Re: The correct derivation

[Mark Hadley]

Bryan,

I do not assume a single space. Quite the opposite. The derivation and illustration are all for two spaces. As is immediately obvious.

 

Bells makes no assumption about the spaces.

The maths derivation is high school algebra. It is valid from step to step, from start to finish. If you want to dismiss them show the fallacy.

Yesterday you claimed that I had not sent you a refutation, had not shown why you were wrong. That was false and insulting - as everyone can see. I sent these to you and you never responded. That's why you should apologise.

Your work has been refuted. Until you show a mistake in my maths, or a false step in Bells, or account for the absurdities revealed in the other email. 

Your ability to accept criticism matches Fred's You are more polite than Fred, but seek to profit from your false statements.

Mark

On Wed, 14 Jan 2026, 09:02 Bryan Sanctuary, <bryancs...@gmail.com> wrote:

Dear Mark,

Thank you for going back to find your past argument. They all fall into the same category and I rejected them at that time,   You  assume a single space and therefore is fallacious. The correlations arise from two spaces. That point is now clearly articulated in the Two channels note, and it is there you must find errors. So I never accepted those responses, and I never agreed with them. You, Richards, Jan Ake  and all argued as you do, I did not agree, so it was a stalemate.   You must find errors in that note,

You ask for an apology  from me!!!!!!!!!  You repeatedly called me a liar, dismissed my arguments as a High School math error, and made personal comments, to which I did not reciprocate in kind. You are living in a fantasy world of Bell arrogance and a signal probability space.  I will never apologize when faced with such belligerent behavior. You arrogantly dismiss my responses, assuming you have answered it, when you had failed. 

Your only recourse is to find errors in my two channel paper, which you have not done. I want your capitulation to the two channels, which by your silence you have already tacitly given.

I hope this is clear: I respond only to technical arguments, like the abortive one you gave here.

Bryan

Best regards,
Bryan

On Tue, Jan 13, 2026 at 11:42 PM Mark Hadley <sunshine...@googlemail.com> wrote:

Dear Bryan,

I sent this as far back as 22feb 2023

It derives the correct formula for combining two populations.

You never responded.

I expect an apology: you have said dozens of times that nobody found fault in your work. Here it is in detail and unanswered.

Cheers

Mark 

[Mark Hadley]

Cos theta does not feature in the derivation of bells Inequalities

Nor my derivation of correlation coefficient 

Nor in any of the qualitative refutations.

This snippet of a paper does not relate to or affect any of the disproofs.

If you want to refute BI then use the CSHS version it's the simplest and clearest.

Let's be clear. I have disproven your work in four different ways. I claim they are all valid, but if only one of them is valid, then your work is disproven. 

To recover your work and credibility you need to deal with each disproof.

Mark

Mark

Mark 

On Wed, 14 Jan 2026, 12:09 Bryan Sanctuary, <bryancs...@gmail.com> wrote:

Dear Mark

Bryan

On Wed, Jan 14, 2026 at 12:03 PM Mark Hadley <sunshine...@googlemail.com> wrote:

Bryan,

If you claim that Bell makes a hidden assumption. Show us where he uses that assumption in the derivation. Nobody else can see it. Until you show where that is used it remains a figment of your imagination.

My correlation derivation is a few simple maths steps. If you think that is wrong you should show us the step that is invalid in your physics

You have a very strange addition rules for correlations. It is remarkable, it has been challenged by people who have studied your paper. And it was never derived. It is to say the least fundamentally important to your result and quite remarkable. As a scientist you need to derive results that are important to you, disputed, and unique to your paper. The standard combination of distributions is well known and is derived, not assumed.

And you have not addressed the qualitative criticism of your addition formula - that it can give correlations larger than 1, and that the observed correlation is independent of the number of vector and covector events. That's how scientists and mathematicians do a sanity check on a strange equation.

So your work has been challenged in three independent ways and you have not been able to respond to them as a scientist. 

Your result has been disproven by Bell, it has been disproven by the derivation of correlation coefficients and shown to be nonsensical based on a qualitative analysis.

There is nobody, including you, who can defend your work against these refutations. And I think you know that, but cannot emotionally admit it.

Mark

On Wed, 14 Jan 2026, 10:23 Bryan Sanctuary, <bryancs...@gmail.com> wrote:

Mark,

I only reply because you raised technical points.  Your analysis confirms Bell's statistics, and I refute that then and now. Your arguments in no way assail my two-channels.  Of course Bell assumes a single space, as I clearly show in my two-channel paper. You have only convinced yourself, or other gatekeepers of Bell, without moving me. 

You conflate the two sources into one exactly the same error as Christian and Diether made, Your arguments are no threat or answer me.  Also mine works and yours does not.

Bryan

[Mark Hadley]

[Bryan Sanctuary]

Mark,

I only reply because you raised technical points.  Your analysis confirms Bell's statistics, and I refute that then and now. Your arguments in no way assail my two-channels.  Of course Bell assumes a single space, as I clearly show in my two-channel paper. You have only convinced yourself, or other gatekeepers of Bell, without moving me. 

You conflate the two sources into one exactly the same error as Christian and Diether made, Your arguments are no threat or answer me.  Also mine works and yours does not.

