to respond and state his position.  I invite him to give his comments and suggestions on the above debate and agree to debate them according to our agreed rules.  I ask him not to start the debate.  I go first; he then follows.

With the agreement by both of us, then the debate can begin.

             

Nature follows logic

Nature is described by mathematics; mathematics goes beyond Nature. We must know how to distinguish that Infamous Boundary articulated by David Wick: https://philpapers.org/rec/WICTIB

             

Two roads diverged in a wood, and I—

I took the one less traveled by,

And that has made all the difference.

                                         -Robert Frost.

             

Bryan Sanctuary

January 16, 2026

[Fred Diether]

Sorry, but CHSH is simply "broken physics".  They forgot to take account of event timing when formulating.

[Richard Gill]

Dear Bryan, dear Bell group

Bryan, please don’t start email lists without consent of participants. Sabine Hossenfelder no longer uses that gmail address for very good reasons.

Bryan writes about myself “He is prone to discrediting and dismissing Bell dissenters without substance, rather than engaging”. This is libellous and untrue. I am prone to engage and find substantial errors. As I am doing right now with this response.

I don’t accept your rules. The statement “Bell used only one channel” is false. Please read “Bertlmann’s socks and the nature of reality” Section 4 “General argument”.

You’ll need to rewrite the rules separating what is generally agreed from what is Sanctuary’s point of view.

There is nothing whatsoever in that “Section 4” which restricts the physics. There can be hundreds of channels through which information propagates in the physical systems involved.

Note in particular Bell’s words “Consider the general experimental set-up of Fig. 7. To avoid inessential details it is represented just as a long box of unspecified equipment, with three inputs and three outputs.”

[Mark Hadley]

Dear Bryan,

I don't know what this nonsense is.

Your work has been criticised in detail and disproven already, in a public forum. It has been debated extensively with the same unanswered criticism being presented again and again in different ways.

The extraordinary claims that you make have been presented by you without justification or derivation.

You present what the world describes as a a local hidden variable model and then claim BI does not apply to it. It does apply. BI is a disproof of your result.

You make a mathematical error combining distributions. This error is on the record and a correction has been given.

Mark

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[anton vrba]

Dear Bryan,  please excuse the audience interjection:

Your proposed debate conflates two distinct issues that must be kept separate.

Bell’s theorem is not an ontological statement.
It is a theorem about the structure of probability models for scalar measurement outcomes under locality (factorization) and statistical independence. Bell is explicitly agnostic about ontology: local or global hidden variables, fields, particles, bivectors, or anything else are all allowed provided they define a Kolmogorov probability space for detector outcomes. Changing the ontology does not alter the theorem.

Accordingly, introducing a second “spin channel,” a bivector ontology, or a BiSM framework does not refute Bell. It simply moves outside the domain of the theorem. That is not a disproof; it is a category change. Bell remains mathematically intact.

If one wishes to replace the Standard Model or its foundations, that is a separate—and much larger—enterprise. Historically and conceptually, such an enterprise must pass through Maxwell theory and the operational foundations of measurement, as already emphasized by Poincaré in 1906: (see below) invariance precedes ontology, and geometry is fixed by how measurements are defined, not by postulated internal structures.

Your program does not engage this level. It replaces quantum formalism with a new ontology while leaving untouched the operational and probabilistic framework to which Bell applies. That is why debates framed as “Sanctuary versus Bell” or “Sanctuary versus Gill” generate heat but no resolution.

In short:

• Changing fundamental assumptions does not invalidate Bell.

• Bell is agnostic to BiSM versus SM.

• A genuine paradigm shift would have to re-derive measurement, locality, and probability from the ground up—starting with Maxwell, not bypassing him.

For these reasons, I do not see the proposed debate format as capable of resolving the issue it claims to address.

Regards,
Anton

"If we were to admit the postulate of relativity, we would find the same number in the law of gravitation and the laws of electromagnetism—the speed of light—and we would find it again in all other forces of any origin whatsoever. This state of affairs may be explained in one of two ways: either everything in the universe would be of electromagnetic origin, or this aspect—shared, as it were, by all physical phenomena—would be a mere epiphenomenon, something due to our methods of measurement.  How do we go about measuring? The first response will be: we transport solid objects considered to be rigid, one on top of the other. But that is no longer true in the current theory if we admit the Lorentzian contraction. In this theory, two lengths are equal, by definition, if they are traversed by light in equal times.

Perhaps if we were to abandon this definition Lorentz’s theory would be as fully overthrown as was Ptolemy’s system by Copernicus’s intervention. Should that happen someday, it would not prove that Lorentz’s efforts were in vain, because regardless of what one may think, Ptolemy was useful to Copernicus. "

M. H. Poincaré (1906). Sur la dynamique de l’électron. In: Rendiconti del Circolo matematico di Palermo 21.1, pp. 129–175. Translated by Scott Walter In J. Renn (ed.), The Genesis of General Relativity Vol. 3: Theories of Gravitation in the Twilight of Classical Physics; Part I (Boston Studies in the Philosophy of Science 201)

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

From "Bryan Sanctuary" <bryancs...@gmail.com>

To "Bell inequalities and quantum foundations" <bell_quantum...@googlegroups.com>

Cc sabine.ho...@gmail.com; Anton.Z...@oeaw.ac.at; alain....@institutoptique.fr; jo...@jfcbat.com; "Bengt Nordén" <nor...@chalmers.se>; olle.e...@physics.uu.se; lsm...@perimeterinstitute.ca; "Han Geurdes" <han.g...@gmail.com>; "Karl Hess" <karl...@gmail.com>; ben...@watson.ibm.com; Nicola...@unige.ch

Date 1/17/2026 1:48:49 AM

Subject [Bell_quantum_foundations] Debate on Bell: Sanctuary versus Gill

[Mark Hadley]

Anton,

Introducing a second spin channel does not move the model outside the realm of BI.

BI make no assumptions about how many channels there are.

If you are in any doubt about that: when you have local hidden variables for two distinct channels you can explicitly rewrite it as a single local  hidden variable function as required to enter into the BI proof.

Bryan knows this criticism, it's been published on the forum and peer reviewed.

Cheers

Mark

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[anton vrba]

Thank you, Mark — you are right, and I realized that shortly after sending my previous reply.

It became clear to me once I read Richard post with the diagram (three inputs, three outputs) and that Bell is agnostic to the internal structure of the inputs. Multiple “channels” can always be absorbed into a single local hidden variable without leaving the scope of Bell’s theorem. So the channel count itself is not the issue.

What I am now wondering is whether Bryan may be conflating two distinct notions: 

• a local hidden variable in Bell’s sense, versus

• a single global geometric hidden variable with internal structure that is not probabilistic in the Kolmogorov sense.

Here an extract from the chatGPT analysis of Bryan's work

which makes clear, the same internal object feeds both outcomes. This is a single global structure with multiple contextual projections, not independent local random variables in Bell’s sense.

If the latter is what is intended, then the presentation as a “disproof of Bell” is, in my view, misleading. Bell remains intact. However, framed differently, the work could be read as something else entirely: a proposal that replaces probabilistic description with causal geometric structure, while reproducing the observed correlations.

From that point of view, the claim would not be “Bell is wrong,” but rather:
here is a deterministic, possibly global, geometric model that reproduces Bell-test statistics without invoking nonlocal influences in spacetime.

That would shift the discussion away from Bell’s theorem itself and toward the interpretation of quantum mechanics (e.g. Copenhagen vs causal/geometric alternatives), where Bell is explicitly agnostic.

I offer this as a constructive reframing, not as a dismissal.

Regards,
Anton

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

From "Mark Hadley" <sunshine...@googlemail.com>

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

Cc "Bryan Sanctuary" <bryancs...@gmail.com>; "Bell inequalities and quantum foundations" <bell_quantum...@googlegroups.com>

Date 1/17/2026 10:48:51 AM

Subject Re: [Bell_quantum_foundations] Debate on Bell: Sanctuary versus Gill

[Richard Gill]

A friend of mine, a guy called Engel Wichmann (successful business man, now a part time “mature student” at the University of Amsterdam - he chats to Gerard ‘t Hooft and Eric Verlinde and the like) is deeply invested in a proposal that radically replaces probabilistic description with causal geometric structure. 

It is inspired by QFT and is explicitly non local and superdeterministic.

[Mark Hadley]

Dear Anton,

I think you are suggesting that Bryan has used a global variable dependent on detector angles. Which would be a simple non local hidden variable theory to which BI does not apply.

I don't know if you are right or not, but certainly Bryan claims that both channels independently satisfy BI.