Bryan

On Wed, Jan 14, 2026 at 10:30 AM Mark Hadley <sunshine...@googlemail.com> wrote:

[Bryan Sanctuary]

Dear Mark

Bryan

On Wed, Jan 14, 2026 at 12:03 PM Mark Hadley <sunshine...@googlemail.com> wrote:

Bryan,

If you claim that Bell makes a hidden assumption. Show us where he uses that assumption in the derivation. Nobody else can see it. Until you show where that is used it remains a figment of your imagination.

My correlation derivation is a few simple maths steps. If you think that is wrong you should show us the step that is invalid in your physics

You have a very strange addition rules for correlations. It is remarkable, it has been challenged by people who have studied your paper. And it was never derived. It is to say the least fundamentally important to your result and quite remarkable. As a scientist you need to derive results that are important to you, disputed, and unique to your paper. The standard combination of distributions is well known and is derived, not assumed.

And you have not addressed the qualitative criticism of your addition formula - that it can give correlations larger than 1, and that the observed correlation is independent of the number of vector and covector events. That's how scientists and mathematicians do a sanity check on a strange equation.

So your work has been challenged in three independent ways and you have not been able to respond to them as a scientist. 

Your result has been disproven by Bell, it has been disproven by the derivation of correlation coefficients and shown to be nonsensical based on a qualitative analysis.

There is nobody, including you, who can defend your work against these refutations. And I think you know that, but cannot emotionally admit it.

Mark

On Wed, 14 Jan 2026, 10:23 Bryan Sanctuary, <bryancs...@gmail.com> wrote:

[Bryan Sanctuary]

Dear Mark,

Years ago I looked at Bell and when I understood it meant non-locality was the consequence, I said to myself, that is absurd.  That, however, is not enough.  I must prove it is absurd and so there must be an alternate explanation.  It is not enough to say my work is nonsense etc.  You must show it. I suggest that you look at the geometric product of Pauli matrices and see that it consists of a symmetric and antisymmetric part.  That leads to the notion of complementarity of spin, analogous to position-momentum.  You are thinking only of the symmetric contribution, like Bell did.  I have shown that the two distinct sectors of spin are complementary and dual.  In that sense, BI can be applied to each separately.  That is what the first section of the two channel note does, and it gives an algebraic CHSH of 4, which is 2+2.  I have never said that BI are wrong, only that it can be, and must be, applied to each complementary sector independently.

What is the complementary property of spin in your view?

At the fundamental level, you must show, somehow, that the two terms of the geometric product must be averaged, and not added.  I do not think that is possible.

I hope this helps.

Bryan

On Wed, Jan 14, 2026 at 6:11 PM Mark Hadley <sunshine...@googlemail.com> wrote:

Dear Bryan

1) your argument is nonsense. There is no concept of channel in the derivation of BI. All your results ( your clicks in the instrument) are included in BI. You have not found a step in BI that is invalid in your experiment. BI refutes your work until you show otherwise.

2) Even if you want to use BI, twice as you ludicrously suggest, then you are still wrong, your result has been refuted by the correlation calculation that I just resent. It's simple maths, every step is correct and easy to verify and it shows that your two channel result is wrong. You have not shown anything wrong with my derivation. And you have not derived your own result either - your astonishing, incredible , addition formula is presented without proof - unbelievable. My derivation had numbered equations. Which step do you think is wrong.

3) And simple commonsense arguments, the qualitative ones, show that the addition formula cannot be right. I presents two or three separate reasons why the addition formula does not make sense. You have not responded to either of them.

Mark

On Wed, 14 Jan 2026, 16:06 Bryan Sanctuary, <bryancs...@gmail.com> wrote:

Mark,

In that two-channel, I show that spin has two channels.  

I then use Bell's own arguments and confirm that he says one can only agree with experiment by introducing non-locality,  At that point, I assert he missed the second channel, and including it means his non-local argument is replaced by that second channel. Therefore his non-local argument is not needed.  

However, Bell states his theorem, 

"If [a hidden-variable theory] is local, it will not agree with quantum mechanics; if it agrees with quantum mechanics, it will not be local.*

Since the coherence channel exists, non-locality is not needed, and his theorem fails.

I do nothing else.  That all you must refute.  Your arguments do other things, and are out of scope.  

Thanks for looking into it.

Bryan

*Bell, J.S. Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy; Cambridge University Press:

Cambridge, UK, 2004; pp. 139/147.

On Wed, Jan 14, 2026 at 3:40 PM Mark Hadley <sunshine...@googlemail.com> wrote:

You are refuting Bell if you claim it does not apply to your physics.

It applies to any local hidden variable theorem. Applying it twice is absurd. I showed you before how your two distributions can be written mathematically as a single hidden variable distribution that satisfies BI.

You have claimed repeatedly, without proof, that Bell made a secret extra assumption, that invalidated his conclusion. This claim is refuted, his derivation and it's assumptions are well known and published, they do not require any assumptions about the distributions as you suggest.

Mark

On Wed, 14 Jan 2026, 13:10 Bryan Sanctuary, <bryancs...@gmail.com> wrote:

Dear Mark,

I have not, and do expect, to ever refute BI.  

I am only saying Bell must be applied twice, once for each channel. 

Bryan

[Mark Hadley]

Dear Bryan,

Spin analysis and decomposition of the events into different streams have no relevance to the problem.

Look at my proof and derivation of combination of correlation coefficients. It has nothing to do with spin. You can label the populations with spin indices or call them apples and oranges. The maths is the same.  Your formula is wrong. I have disproved it in simple steps in the proof which are labelled - tell us if you don't understand or agree with any.