Bryan only gets a non trivial result because he makes an error combining the two channels. He incorrectly calculates the resultant correlation coefficient. This has been pointed out to him a hundred times and he has been given a proven correct calculation.

Once the error is corrected, his outcomes are consistent with BI and totally unremarkabke.

Bryan can do these calculations correctly himself, but he will not admit the error due to embarrassment.

You are probably aware that Bryan lost a, rather foolish,  bet with Richard. Bryan refuses to pay up. He clings to this result as evidence that he won the bet. Which is another reason that he does not engage with the criticism. But he lost the bet,with or without this result. 

Cheers

Mark

[Richard Gill]

Dear all

I hereby forward you my same day reply to Bryan’s 17 Jan proposal to hold a debate, which he sent to many persons as well as a Google discussion group to which we both belong.

I did not reply to everyone, only to Bryan and the aforementioned group, because spamming like this is “not done”.

As you can read: I did not refuse to debate. I told Bryan that I would not debate publicly with him under the rules which he had proposed (out of the blue). I asked for discussion of the rules before we publicise them.

Bryan never answered that message. 

He did sent a weird message on 18 January with Subject “Careful” and content "You should be careful what you say.”. Apparently he was about to embark on a major hate campaign against me.

Richard

Begin forwarded message:

From: Richard Gill <gill...@gmail.com>

Subject: Re: [Bell_quantum_foundations] Debate on Bell: Sanctuary versus Gill

[Mark Hadley]

Bryan hides from scrutiny.

When I presented a disproof of his work I offered to go through it with him line by line, to see if there was a point of disagreement. He refused to engage ... Much like Fred does.

Mark

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Richard

Sent from my iPad

On 17 Jan 2026, at 02:49, Bryan Sanctuary <bryancs...@gmail.com> wrote:



Debate on Bell:  Sanctuary versus Gill

The Topic

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[anton vrba]

Please be careful when replying to all, only Richard has the right to defend himself to personalities external to the group.

I think the next step in this to-and-fro is to make a collaborative comment on Bryan's mdpi-published works and submit it to mdpi so that the academic record is corrected at mdpi.  

regards
Anton

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

From "'Mark Hadley' via Bell inequalities and quantum foundations" <Bell_quantum...@googlegroups.com>

To "Richard Gill" <gill...@gmail.com>

Cc "Bryan Sanctuary" <bryancs...@gmail.com>; "Bell Inequalities and quantum foundations" <Bell_quantum...@googlegroups.com>; kathrin...@oeaw.ac.at; nicole.tc...@institutoptique.fr; jo...@jfcbat.com; "Bengt Nordén" <nor...@chalmers.se>; olle.e...@physics.uu.se; lsm...@perimeterinstitute.ca; "Han Geurdes" <han.g...@gmail.com>; "Karl Hess" <karl...@gmail.com>; ben...@watson.ibm.com; Nicola...@unige.ch

Date 1/18/2026 2:48:37 PM

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CAN%3D2%2Bo1rN7MmvD1TSACDO_2FXA1XsQ7V_z0Q%3DkRVTUtb4Z3Xxg%40mail.gmail.com.

[Mark Hadley]

Dear Anton,

That's an idea, but I doubt they will be interested. All sorts of rubbish gets published. And ignored. The journals don't want the work or bad publicity of correcting an insignificant paper.

Actually it's main significance is in this forum where Bryan lost his foolish bet but uses the paper to try and justify not paying up.

Mark

[Richard Gill]

Dear Bell-group friends

To continue the debate.

Bryan wrote “My goals are academic and fundamental. I prove Bell’s theorem is wrong, and Gill dismisses it. Gill and I should debate or he must capitulate. Bell’s theorem assumes a single Kolmogorov probability space. I found a second, corresponding to vector and bivector degrees of freedom. This disproves Bell’s theorem.”

Such a debate requires a specification of Bell’s theorem. Bryan likes to quote a Bell-one-liner “But if his extension is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local. This is what the theorem says.” (Locality in quantum mechanics: reply to critics. Epistemological Letters, Nov. 1975, 2–6). “His extension” refers to suggestions by Lochak concerning possible extensions of the Bohmian hidden variables model for EPR-B. Perhaps extensions involving multiple “channels”?

The context is important. I think that Bell would have considered the following to be his “theorem”:

No Kolmogorov probability space Lambda exists on which are defined random variables A_a and B_b, taking values in {-1, +1}, and such that E(A_a B_b) = a . b for all a and b, real unit vectors in R^3.

Bryan: do you agree that you have not disproved this particular mathematical theorem?

A fact: many people are confused by the typical mathematician’s proof of a *non*-existence theorem: a proof by contradiction which (by definition) starts by assuming the opposite to what the mathematician wants to prove.

Anyway, my point is that Bell’s theorem does not *assume* a single Kolmogorov probability space. It assumes a correlation function.

Bell says explicitly that he restricts himself to the outcome space {-1, +1}.

Bell actually says explicitly that what is precisely going on behind the scenes is irrelevant. He merely assumes that it is something classical in nature: “In a more formal way, assuming that any Hermitian operator with a complete set of eigenstates is an ‘observable’, the result is easily extended to other systems. If the two systems have state spaces of dimensionality greater than 2 we can always consider two-dimensional subspaces and define, in their direct product, operators σ_1 and σ_2 formally analogous to those used above and which are zero for states outside the product subspace. Then for at least one quantum mechanical state, the ‘singlet’ state in the combined subspaces, the statistical predictions of quantum mechanics are incompatible with separable predetermination” (Bell, 1964).

Bell (1964) assumed binary outcomes and separable predetermination. He showed that these two assumptions together are incompatible with conventional quantum mechanics.

[Bryan Sanctuary]

Richard,

I acknowledge that my use of the term “Fainthearted” was provocative and unwelcome. I will not use it again, provided that future exchanges refrain from personal characterizations.  For the record, over the past two decades I have been repeatedly subjected to remarks questioning my credentials, my understanding of basic mathematics, and even my mental capacity, rather than engaging with the substance of my arguments. For example:

“I suspect that there could be some gaps (or loss of memory) in Bryan’s basic math education as well as in Fred’s — cf. the confusion about whether you can add correlations or take convex combinations of them. Go back to basics! The textbooks you learnt university level exact sciences math from.”

Such statements do not advance understanding and serve only to discredit rather than engage. I will ignore further remarks of this kind and also third-party accusations about my tone or alleged “bad-mouthing” unless supported by evidence. My concern is solely with the scientific content.  

I am glad that RIchard agreed to debate.

The only substantive claim repeatedly asserted by several defenders of Bell’s theorem is that my work has already been “proven wrong,” and that the matter is therefore closed. In every case, I responded by pointing out that these refutations conflate two distinct correlation channels into a single ensemble. This is not a vacuous claim but the central technical point of my work: spin correlations possess two complementary geometric sectors, and Bell’s original formulation treats them as one.

I am allowed to disagree with prevailing interpretations, and disagreement is not resolved by assertion alone. The existence or nonexistence of a second correlation channel is a technical question, not a matter of authority or consensus.

Geraldo made substantial comments too. I thank him and I will answer them in due course.

That said, I suggest that email threads are not a suitable medium for resolving a foundational issue of this importance. They do not provide a level playing field, encourage digression, and make it difficult to maintain focus. For example, Richard has already presented arguments against my position (see previous email) without engaging me or with the actual construction I have presented.

The universal acceptance and scope of Bell’s theorem are foundational to the current paradigm. I believe the issue deserves a structured and fair examination. I therefore propose the following process:

1. Richard and I jointly and privately agree on three independent scientists to act as adjudicators.
   They must declare no conflict of interest and no prior commitment to either position. Once we have agreement, their names are made public.
2. I submit a written report of my two-channel construction and its implications for Bell’s theorem.
3. Richard submits a written report of his position in answer to my report.
4. Each of us is permitted one written short additional response to the other.
5. During the adjudication period, neither of us engages publicly on the matter, except to answer clarification requests from the adjudicators.
6. The adjudicators are encouraged to consult among themselves, and request clarifications from Richard and me as needed.
7. At the conclusion, they issue either:

               --A single joint report if agreement is reached,    

               --Two reports if disagreement remains.

           

          8. All  report(s) are made public on the forum,  after which open discussion is encouraged.

This process would provide a level playing field, maintain focus, and allow the scientific issues to be assessed on their merits.

If you are willing to proceed in this way, I believe it would be a constructive step forward.

Bryan

[Mark Hadley]

Bryan,

Your maths is wrong. It's simple maths. It's wrong and you have been given a simple proof that it's wrong.