The BI or CHSH derivation introduce a function A( lambda) This function includes any and all variables in your problem. Whatever names you give them. However you analyse them. Both your streams/components/ indices, whatever you call them, all are included in A(lambda) CSHS proves that your result is wrong.

And my small examples show that your addition formula fails fundamental consistency tests.

Mark

On Wed, 14 Jan 2026, 19:27 Bryan Sanctuary, <bryancs...@gmail.com> wrote:

Hi again,

Here is the geo product of Pauli matrices

\sigma_i \sigma_j = \delta_ij + \epsilon _ijk i\sigma_k

Since i cannot be equal and unequal to j simultaneously, the two terms are complementary.  That is the real power of the geo  product, it separates symmetric from antisymmetric. Physics defines spin by only the symmetric term, and I assert it should also include the antisymmetric term.

So what, in your view, are the complementary terms of spin?  I say they are \sigma and i\simga, and I think that is what you miss. You have not addressed that.  Bell used spin from only the symmetric part.  I assert that it is fundamentally incomplete. 

Everything I say and use has its origin in the geometric product above.

Bryan

On Wed, Jan 14, 2026 at 8:13 PM Mark Hadley <sunshine...@googlemail.com> wrote:

Bryan,

I don't just say your work is nonsense. I say it is wrong. Your equations are wrong. I prove that. Your understanding of Bell is simply wrong. Your combination of correlation coefficients is wrong. Mathematically wrong and I disprove it with high school maths. Your addition formula gives ludicrous consequences which I show with examples.

Neither I nor Bell are thinking of only one component. Bells result applies to the totality of components. Your idea that splitting the results into components can give new results or a way round BInis simply wrong.

If you find a step in CSHS that restricts it's application to one component then show us. It does not it involves a local hidden variable that includes ALL components that the experiment could conceivably have. It includes everything in your model and it predicts BI. Your decompositions adds nothing. It is simply irrelevant.

CSHS derivation disproves your result. The algebra of combined distributions disproves your result. They don't just call your ideas nonsense, hey show it is wrong. False mathematically incorrect.

[Bryan Sanctuary]

Dear Mark,

I have not, and do expect, to ever refute BI.  

I am only saying Bell must be applied twice, once for each channel. 

Bryan

[Bryan Sanctuary]

Dear Mark,

Thank you for going back to find your past argument. They all fall into the same category and I rejected them at that time,   You  assume a single space and therefore is fallacious. The correlations arise from two spaces. That point is now clearly articulated in the Two channels note, and it is there you must find errors. So I never accepted those responses, and I never agreed with them. You, Richards, Jan Ake  and all argued as you do, I did not agree, so it was a stalemate.   You must find errors in that note,

You ask for an apology  from me!!!!!!!!!  You repeatedly called me a liar, dismissed my arguments as a High School math error, and made personal comments, to which I did not reciprocate in kind. You are living in a fantasy world of Bell arrogance and a signal probability space.  I will never apologize when faced with such belligerent behavior. You arrogantly dismiss my responses, assuming you have answered it, when you had failed. 

Your only recourse is to find errors in my two channel paper, which you have not done. I want your capitulation to the two channels, which by your silence you have already tacitly given.

I hope this is clear: I respond only to technical arguments, like the abortive one you gave here.

Bryan

Best regards,
Bryan

On Tue, Jan 13, 2026 at 11:42 PM Mark Hadley <sunshine...@googlemail.com> wrote:

[Mark Hadley]

Dear Bryan

1) your argument is nonsense. There is no concept of channel in the derivation of BI. All your results ( your clicks in the instrument) are included in BI. You have not found a step in BI that is invalid in your experiment. BI refutes your work until you show otherwise.

2) Even if you want to use BI, twice as you ludicrously suggest, then you are still wrong, your result has been refuted by the correlation calculation that I just resent. It's simple maths, every step is correct and easy to verify and it shows that your two channel result is wrong. You have not shown anything wrong with my derivation. And you have not derived your own result either - your astonishing, incredible , addition formula is presented without proof - unbelievable. My derivation had numbered equations. Which step do you think is wrong.

3) And simple commonsense arguments, the qualitative ones, show that the addition formula cannot be right. I presents two or three separate reasons why the addition formula does not make sense. You have not responded to either of them.

Mark

On Wed, 14 Jan 2026, 16:06 Bryan Sanctuary, <bryancs...@gmail.com> wrote:

Mark,

In that two-channel, I show that spin has two channels.  

I then use Bell's own arguments and confirm that he says one can only agree with experiment by introducing non-locality,  At that point, I assert he missed the second channel, and including it means his non-local argument is replaced by that second channel. Therefore his non-local argument is not needed.  

However, Bell states his theorem, 

"If [a hidden-variable theory] is local, it will not agree with quantum mechanics; if it agrees with quantum mechanics, it will not be local.*

Since the coherence channel exists, non-locality is not needed, and his theorem fails.

I do nothing else.  That all you must refute.  Your arguments do other things, and are out of scope.  

Thanks for looking into it.

Bryan

*Bell, J.S. Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy; Cambridge University Press:

Cambridge, UK, 2004; pp. 139/147.

On Wed, Jan 14, 2026 at 3:40 PM Mark Hadley <sunshine...@googlemail.com> wrote:

You are refuting Bell if you claim it does not apply to your physics.

It applies to any local hidden variable theorem. Applying it twice is absurd. I showed you before how your two distributions can be written mathematically as a single hidden variable distribution that satisfies BI.