Bells theorem applies to two channels. You never explain why not. And I've given you a mathematical proof that it does.

There is no place for a debate in this.

If you can do the maths then you will know you are wrong. If you can't do the maths then how will a debate solve it. At least three serious academics have checked your work and all if them found the same problem and they told you about it.

Mark

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[Bryan Sanctuary]

Mark

I have no interest in your views.

Bryan

[anton vrba]

Dear Bryan, I do not know of a single case where a true mathematical theorem, that is a statement that has been definitively proven using logic and axioms has been disproved. By this definition, a true theorem can never be "disproven."

On the other hand a theory is a proposition of mathematical formulas that describe something.  So Newton's theory of gravitation was replaced by Einstein's theory of general relativity.

Now, you have produced a Sanctuary theory, which is a bivector spin framework that constitutes a classical geometric theory in which Bell’s theorem does not apply, due to differing assumptions about probability and measurement.  You cannot consider the Sanctuary theory as a counter example to Bell's theorem, the Sanctuary theory is not a mathematical rigorous theorem, rigourous theorems have no heuristic assumptions the Sanctuary theory is build on on a number of heuristic  assumptions.

If you want to disprove Bell's theorem you either (1) need to provide a formal mathematical theorematic prove showing a logical or axiomatic misstep by Bell or (2) provide a rigorous theorem as a counter example.

A Sanctory theory with heuristic assertions and assumptions cannot disprove a formal mathematical theorem.   

There is reason why it is called Bell's theorem and not Bell's theory nor the Bell's conjecture

So any arguments about mathematical techniques being right or wrong, or long winded arguments and debating challenges with Richard are fruitless endeavours, a theorem remains a theorem.

But now to be positive, what you did do: you provided a 

• A coherent classical geometric model of spin, formulated using bivectors and quaternions;
• A contextual correlation framework that produces expectation values resembling quantum correlations, but arising from a shared global algebraic object rather than ±1-valued independent random variables;
• A demonstration that the standard Kolmogorov probabilistic assumptions underlying Bell-type non-existence theorems are not satisfied, clarifying the domain in which Bell’s theorem applies.

Regards
Anton.

[Mark Hadley]

Bryan,

Oh and why would that be? Perhaps because I have been so precise about your erroneous work.

For years you have falsely claimed that nobody had found a fault in your work.

I've disproven your work. With maths, not opinions. Mathematical facts. That you refuse to respond to.

They prove your work is false. Do you understand that? If so, have you found fault with my proofs? Or do you accept that your work is wrong. If you don't understand my disproofs then Richard is right to be rude about your maths.

What is worse, a few months ago you actually invited comments on the addition formula. Claiming that you would collate the responses and reply. I'm still waiting for the reply. I would warn Richard and others that with the debate  you are trying to turn it into a circus with not intention of respecting the outcome.

If a high school student gets simple maths wrong, you don't organise a debate and panel if experts, it's totally inappropriate.

Mark

[Bryan Sanctuary]

Mark,

Like I said, you hide behind orthodoxy.  I have no interest in anything you say, and you continue to question me rather than the logic.

Bryan

[Bryan Sanctuary]

Anton, 

I definitely have no interest in what you say.  Please refrain

Bryan

[Mark Hadley]

No Anton,

Definitely not. He has not produced any work at all that departs from Bells assumptions.

He makes the astonishing assertion that BI does not apply to a two channel distribution. That is a false statement and I have disproven it. Months ago and reposted recently.

Since Bryan never substantiated his wild assertion, we have BI and my proof that Bryan's model is in conformance.

His papers also have a false elementary mathematical step without which his papers become an unremarkabke LHV model with satisfies BI and cannot therefore reproduce the results of QM. The paper is an academic irrelevance.

Mark

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[Bryan Sanctuary]

Mark,

Your claims are wrong.  Like I said, do not rely on orthodoxy to guard Bell, it has led a lot of people in the wrong direction.

Please refrain from comments, they make you sound repetitive and weak.  Please get my message, I have no interest in anything you say.

Bryan

[Mark Hadley]

Bryan. I have given you a mathematical proof of the mistakes in your paper.

Just high school maths. Do you call that orthodoxy?

And I call in you to try and prove the two big assertions that you make. If you make extraordinary claims it is up to the author to justify them.

Mark

[Bryan Sanctuary]

Mark,

You do not get it, I am being polite to tell you I have no interest in your comments. and I will no longer respond.

Bryan

[Mark Hadley]

You are in a forum about BI.

You are making false, and quite frankly stupid, statements about the theirem. I will respond with science and maths. That's the purpose of this forum.

It will be retentive, because high school maths does not change just because Bryan doesn't like it. If you want to stop the repetition then withdraw you work from the forum.

That's the science. When you behave with a lack of integrity I will call you out.

Mark

[Mark Hadley]

Are you telling the forum that you have no interest in people who have found the faults in your work!!!!

Why not shut me up. Take my maths and show where it is wrong.

Mark

[Bryan Sanctuary]

Mark,

If it is HS math, Richard will easily prevail.  I told you that your proof falls apart in your hands. It is not just flawed but "silly" and "foolish".  because you conflate two elements of reality like Bell does, and I contest that.  I will not say more, except, please accept that what you say has no effect on me and I have no interest in any of your views.

Bryan

[Mark Hadley]

Richard has already told you the same thing.

Every step of the maths is valid for your model.

The addition formula is specially about combining two distributions. 

And the application of BI also takes two distributions and shows that BI applies.

But you know that? Every step of my maths is correct and irrefutable.

Mark

[Bryan Sanctuary]

Mark,

You missed the clue:  Bell thought he disproved von Neumann's theorem, (an example of disoroving such a theorem you sought), and I continue to assert, NO interest and ANYTHING you say.  .

Richard said after Faintheart, that he would debate. I am waiting for his reply to the set up.

Bryan

[Mark Hadley]

Bryan, your maths is wrong. What's the point of a debate. How will that resolve it?

Just say " explain line 6" or "I don't agree with the assumption on line 2" that's how we resolve maths.

Why can't you do that?

You are very rude, you specifically asked for precise criticism and then when I take the trouble to do that you discard it 

Mark 

[Bryan Sanctuary]

Mark,

First, scientists must challenge.  I have points that you have not encountered, and recently found.  You do not know those.  

There is an additional reason to prove me wrong. The consequences are far-reaching and profound. I made a list of some of the consequences of disproving Bell's theorem.   The stakes are so high, I cannot be dismissed, which is why I will not give up. I am serious, and you appear not to be,

Bryan

·        The ontology of the foundations is changed.

·        Nature is local, real, and deterministic.

·        The EPR paradox is resolved, and quantum “weirdness” is explained.

·        Bell’s theorem is invalid as a foundation for physics.

·        Non-locality is not a physical phenomenon.

·        Parity is not violated in Nature.

·        Quantum field theory is replaced by geometric-algebra.

·        The Standard Model is replaced by the Bivector Standard Model (BiSM).

·        Dirac’s matter–antimatter interpretation is replaced by a bivector.

·        Particles are not excitations of a ubiquitous chiral field with gauge-maintained local symmetry.

·        Spin has a classical origin as a real bivector embedded in spacetime.

·        Spin is not a chiral vector in a 2D Hilbert space but a real two-dimensional rotor.

·        Spin does not need to be postulated: in isotropy it is massless and electromagnetically inert;

·        In a polarizing field, polarization, chirality, and charge emerge naturally.

·        The point-particle electron is replaced by an bivector structure, whose geometry determines its function.

·        Energy is hosted by bivector structure and becomes quantized through geometry.

·        The quantum limit of spin is a confined double-helical mass structure.

·        Fermions are not fundamental particles but polarized blades of bivectors.

·        Pauli matrices describe classical bivector chirality, not intrinsic quantum spin.

·        Superposition of spin states is replaced by rotation and projection of real objects in spacetime.

·        Teleportation is not physically possible;

·        Quantum information must abandon Bell-based assumptions.

·        Quantum computing abandons qubits; the bivector internal clock  replaces it

·        Neutrinos do not exist..

·        Past and current research programs based on non-locality are misdirected.

·        A large fraction of the Bell-based literature is structurally unsound.

·        Many ongoing research programs premised on non-local phenomena must terminate.

·        Future research funding should not be committed to non-local interpretations.

·        Technological efforts based on Bell-theorem-driven quantum information will fail.

·        The 2022 Nobel Prize in Physics was awarded for the wrong physical reason. 

[anton vrba]

Mark, I think Bryan who wants to change the ontology of physics will be better off organising a 2026 Copenhagen Solvay Conference than trying to find recognition on this forum. 