You have claimed repeatedly, without proof, that Bell made a secret extra assumption, that invalidated his conclusion. This claim is refuted, his derivation and it's assumptions are well known and published, they do not require any assumptions about the distributions as you suggest.

Mark

[Bryan Sanctuary]

Dear Mark,

I agree in the sense that Bell's work is classical, not quantum.  He and most of modern physics, however, agree Bell is about quantum, like the title of Bell's paper.  I simply say, they missed something, and what they miss in his classical theory is coherence (antisymmetry). Spin is more than up and down states in my view. Spin is a bivector, and is classical. It has a quantum limit. 

I think we are at a point where some cogitation is needed. My approach does not follow Bell because Bell's statistics are restricted to a single probability space, but I say it has two spaces, like pos-mom, energy-time and angle-ang mom.  I asked you what is the complementary variable of spin polarization? I would be interested in your reply.

Bryan

[Mark Hadley]

Bryan,

If you claim that Bell makes a hidden assumption. Show us where he uses that assumption in the derivation. Nobody else can see it. Until you show where that is used it remains a figment of your imagination.

My correlation derivation is a few simple maths steps. If you think that is wrong you should show us the step that is invalid in your physics

You have a very strange addition rules for correlations. It is remarkable, it has been challenged by people who have studied your paper. And it was never derived. It is to say the least fundamentally important to your result and quite remarkable. As a scientist you need to derive results that are important to you, disputed, and unique to your paper. The standard combination of distributions is well known and is derived, not assumed.

And you have not addressed the qualitative criticism of your addition formula - that it can give correlations larger than 1, and that the observed correlation is independent of the number of vector and covector events. That's how scientists and mathematicians do a sanity check on a strange equation.

So your work has been challenged in three independent ways and you have not been able to respond to them as a scientist. 

Your result has been disproven by Bell, it has been disproven by the derivation of correlation coefficients and shown to be nonsensical based on a qualitative analysis.

There is nobody, including you, who can defend your work against these refutations. And I think you know that, but cannot emotionally admit it.

Mark

On Wed, 14 Jan 2026, 10:23 Bryan Sanctuary, <bryancs...@gmail.com> wrote:

[Bryan Sanctuary]

Mark,

In that two-channel, I show that spin has two channels.  

I then use Bell's own arguments and confirm that he says one can only agree with experiment by introducing non-locality,  At that point, I assert he missed the second channel, and including it means his non-local argument is replaced by that second channel. Therefore his non-local argument is not needed.  

However, Bell states his theorem, 

"If [a hidden-variable theory] is local, it will not agree with quantum mechanics; if it agrees with quantum mechanics, it will not be local.*

Since the coherence channel exists, non-locality is not needed, and his theorem fails.

I do nothing else.  That all you must refute.  Your arguments do other things, and are out of scope.  

Thanks for looking into it.

Bryan

*Bell, J.S. Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy; Cambridge University Press:

Cambridge, UK, 2004; pp. 139/147.

On Wed, Jan 14, 2026 at 3:40 PM Mark Hadley <sunshine...@googlemail.com> wrote:

You are refuting Bell if you claim it does not apply to your physics.

It applies to any local hidden variable theorem. Applying it twice is absurd. I showed you before how your two distributions can be written mathematically as a single hidden variable distribution that satisfies BI.

You have claimed repeatedly, without proof, that Bell made a secret extra assumption, that invalidated his conclusion. This claim is refuted, his derivation and it's assumptions are well known and published, they do not require any assumptions about the distributions as you suggest.

Mark

[Mark Hadley]

You are refuting Bell if you claim it does not apply to your physics.

It applies to any local hidden variable theorem. Applying it twice is absurd. I showed you before how your two distributions can be written mathematically as a single hidden variable distribution that satisfies BI.

You have claimed repeatedly, without proof, that Bell made a secret extra assumption, that invalidated his conclusion. This claim is refuted, his derivation and it's assumptions are well known and published, they do not require any assumptions about the distributions as you suggest.

Mark

[Mark Hadley]

Bryan,

I don't just say your work is nonsense. I say it is wrong. Your equations are wrong. I prove that. Your understanding of Bell is simply wrong. Your combination of correlation coefficients is wrong. Mathematically wrong and I disprove it with high school maths. Your addition formula gives ludicrous consequences which I show with examples.

Neither I nor Bell are thinking of only one component. Bells result applies to the totality of components. Your idea that splitting the results into components can give new results or a way round BInis simply wrong.

If you find a step in CSHS that restricts it's application to one component then show us. It does not it involves a local hidden variable that includes ALL components that the experiment could conceivably have. It includes everything in your model and it predicts BI. Your decompositions adds nothing. It is simply irrelevant.

CSHS derivation disproves your result. The algebra of combined distributions disproves your result. They don't just call your ideas nonsense, hey show it is wrong. False mathematically incorrect.

Mark

[Mark Hadley]

Bells is a classical result with relevance to quantum theory. We know that.

It says all classical physics makes this prediction.

That's the proof. That's why it disproves your work and your result. 

It did not miss anything. You have not added anything that can possibly change Bells results. That's why it is a disproof of your claim. That's what tells us your conclusion was wrong. And when we look we find your error. You combine distributions in a way that is wrong. And we have proven that you made a fatal error. Leading you to think you have found something new.

An understanding of spin is not required to derive or understand BI.

CSHS have a general probability distribution. It can be built from several other distributions. Your model is totally compatible with Bells assumptions. He uses A(lambda) to cover any probability function A of any coordinate space lambda. It is incredibly general and covers your set up with ease.

If you want to claim otherwise you would have to PROVE that your set up could not be described by any function A( lambda) for any A and any lambda. But I showed you exactly how you can create A(lambda) from your two distributions. It is simple to do. So CSHS applies and it disproves your work.

Bell disproves your result and the combination of correlation coefficients proves where your mistake is 

Mark

[anton vrba]

Dear Bryan, you say: Spin is a bivector, and is classical. It has a quantum limit.   

Please clarify these claims in precise mathematical and physical terms.

If spin is classical, then please describe explicitly how spin is represented as a bivector and how this bivector configures a photon without invoking configuration space (Hilbert space). A photon is classically defined by the Maxwell equations; where, exactly, does your bivector appear within Maxwell theory? What field, equation, or geometric object does it correspond to?

You also state that spin has a “quantum limit.” What do you mean by quantum limit? Is this a mathematically defined limiting procedure, a quantisation condition, a topological constraint, or something else? Please state it explicitly and show how it yields the observed quantum behaviour.

Unless these claims can be demonstrated mathematically and connected to empirical physics without handwaving or unproven heuristic assumptions, what you are proposing amounts to a new heuristic model of natural philosophy intended to replace the (also heuristic) Copenhagen interpretation of quantum mechanics.

Current physical models, while heuristic, are empirically corroborated and consistent with existing measurement frameworks. Replacing them with alternative heuristic models that simultaneously require changes to the measurement framework just does not play, in my opinion. As I have said before, Bell is a measuring tool, not physics. You are proposing changes both to the physics and to the measuring tools. The proper order, in my view, is first to convince the physics community of the physical model, and only then to revisit the measurement framework.

You have not yet convinced me of the physics.

BTW. I only understood Bell and CHSH after reading Freedmans Ph.D thesis {https://escholarship.org/uc/item/2f18n5nk},  a 100 page document.  The important part is understanding Bell and CGSH in conjunction with the measuring apparatus in all its fascists.  

Regards

Anton

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

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

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

Cc "Bell inequalities and quantum foundations" <Bell_quantum...@googlegroups.com>

Date 1/14/2026 9:11:53 PM

Subject [Bell_quantum_foundations] Re: The correct derivation

[GeraldoAlexandreBarbosa]

Just to relieve tensions due to Bryan's classical double-"spin": see attachment with classical similar effects.

(From left to right: Geraldo Barbosa, Ricardo Horowicz, Luiz Davidovich)

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

--
You received this message because you are subscribed to the Google Groups "Bell inequalities and quantum foundations" group.
To unsubscribe from this group and stop receiving emails from it, send an email to Bell_quantum_found...@googlegroups.com.
To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/em7323af4a-51b9-49ba-a5f4-7d24d4a16459%40c086a822.com.

[GeraldoAlexandreBarbosa]

Adding to my last email: Pay attention to the bottle and glass.

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

On Thu, Jan 15, 2026 at 4:22 PM anton vrba <anto...@gmail.com> wrote:

[Richard Gill]

Bryan, Bell-CHSH allows as many channels as you like. 

It does assume binary measurement measurement outcomes and binary setting choices.

One calls this the 2 x 2 x 2 case: 2 parties, 2 settings per party, 2 outcomes per settin per party.

But it has been extended to more general experimental lay-outs. If Alice and Bob each have two measurement devices, and if they all have binary measurement outcomes, and binary setting choices, then we are in the 4 x 2 x 2 case. Have you looked up what generalised Bell inequalities are available for that case? If not, why not?

Sent from my iPad

On 15 Jan 2026, at 11:02, Bryan Sanctuary <bryancs...@gmail.com> wrote:



--

You received this message because you are subscribed to the Google Groups "Bell inequalities and quantum foundations" group.
To unsubscribe from this group and stop receiving emails from it, send an email to Bell_quantum_found...@googlegroups.com.

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CALLw9YynzS-5O%3Dry_UxJPdZvWLYiN_S8-fxxH4%2BoGu0eoXJz%2BQ%40mail.gmail.com.

[Richard Gill]

Bryan

Classical physical reasoning leads to the possibility to define actual and counterfactual outcomes as random variables defined on a single probability space. The “single probability space” does not need to be *assumed*. It can be mathematically *constructed*.

arXiv:2211.05569  [pdf, other]   quant-ph stat.AP

Bell's theorem is an exercise in the statistical theory of causality

Authors: Richard D. Gill

Abstract: In this short note, I derive the Bell-CHSH inequalities as an elementary result in the present-day theory of statistical causality based on graphical models or Bayes' nets, defined in terms of DAGs (Directed Acyclic Graphs) representing direct statistical causal influences between a number of observed and unobserved random variables. I show how spatio-temporal constraints in loophole-free Bell experiments, and natural classical statistical causality considerations, lead to Bell's notion of local hidden variables, and thence to the CHSH inequalities. 

[Richard Gill]

Bryan

Bell is about certain constraints which classical physical principles automatically imposes on observed correlations between macroscopic measurement outcomes in some simple experiments. 

Quantum concepts are not introduced, by design. Bell *deliberately* does not use words like “particle”, “wave”, “field”, “interference”, “spin”. He does not say anything whatsoever about what is going from a source to Alice and Bob’s apparatus.

If you think that *quantum theorists* have missed something then please get to work with some enterprising quantum experimentalists and get them to do the experiments which might confirm or disprove the existence of some new quantum properties of whatever “particles” might carry them. 

Bell’s work has long ago been generalised from the simple 2x2x2 case (2 parties, 2 settings, 2 outcomes). Tell us what case you will need, once the new kinds of detectors have been engineered.

Richard 

Sent from my iPad

--

You received this message because you are subscribed to the Google Groups "Bell inequalities and quantum foundations" group.
To unsubscribe from this group and stop receiving emails from it, send an email to Bell_quantum_found...@googlegroups.com.

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CALLw9YwHFqqfraYLDKzGz%2BE0eC5YwttJu7AnxDEgcZW9%3DaJQzg%40mail.gmail.com.

[Bryan Sanctuary]

Anton

Please see this paper

Sanctuary, B. The Classical Origin of Spin: Vectors Versus Bivectors. Axioms 2025, 14, 668. https://doi.org/10.3390/axioms14090668

The answers to all your questions are there.  Please read the first 3 sections, which are mostly Classical Mechanics.

Let me know if you have other questions.  

Bryan

[Bryan Sanctuary]

Richard,

Then you do not see very far. Either you have not read my papers, or if you did, you do not understand them.

Do not pander me

Bryan

On Fri, Jan 16, 2026 at 6:59 AM Richard Gill <gill...@gmail.com> wrote:

Bryan

You include in your paper Bell’s famous summary “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.”

As far as I can see, your theory does not agree with QM.

Richard

Sent from my iPad

On 16 Jan 2026, at 12:49, Bryan Sanctuary <bryancs...@gmail.com> wrote:



--
You received this message because you are subscribed to the Google Groups "Bell inequalities and quantum foundations" group.
To unsubscribe from this group and stop receiving emails from it, send an email to Bell_quantum_found...@googlegroups.com.

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CALLw9Yx0CJ0eaVirdS4TbsPJfc%2BNwrRxQu2sksOkJdg%3DUHYP_w%40mail.gmail.com.

[Mark Hadley]

Dear Bryan,

You papers claim to agree with QM. But they are flawed.

Now is the time for you to acknowledge that your work has been criticeised. In particular:

1) we do not agree to disagree

2) We have pointed out specific errors in your work.

     2.1 Bells theory CSHS ( for expample) disproves your claimed results.

3) We have presented two separate proofs that your work is faulty

4) You have not yet responded to either

5) 

[Bryan Sanctuary]

Mark,

"Yourpapers claim to agree with QM. But they are flawed."  NOT ENOUGH, Give me the exact references in my papers.  Your opinions are of no value without substance.  

Bryan

[Mark Hadley]

Dear Bryan,

I gave you those before, and resent them a few days ago!!!!! 

We keep giving you disproofs of your work and you keep denying having received  them!!!

If you do not admit that your work has not just been criticised, but proofs or its falsity have been given to you, then I will resume calling you a liar. I am offering you an opportunity to fairly set the record straight.

We have sent to you, and this forum, proof that your work is false. By all means challenge our work. But do not deny that it has been delivered time and again.

Mark

[Bryan Sanctuary]

Mark

No one has found errors in my two-channel paper. You are arguing from a different ontology, without recognising mine. I completely understand all your arguments and those of others, but you restrict yourself to one probability space, and I do not. Until you engage with my two-channel and repudiate them, your arguments are inconclusive and do not focus on what is new.

Bryan

 

[Mark Hadley]

Yes they have found errors in your two channel paper. Your addition formula, stated but not proven, is false. I have given you a correct derivation.

That IS an engagement with your two channel paper. And it is a disproof.

BI also applies to your two channel paper. Suggesting otherwise is an extraordinary claim. But you state it without proof or justification. BI disproves your paper results because it DOES apply to two or more channels. You have been told that. 

Do you want me to prove YET AGAIN that BI applies to two channels?

You are rude and dishonest if you claim you have not been given disproofs of your paper.

Mark

[Mark Hadley]

Dear Bryan,

Attached is a formal result that BI applies to two channels.

[Bryan Sanctuary]

Mark

My two channel argument follows objective math steps. Those steps have not been challenged. That you  do not like the result and think in a  different ontology has no bearing on my results. 

Until you point to incorrect steps in the two channels, within that framework, your rejections cannot be supported.  First find errors, and then correct them.  You have found no errors, so there is nothing to correct. You have not understood spin complementarity. You think in one probability space. You think you are correct, but  you ignore my responses that I express again above: you have not engaged in the details. 

Bryan

[Bryan Sanctuary]

Mark,

Thanks for trying, but it does not stand up.

Your proof fails since it does not express spin complementarity and is restricted to a single prob space.  I have repeatedly said this, and you simply repeat the same arguments for reasons that cannot be supported and I have shown to be false.

You make the same error as Christian, Diether, Bell and Gill make. You conflate binary pairs to a single space and then average. That is backwards: you should find the average, or geometrical structure, of the two channels, and then convert those to binary pairs.  First do  the algebra and then simulate, not the reverse. What you do  destroys geometrical content, exactly what I retain 

Your proof does not counter my two channel description. Try again.

Bryan

[Bryan Sanctuary]

Richard,

I have no more time at the present. Your arguments are rejected for the same reason Mark's are rejected which  is also the shortcoming of Bell 64 I pointed out.

REPEATEDLY I SAY: Find an objective error in the two channels. That is your only option. Then I might listen to your coflation of objects notion

Bryan

On Fri, Jan 16, 2026 at 10:06 AM Richard Gill <gill...@gmail.com> wrote:

Bryan

I asked you for the errors in my little causality paper and you do not even reply. Note: it *derives* a single probability space model from classical causality arguments. It does not *assume* one. This contradicts some comments by you which we have heard in this forum.

No one has found errors in it. 

It has been peer reviewed and published (as a section in a larger paper giving a critique of the work of a certain Polish-American gentleman - Marian Kupcszynski).

So Bell’s theorem is true!

Richard

Sent from my iPad

On 16 Jan 2026, at 15:29, Bryan Sanctuary <bryancs...@gmail.com> wrote:



[Mark Hadley]

I found an error in your combination of distributions and I corrected it.

I sent you the proof. Three times now.

[Bryan Sanctuary]

Mark

I repeat: find an error in two-channel, the very line or argument that is wrong.  Do not give me your analysis, engage with mine. 

That is the only way to proceed

I am busy otherwise, now

Bryan

[Mark Hadley]

Read it again. It does the opposite. It can't be much simpler.

It takes any two probability spaces. And shows how they can always be combined to create a single space. BI then applies and proves your result must be incorrect.

Check it. It sets up two probability spaces. Anything wrong there? And then defines a new function. Is that clear enough? And then CSHS applies - agreed.

Mark

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CALLw9YyNOsgaY%2BQROWmoSbOXCyjmkJ3r7obQviUcd_EAGqunUQ%40mail.gmail.com.

[Mark Hadley]

I told you which equation is wrong. we all did.

Are you denying that?

And I corrected it.

I can't do much more 

Your incorrect equation ( the additive one) was stated without proof, or derivation in anyway. So there is nothing left to correct.

One numbered equation: identified and corrected, just as you expect of us.

Mark

[Bryan Sanctuary]

Mark, 

If so, and you get one space from the two channels, then tell me how position and momentum can be conflated into a single probability space.

They cannot, because they are distinct and dual.  Also,  neither can the two channels be conflated, they are distinct and dual too. You are missing the essence of complementarity debated by Einstein-Bohr. 

Basically, you miss the most basic property of Nature:  it has two distinct sectors:  symmetric and antisymmetric; matter and force; even parity and odd parity. There is nothing else in Nature than those two sectors and all applications must treat them as distinct because they live in dual spaces. That is the essence of the geometric product in GA. There lies your resolution and the failure of your proof.

Bryan

[Mark Hadley]

No, position and measurement cannot be measured with the same experiment. And you cannot calculate a correlation. You are not describing a position and momentum experiment.

You describe one experiment with two different channels contributing to the result.

You describe sound measurements.

You say each channel satisfies a BI ( that's not so for position or momentum)

You say you have to add the distributions again, you can't add position and momentum.

But you don't have to guess or speculate, I have given you a proof. That YOUR two channels can be written as a single channel to calculate BI.

You don't need to rely on me. Find a single mathematical physicist who you trust and ask then to explain it to you. Or indeed see if your work can be recovered.

Mark

[Mark Hadley]

Actually Bryan, there is a simpler answer,

If you read my consolidated hidden variable equation, it treats your two channels as mutually exclusive ( I think you call that complementary) The experiment measures one or the other not both together. That's what my hidden variable function does.

So I have used your exact set up and shown it must satisfy BI. 

I haven't talked about, or called it nonsense, I've just done a rigorous mathematical proof that it must satisfy BI

Mark

[Bryan Sanctuary]

Mark,

Your proof fails since coflating loses content.  I agree that position and momentum need different experiments.  So you agree with me that pos and momentum give two experimental channels.  You are getting there, good. 

EPR coincident experiments are different and you have not grasped it yet. It is not trivial. Spin is contextual, and is sometimes a vector and sometimes a bivector in the same experiment. It depends on how Alice and Bob choose their settings: Those settings define the channels, so the experiment sometimes probes one and other times the other.  Never the two simultaneously.

Specifically I show,  one quarter of the time, A and B display bivector correlation, and three quarters of the time they correlate as vectors. That gives two channels in one experiment.  It all works out, but you are far from it since you have not studied the dynamics of a bivector.  I doubt you will, but hope you do.  Eventually, the light will dawn and you can then sort Richard out. You think spin is a vector but it is not.  It is a bivector and that plane spins. It means spin is a quaternion, which makes sense to me. Spin is not a chiral vector in an abstract Hilbert space in the BiSM. It is a real spinning plane in Minkowski space.

I have given you more than enough.  It is now up to you to understand it.  I can add little more than I have done above. You have no basis that supports your proof since symmetric and antisymmetric are exclusive.

Bryan

[Bryan Sanctuary]

Mark,

I read your proof, of course I did, but you do not read mine and so you have the wrong mine set. Great, so you get two mutually exclusive channels. That means they live in distinct spaces and cannot be averaged.  

You are tacitly agreeing with me. You must make those ideas concrete. If you have two sectors, then each independently obeys BI. 

No more comments, they are now repetitive. You have enough. Think about the meaning of duality. I hope you see the light.

Bryan

[Mark Hadley]

Bryan,

The hidden variable formula is quite happy combining results from two different distributions. It needs a hidden variable function. I have shown you how easily that is constructed. It's maths. So does not need fancy words. I have defined a hidden variable function that does exactly what you describe. Sometimes it's a vector event sometimes it's a bivectir. ( The names don't matter). The dynamics don't matter for BI

So the hidden variable function exists. Which means the experiment must confirm with BI. It's proven.

I have just proven that if two channels each obey BI then they must obey it when combined.

The result in your paper is proven to be false.

The ddisoroifvus valid independently if the dynamics. Any dynamics will give correlations that obey BI. BI  is independent of dynamics 

Mark

[Bryan Sanctuary]

Mark and Anton

I realized that Mark does not know what I mean by "do not conflate two channels".  Use a boolean operator to distinguish coincidences from pol (even) and coh (odd).  That separates them and they do not conflate.  Tell me what you get.

Both of you.  I think you are now in a position to understand my classical paper. https://doi.org/10.3390/axioms14090668 

You must now read carefully because I have no time to continue to tutor you guys.  Read it with understanding, and do not leave one paragraph without understanding the previous one.  If you do not understand a paragraph, copy it to Chat GPT. Do not jump around and think this and that is wrong or makes no sense.  It will not take long, a couple of hours reading is better than guessing wrong and doing stuff wrong .  Do the first three sections judiciously and get the picture.  I can only discuss more with you after you have understood those three sections. 

 As I said, all questions that you ask are there.  The double cover of the bivector, SU(2) , is explained geometrically.  Understand what the geometric product, S_1 S_3 means. Understand the quantum limit and the section on complementarity. 

Bryan

[Mark Hadley]

Dear Bryan,

You don't need to tutor me.

Your model has the structure of a local hidden variable theory. We can prove that and BI proves your result is wrong 

It's a simple mathematical calculation based on the premises in your models. I've given you the proof.

The proof is independent of the dynamics.

So your paper must have a mistake in it. We have found that too, told you where it is and given you a correct derivation.

We have also shown that your erroneous correlation equation predicts correlations greater than one and results independent of the frequency of each channel.

So it is finished. Specific errors identified, proven and even  corrected for you.

If you claim we have not given this refutation and these proofs and this detail, then I will call you out.

Mark

[Richard Gill]

“Bell is a measuring tool, not physics. You are proposing changes both to the physics and to the measuring tools”.

These are very wise words. I only really understood Bell’s theorem when I had read the whole “Speakable and unspeakable” volume and especially the Bertlmann’s socks chapter, which also needed re-reading a number of times.

Bell’s measuring tool has moreover, over the years, been extended, refined, and strengthened. Once Bryan gets his physics sorted out (if that ever happens), I’m pretty sure Bell 2.0 will be waiting for him.


Sent from my iPhone

[Richard Gill]

Bryan

You include in your paper Bell’s famous summary “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.”

As far as I can see, your theory does not agree with QM.

Richard

Sent from my iPad

On 16 Jan 2026, at 12:49, Bryan Sanctuary <bryancs...@gmail.com> wrote:



[Richard Gill]

Bryan

I asked you for the errors in my little causality paper and you do not even reply. Note: it *derives* a single probability space model from classical causality arguments. It does not *assume* one. This contradicts some comments by you which we have heard in this forum.

No one has found errors in it. 

It has been peer reviewed and published (as a section in a larger paper giving a critique of the work of a certain Polish-American gentleman - Marian Kupcszynski).

So Bell’s theorem is true!

Richard

Sent from my iPad

On 16 Jan 2026, at 15:29, Bryan Sanctuary <bryancs...@gmail.com> wrote:



[Richard Gill]

I did find objective errors, you don’t see them because your grasp of logic is almost as weak as Fred Diether’s.

Sent from my iPhone

On 16 Jan 2026, at 16:22, Bryan Sanctuary <bryancs...@gmail.com> wrote:



Richard,

I have no more time at the present. Your arguments are rejected for the same reason Mark's are rejected which  is also the shortcoming of Bell 64 I pointed out.

REPEATEDLY I SAY: Find an objective error in the two channels. That is your only option. Then I might listen to your coflation of objects notion

Bryan

On Fri, Jan 16, 2026 at 10:06 AM Richard Gill <gill...@gmail.com> wrote:

Bryan

I asked you for the errors in my little causality paper and you do not even reply. Note: it *derives* a single probability space model from classical causality arguments. It does not *assume* one. This contradicts some comments by you which we have heard in this forum.

No one has found errors in it. 

It has been peer reviewed and published (as a section in a larger paper giving a critique of the work of a certain Polish-American gentleman - Marian Kupcszynski).

So Bell’s theorem is true!

Richard

[Bryan Sanctuary]

No problem. 

Bryan

[Bryan Sanctuary]

Mark,

Forgot to add, go ahead and go public. Richard will not, I asked him to.  If you go public, whatever that means, it gives me a forum to prove my case and you will lose.

Bryan

[Mark Hadley]

Bryan,

This is public enough. It is of no wider interest and the disproofs have been peer reviewed here. If you think you can prove your results go ahead, why would you wait.

A journal won't publish simple high school  mathematical corrections to an obscure paper that has attracted little or no interest.

You have made two extraordinary claims with zero prove and no justification. So it's clear what you need to do. And make no mistake, it is the authors responsibility to justify extraordinary claims, not the reader.

1) prove that BI does not apply to two channels.

2) derive your formula for correlation coefficients of two combined channels.

Since I have given a detailed step by step disproof of both claims, that is where the world stands, extraordinary claims, unsupported, disproved and of little interest.

I think you know that and only embarrassment stops you admitting it 

Mark