Bryan, having no interest, why?  I have my ideas why but will not voice them as that would get personal.

You also have stated clearly in a past discussion here on the forum, that your model is mechanical, about electrons and not photons.  You do not care about Maxwell, but you show travelling bivectors, labelling them as Q-Spin in free flight.  What is in free flight? A particle or marble as you already excluded photons.

But,  Bell-CSHS experiments are optical experiments, Q-Spin in free flight is not a photon, hence we have no Bell-CSHS test, hence Bell theorem is not applicable to Sanctuary-theory.

Then this preprint Beta Decay with No Neutrinos and Parity Conservation,  https://www.preprints.org/manuscript/202401.0118/v3  contradicts experimental evidence, more than enough reason that your ansatz has no scientific interest.

Mark and Richard have shown you mathematical shortcomings and interpretation errors regarding Bell. I have shown you shortcommings in various papers, why a theory cannot disprove a theorem, and now have shown you by your own words and explanations the contradictory nature of Q-Spin to natural philosophy. 

I am at a loss of words for your continual insistence for a debate that you cannot win, no adjudicator who needs to study your complete work to make sense of the debate contents, will support you on the grounds that I have listed.   Richard only needs to collate his, Mark's and my comments, If he does so your dismissal of Mark's and my views are short-sighted as you then need to answer them and not ignore them.

Regards
Anton 

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

From "Mark Hadley" <sunshine...@googlemail.com>

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

Cc "Bryan Sanctuary" <bryancs...@gmail.com>; "Richard Gill" <gill...@gmail.com>; "Bell inequalities and quantum foundations" <bell_quantum...@googlegroups.com>

Date 1/20/2026 10:09:48 PM

Subject Re: [Bell_quantum_foundations] Debate on Bell: Sanctuary versus Gill

[Mark Hadley]

The stakes are high. bI is exciting, I expect an explanation to come in due course.

How can you say I am not serious. I've studied the paper that you presented. I've found two fatal flaws and given a mathematical proof of both. What could be more serious?

The stakes are high, your claims are astounding.but the significant parts you present without proof, without justification.

You state without proof that BI does not apply to two channels. The onus is on you to prove it.

You combine expectation values in a way that everyone says is wrong, but you don't drive the result. It's simple maths. The onus is on you to prove you peculiar result. But you make no attempt to prove it or justify it or relate to a normal proof.

[Bryan Sanctuary]

Anton

No neutrino has been detected. 

Bryan

[anton vrba]

Bryan,  two points (the second is philosophical and above the correct or incorrect maths arguments here)

(1) in reply to "No neutrino has been detected" and where have I seen a Q-Spin in free flight?

(2) I am serious in suggesting, should you be that convinced, to organise a 2026 Copenhagen Solvay Conference.  The numerous points you list can only be taken seriously once you linked Q-Spin to physical phenomena and not impose on nature a Sanctuary-theory. Nature does not bend its laws to figments of imagination created by human ignorance.

Please study fundamental physics, the 19th century natural philosophers where more thoughtful than modern physicist.  Today you have a community of seemingly specialist who have no sense of the greater picture.  You seem to be a specialist in Q-Spin (what ever that is) but have you read or know intimately the works of Faraday,  Ampere, Maxwell, Heaviside, Poincare, etc and the integral theorems of Gauss, Green and Stokes, all necessary to understand Electromagnetics. 

Poincare is telling us where to look:

If we were to admit the postulate of relativity, we would find the same number in the law of gravitation and the laws of electromagnetism—the speed of light—and we would find it again in all other forces of any origin whatsoever. This state of affairs may be explained in one of two ways: either everything in the universe would be of electromagnetic origin, or this aspect—shared, as it were, by all physical phenomena—would be a mere epiphenomenon, something due to our methods of measurement.  How do we go about measuring? The first response will be: we transport solid objects considered to be rigid, one on top of the other. But that is no longer true in the current theory if we admit the Lorentzian contraction. In this theory, two lengths are equal, by definition, if they are traversed by light in equal times.

Perhaps if we were to abandon this definition Lorentz’s theory would be as fully overthrown as was Ptolemy’s system by Copernicus’s intervention. Should that happen someday, it would not prove that Lorentz’s efforts were in vain, because regardless of what one may think, Ptolemy was useful to Copernicus.

M. H. Poincaré (1906). Sur la dynamique de l’électron. In:  Rendiconti del Circolo matematico di Palermo  21.1, pp. 129–175.  Translated by Scott Walter  In J. Renn (ed.),  The Genesis of General Relativity Vol. 3: Theories of Gravitation in the Twilight of Classical Physics; Part I  (Boston Studies in the Philosophy of Science 201)

Poincaré is not making a claim about electromagnetic reductionism. He is making a claim about measurement, convention, and invariance. His core point is:

If all interactions share the same invariant speed, then either
(a) one interaction is ontologically fundamental, or
(b) the invariant speed is a structural feature of how we measure and relate phenomena, not of what phenomena are “made of”.

He explicitly keeps both options open. But, I interpret Poincaré’s instinct was that Maxwell’s theory is not just another force law. It is:

* the first fully relativistic field theory (speed of light constant),
* the first theory where invariance precedes ontology,
* the first theory where geometry constrains dynamics.

This is why Poincaré suspected that unification, if it exists, must pass through Maxwell—not around it. Because, Maxwell’s equations: 

* already contain c, 
* already demand Lorentz symmetry, 
* already unify electricity, magnetism, and optics, 
* already force space-time (R^3+R) structure onto matter.

Every later theory inherits this structure and must conform to it 

* Gravity did not introduce c; it had to accommodate it. 
* Quantum theory did not introduce c; it had to respect it.

So, in my opinion, we must understand Maxwell "fully" and develop Maxwell (find the missing links) as a possible path to unification. Sanctuary-theory definately will not do in its present form.

And then consider William Mitchinson Hicks put it in his 1895 presidential address [1] :  

 “The ultimate aim of pure science is to be able to explain the most complicated phenomena of nature as flowing by the fewest possible laws from the simplest fundamental data. A statement of a law is either a confession of ignorance or a mnemonic convenience. It is the latter, if it is deducible by logical reasoning from other laws. It is the former when it is only discovered as a fact to be a law.

While, on the one hand, the end of scientific investigation is the discovery of laws, on the other, science will have reached its highest goal when it shall have reduced ultimate laws to one or two, the necessity of which lies outside the sphere of our cognition. These ultimate laws—in the domain of physical science at least—will be the dynamical laws of the relations of matter to number, space, and time. The ultimate data will be number, matter, space, and time themselves.

When these relations shall be known, all physical phenomena will be a branch of pure mathematics. We shall have done away with the necessity of the conception of potential energy, even if it may still be convenient to retain it; and—if it should be found that all phenomena are manifestations of motion of one single continuous medium—the idea of force will be banished also, and the study of dynamics replaced by the study of the equation of continuity.”

Now take Hicks word seriously: A statement of a law is either a confession of ignorance or a mnemonic convenience

Your work has may confessions of ignorance,  Maxwell has none, Bell's theorem has none, Einstein's theories has many, Copenhagen interpretation has many.  Ontology will not change from one statement of ignorance to another statement of ignorance. Ontology will only change when somebody shows that  all physical phenomena will be a branch of pure mathematics. You are not doing pure mathematics.

[1] Hicks, W.M. (1895) “The Presidential Address,”  Nature: A Weekly Illustrated Journal of Science, 52, p. 472. https://dbc.wroc.pl/Content/17181/PDF/19319.pdf

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

From "Bryan Sanctuary" <bryancs...@gmail.com>

To "Mark Hadley" <sunshine...@googlemail.com>

Cc "Richard Gill" <gill...@gmail.com>; "Bell inequalities and quantum foundations" <bell_quantum...@googlegroups.com>

Date 1/20/2026 11:37:34 PM

Subject Re: [Bell_quantum_foundations] Debate on Bell: Sanctuary versus Gill

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CALLw9Yw9zJyQKkE3AA1F1Cxn4i5ZjkjTuKwud6CmfSLvx9EJpw%40mail.gmail.com.

[Richard Gill]

Dear Anton

Hicks’ address and your closing comments are wonderful!

I’m in full agreement with everything you and Mark have written in the last 12 hours.

But I will discuss privately with Bryan the idea to have a formal debate with a jury of three. There is a concurrent FaceBook discussion which provides some possible names of persons who are interested but haven’t taken a strong position yet.

Richard

Sent from my iPad

On 21 Jan 2026, at 01:38, anton vrba <anto...@gmail.com> wrote: