Clarifying the add vs average issue and Irreducible Cartesian Tensors

[Bryan Sanctuary]

Dear Richard,

Now that the Diether debacle has subsided, I would like to discuss and focus on the substantive issues.

I was disappointed by your recent remark suggesting gaps in my basic mathematical education and comparing me with Fred. After the prolonged ad hominem attacks from Fred, I had hoped we could now proceed in a more collegial and technical spirit. I ask that we all, and you, refrain from personal characterizations and keep the discussion focused on mathematics and physics. I have not made ad hominem remarks about anyone in this group to my knowledge, and I intend to keep it that way.

I readily acknowledge that my formal mathematical training does not match yours. That is not in dispute. My background was shaped by Bob Snider and John Coope at UBC when I was in grad school, particularly through Irreducible Cartesian tensors (ict), which Bob later summarized in his book. I attach a copy of ict.pdf for anyone who is interested in that subject: I most certainly benefited from it. That background led me naturally to geometric algebra and how I think about spin. Whether my approach is correct is, of course, a matter for technical discussion, not credentials

What concerns me in your remark is your specific phrase:

 “the(sic your) confusion about whether you can add correlations or take convex combinations of them.”

This is a key point, and I raised it in Section 2.4 of my response to Diether. There I show that reproducing the full EPR correlation requires two distinct contributions, not one. That conclusion is not my opinion but follows from a decomposition and an isotropic average. I am certain this was not lost on you.

I would very much welcome a clear, technical critique of that. If you believe Section 2.4 is mathematically incorrect, I ask you to identify precisely where the reasoning fails. If, on the other hand, you believe the calculation is correct but physically irrelevant, I ask you to state why.

You have privately shared with me that Anton asked ChatGPT to analyze parts of my work. I am not opposed to such critiques, but I would prefer that objections be stated openly here for the group, rather than by implication or dismissal. If you are willing, I suggest opening a new thread focused specifically on the add-versus-average issue in the context of EPR correlations. I will respond in good faith.

This question is not marginal but central to Bell. If the two-channel structure is valid, the implications are substantial. If not, then it should be possible to say exactly why. Either way, this seems squarely within the purpose of this group.

Bryan

[Mark Hadley]

Dear Bryan,

Yes, I thought Fred behaved just like you with the mathematical arguments, except he added in rudeness - you remain polite. It was amusing seeing you argue. A case of the kettle calling the pot black.

Your mathematical mistakes have been pointed out so many times and in so many different ways, by several people. and each time you ignore the comments or deny very simple maths.

Correlations of combined populations is high school maths. I know you can do that. I know you don't like the result. Your position in this is not scientific, it is emotional and fraudulent. I don't know why you have raised it again. You have been shown how to combine correlations in small simple detailed steps. You have been shown the structural nonsense off you equation. And you have been told how to disprove by example using a spreadsheet.

You persist in presenting new material to the group. But I won't look at it because you have destroyed your own credibility. Others are welcome to engage with you, but I would caution them not to.

Mark

[Jan-Åke Larsson]

Bryan was not polite in the end to me, when I did exactly what he is asking for: 

Show that even if the full EPR correlation requires two distinct contributions, not one, correlations are created by convex combinations. 

This is always the case, whatever the underlying distribution. With Bryan's method, the total probability is strictly larger than 1 which is nonsense, of course.

After I pointed this out to Bryan he resorted to name-calling.

I will not rejoin the group.

/Jan-Åke

--
Jan-Åke Larsson
Professor, Head of Department

Department of Electrical Engineering SE-581 83 Linköping Phone: +46 (0)13-28 14 68 Mobile: +46 (0)13-28 14 68 Visiting address: Campus Valla, House B, Entr 27, 3A:512 Please visit us at www.liu.se

[Richard Gill]

Chat GPT made the same analysis as I did! You are making category errors.

Of course you can express 3 as 2 + 1. You can separate terms and then use fancy words, and come up with a story about helucity and spin. But what you say about dual convex sets is just non-sense. And what you say about statistical data analysis for Bell experiments is non-sense too.

Many people asked for literature references but you gave none. My guess is that you are recycling technical words which you saw in a different context long ago, without actual mathematical understanding of the resulting sentences.

In this sense your grasp of maths is similar to Fred’s. In all other respects you are incomparable.

Sent from my iPad

On 12 Jan 2026, at 09:33, Bryan Sanctuary <bryancs...@gmail.com> wrote:



<ict.pdf>

[Bryan Sanctuary]

Jan-Åke

Please tell me what names I called you?  Please copy them to the group.

 If you recall you continually said that I failed probability 101, and ridiculed me for adding.  You simply stated I was wrong without engaging as to why. No issue if you are not interested but you have nor replied in substance.. 

I will reply to Mark soon, and I will copy you for the last time. After that it is up to you if you wish to engage or not.

Regards

Bryan

 

[Richard Gill]

Honestly Bryan,  I am sure you passed Probability 101, but I do guess it was a long time ago. And what about Statistics 201?

Sent from my iPad

On 12 Jan 2026, at 11:30, Bryan Sanctuary <bryancs...@gmail.com> wrote:



[Mark Hadley]

Jan did tell you why you were wrong.

Repeatedly, he put a lot of effort into helping you. As did others including myself. We gave you very detailed explanations of what you were doing wrong.

[Mark Hadley]

I personally do think Bryan can do the maths.

He made a maths error, we all do at times. But he liked the wrong result, it played to his narrative. So he refused to correct it.

Bryan's formula show a lack of integrity, not an inability at maths.

Mark

[Richard Gill]

Adding is just wrong. Bryan just does it, he does not give mathematical justification.

“Convex duality”, Minkowski sums and now Cartesian Tensors have nothing whatever to do with this.

Sent from my iPad

On 12 Jan 2026, at 11:30, Bryan Sanctuary <bryancs...@gmail.com> wrote:



[anton vrba]

Mark and Jan-Ake nice to see both of you back here.

May I suggest to reset this group that past animosities are put to rest, we adopt an implied apology from everyone to everyone and get to the nitty gritty of maths, physics, probabilities and statistics.  If we are going to continue the non-Gill-Sanctuary-bet debate at ad infinitum then this will drain the good will energy of the group and will lead to its demise.  There is no point in discussing add vs average, if there is an underlying problem in a paper that then requires goal seeking by heuristically adopting to achieve a result, which by definition voids any disproof of a theory that requires addition of said parameters.

Regards

Anton

[Jan-Åke Larsson]

I explained why you are wrong in detail. Whereupon you attacked my person.

Never send me email again.

[Richard Gill]

Hear hear!


Sent from my iPhone

> On 12 Jan 2026, at 21:42, anton vrba <anto...@gmail.com> wrote:
>
> 

[Bryan Sanctuary]

Dear Richard, Jan-Åke, Mark, and Anton,

I am dismayed that after the Diether episode finally subsided, the discussion immediately reverted to personal attacks on my credentials and repeated assertions that I “failed probability” or “basic mathematics,” rather than engagement with the substance. I opened the recent thread explicitly asking that we refrain from this and focus on the technical issues. That request was not respected, with three of you responding in the Diether-style attack without substance that I had hoped had ended. Moreover, there is no evidence that I used derogatory language or called people names, as suggested.

I also have seen no argument from anyone demonstrating why averaging is mandatory in the situation of EPR correlations.  I only heard repeated statements that it is “obvious,” without explanation. Assertions about me failing Probability 101 or attacks on my credibility do not constitute a technical response. If there is a mathematical error in my reasoning, it should be possible for you to identify it explicitly.

I attach Two channels.pdf, which gives my final, concise explanation of why EPR correlations involve two distinct channels and why the correct procedure is to add their contributions rather than average them. This includes an explanation of why the algebraic content exceeds the observed CHSH value and why the operational bound is CHSH = 2 + 1 = 3. There is nothing subjective in this analysis.

I thank Anton for running my papers through ChatGPT. I agree with that analysis insofar as it concludes that my framework is not consistent with Bell’s single-channel statistical assumptions. That is expected: Bell treats one channel, whereas my model treats two. In my view, the question Anton posed was therefore the wrong one. The correct question is not “Does Bryan’s model satisfy Bell’s premises?” but rather “Are Bell’s premises physically complete for EPR coincidence experiments?”

I will respond only to objective, technical critiques that identify specific errors in the attached note. In the absence of such responses, I will consider the matter closed and my procedure which adds correlations is justified, thereby rejecting the average.

Regards,
Bryan

On Tue, Jan 13, 2026 at 9:29 AM Mark Hadley <sunshine...@googlemail.com> wrote:

I also explained it detail in there different ways.

With steps so small and simple a child could follow them

On Mon, 12 Jan 2026, 08:33 Bryan Sanctuary, <bryancs...@gmail.com> wrote:

[Richard Gill]

Dear Bryan

Bell has no premises at all on the physics. He proposes a way to test the hypothesis of local realism. It assumes binary inputs and binary outputs. More general scenarios have been worked out by other researchers.

If you want a Bell-type experiment with more output channels please just study the literature.

Richard 

Sent from my iPad

On 13 Jan 2026, at 15:22, Bryan Sanctuary <bryancs...@gmail.com> wrote:



<Two channels.pdf>

[Bryan C. Sanctuary, Dr.]

Please see the attached which shows the error in your analysis, therefore EPR correlations must add, not average, and respect locality. 

Bryan

---

From: Richard Gill <gill...@gmail.com>
Sent: January 13, 2026 4:26 AM
To: Bryan C. Sanctuary, Dr. <bryan.s...@mcgill.ca>
Cc: bell_quantum...@googlegroups.com <bell_quantum...@googlegroups.com>; Jan-Åke Larsson <jan-ake...@liu.se>; Mark Hadley <sunshine...@googlemail.com>
Subject: Re: Clarifying the add vs average issue and Irreducible Cartesian Tensors

 

Bryan wrote:

This is a key point, and I raised it in Section 2.4 of my response to Diether. There I show that reproducing the full EPR correlation requires two distinct contributions, not one. That conclusion is not my opinion but follows from a decomposition and an isotropic average. I am certain this was not lost on you.

The question is not whether one can distinguish two different contributions, but whether you can explain Bell experiments in a locally realistic way.

The decomposition is obviously possible in a mathematical sense. I don’t know what Bryan means by “isotropic” average. He seems to think that it corresponds to two distinct physical processes, but as long as we don’t separate them experimentally, this does not prove anything at all. It is speculation.

Bell’s theorem is not a theorem about quantum mechanics. It is not even a theorem about physics. It is a true theorem about distributed (classical) computing.

Bryan: please study my preprint

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

and let me know if there is something you don’t understand. Have you read Judea Pearl’s book on causality? There exist plenty of compact pedagogical presentations focussed on readers from different fields of science. I’m sure some physicists have picked up on this.

Richard 

[Mark Hadley]

I also explained it detail in there different ways.

With steps so small and simple a child could follow them

On Mon, 12 Jan 2026, 08:33 Bryan Sanctuary, <bryancs...@gmail.com> wrote:

[Richard Gill]

Bryan wrote:

This is a key point, and I raised it in Section 2.4 of my response to Diether. There I show that reproducing the full EPR correlation requires two distinct contributions, not one. That conclusion is not my opinion but follows from a decomposition and an isotropic average. I am certain this was not lost on you.

[Mark Hadley]

Bryan,

That is most unfair.

After the reset, you posted another message about correlations. I did not raise it.

I strongly object to your repeated claims that nobody has shown you the errors in your method. That is insulting and disrespectful. I have spent hours looking at your work (as have others) and explaining the errors to you. In several different ways and have shown you how to check yourself with spreadsheet simulations, and simple logic.

You are lying to this group and I suspect you are lying to yourself. 

Mark

[Richard Gill]

Bryan

I would say that your error is a failure in logical reasoning.

It is time you wrote to the 2022 Nobel prize winners.

Richard

Sent from my iPad

On 13 Jan 2026, at 18:15, Bryan Sanctuary <bryancs...@gmail.com> wrote:



Dear Mark,

 I object as strongly as I can that you call me a liar once again. That is totally unacceptable.  You repeatedly suggest that my error is "High School" math without elaboration. If my error is so simple, then show it to me in that two channel paper.  

Find one past email, please do a small search, by anyone who has shown me wrong.  It does not exist. Rather you have no alternative but to admit Bell missed a channel and his non-local inference is shot down in flames.

I do not think you are able to admit your failure.  Nonetheless, your reply confirms your tacit capitulation.  With your and Richard's unable to respond, we are left with Jan-Ake to reply.  

With that, the question is answered: the correlations from two channels disproves Bell's theorem.  It is now time for the 2022 Nobel winners to stand up and defend their positions.  

The challenge is there. The paradigm shift will follow.

Bryan

[Jan-Åke Larsson]

I don't know if this makes it to the group or not but I do not care

I quote "You are now attempting to obfuscate, which is your tactic when you have no answer."

STOP ATTACKING RICHARD'S PERSON

I do not believe this is so hard to understand

On 1/13/26 16:41, Bryan Sanctuary wrote:

Dear Richard,

You are now attempting to obfuscate, which is your tactic when you have no answer.  The paper your quote to refute mine is not incorrect, but rather  has the premise that all physically relevant correlations can be represented as jointly defined binary random variables on a single probability space. That is, you are repeating exactly Christian and Diether's error: conflate polarization and coherence and therefore lose geometric content.

Until you find errors in my paper, you must accept that Bell missed the second channel.  Your comments confirm your capitulation, whether you realize it or not.

Bryan

On Tue, Jan 13, 2026 at 4:31 PM Richard Gill <gill...@gmail.com> wrote:

Dear Bryan

Bell’s single channel analysis is appropriate and correct regarding single channel experiments. We now know that local realism has been experimentally excluded by the findings of some single channel experiments. Your work does not change that.

You’re better encourage experimenters to figure out how to experimentally distinguish helicity from spin, if these two hypothetical quantities are actually physically real. This cannot change the findings from past Bell-type experiments.

The add vs average issue has been settled. Adding makes no sense.

Suppose someone did a two-channel experiment which found CHSH = 2.8. Then I could say - wait, there are actually three components to spin, and 2.8 = 1 + 1 + 0.8. Therefore their wonderful experiment is a waste of time.

That’s your logic, Bryan! I get the impression that you don’t understand Bell’s logic.

Many people have had difficulties with it. They are becoming less common, but I still get one email a month from a new person looking for my blessing on their disproof on Bell’s theorem. They are always pretty intelligent, creative, critical. Good qualities. But till now at least, they’ve always been wrong.

Richard

Sent from my iPad

On 13 Jan 2026, at 16:11, Bryan Sanctuary <bryancs...@gmail.com> wrote:



Dear Richard,

I am long aware of your papers, and also the one you asked me to review.  Your analysis derives CHSH under the assumption of a single binary outcome channel; it does not address, and therefore does not invalidate, my two-channel model in which the additional coherence channel is introduced.

Therefore, your paper supports Bell's single channel analysis.  In the absence of you finding technical errors in my paper, I conclude that you have capitulated and must accept the two channel addition.

Bryan

On Tue, Jan 13, 2026 at 4:01 PM Richard Gill <gill...@gmail.com> wrote:

Dear Bryan

Bell has no premises at all on the physics. He proposes a way to test the hypothesis of local realism. It assumes binary inputs and binary outputs. More general scenarios have been worked out by other researchers.

If you want a Bell-type experiment with more output channels please just study the literature.

Richard 

Sent from my iPad

On 13 Jan 2026, at 15:22, Bryan Sanctuary <bryancs...@gmail.com> wrote:



Dear Richard, Jan-Åke, Mark, and Anton,

I am dismayed that after the Diether episode finally subsided, the discussion immediately reverted to personal attacks on my credentials and repeated assertions that I “failed probability” or “basic mathematics,” rather than engagement with the substance. I opened the recent thread explicitly asking that we refrain from this and focus on the technical issues. That request was not respected, with three of you responding in the Diether-style attack without substance that I had hoped had ended. Moreover, there is no evidence that I used derogatory language or called people names, as suggested.

I also have seen no argument from anyone demonstrating why averaging is mandatory in the situation of EPR correlations.  I only heard repeated statements that it is “obvious,” without explanation. Assertions about me failing Probability 101 or attacks on my credibility do not constitute a technical response. If there is a mathematical error in my reasoning, it should be possible for you to identify it explicitly.

I attach Two channels.pdf, which gives my final, concise explanation of why EPR correlations involve two distinct channels and why the correct procedure is to add their contributions rather than average them. This includes an explanation of why the algebraic content exceeds the observed CHSH value and why the operational bound is CHSH = 2 + 1 = 3. There is nothing subjective in this analysis.

I thank Anton for running my papers through ChatGPT. I agree with that analysis insofar as it concludes that my framework is not consistent with Bell’s single-channel statistical assumptions. That is expected: Bell treats one channel, whereas my model treats two. In my view, the question Anton posed was therefore the wrong one. The correct question is not “Does Bryan’s model satisfy Bell’s premises?” but rather “Are Bell’s premises physically complete for EPR coincidence experiments?”

I will respond only to objective, technical critiques that identify specific errors in the attached note. In the absence of such responses, I will consider the matter closed and my procedure which adds correlations is justified, thereby rejecting the average.

Regards,
Bryan

On Tue, Jan 13, 2026 at 9:29 AM Mark Hadley <sunshine...@googlemail.com> wrote:

I also explained it detail in there different ways.

With steps so small and simple a child could follow them

On Mon, 12 Jan 2026, 08:33 Bryan Sanctuary, <bryancs...@gmail.com> wrote:

Dear Richard,

Now that the Diether debacle has subsided, I would like to discuss and focus on the substantive issues.

I was disappointed by your recent remark suggesting gaps in my basic mathematical education and comparing me with Fred. After the prolonged ad hominem attacks from Fred, I had hoped we could now proceed in a more collegial and technical spirit. I ask that we all, and you, refrain from personal characterizations and keep the discussion focused on mathematics and physics. I have not made ad hominem remarks about anyone in this group to my knowledge, and I intend to keep it that way.

I readily acknowledge that my formal mathematical training does not match yours. That is not in dispute. My background was shaped by Bob Snider and John Coope at UBC when I was in grad school, particularly through Irreducible Cartesian tensors (ict), which Bob later summarized in his book. I attach a copy of ict.pdf for anyone who is interested in that subject: I most certainly benefited from it. That background led me naturally to geometric algebra and how I think about spin. Whether my approach is correct is, of course, a matter for technical discussion, not credentials

What concerns me in your remark is your specific phrase:

 “the(sic your) confusion about whether you can add correlations or take convex combinations of them.”

This is a key point, and I raised it in Section 2.4 of my response to Diether. There I show that reproducing the full EPR correlation requires two distinct contributions, not one. That conclusion is not my opinion but follows from a decomposition and an isotropic average. I am certain this was not lost on you.

I would very much welcome a clear, technical critique of that. If you believe Section 2.4 is mathematically incorrect, I ask you to identify precisely where the reasoning fails. If, on the other hand, you believe the calculation is correct but physically irrelevant, I ask you to state why.

You have privately shared with me that Anton asked ChatGPT to analyze parts of my work. I am not opposed to such critiques, but I would prefer that objections be stated openly here for the group, rather than by implication or dismissal. If you are willing, I suggest opening a new thread focused specifically on the add-versus-average issue in the context of EPR correlations. I will respond in good faith.

This question is not marginal but central to Bell. If the two-channel structure is valid, the implications are substantial. If not, then it should be possible to say exactly why. Either way, this seems squarely within the purpose of this group.

Bryan

<Two channels.pdf>

--
Jan-Åke Larsson
Professor, Head of Department

Department of Electrical Engineering SE-581 83 Linköping Phone: +46 (0)13-28 14 68 Mobile: +46 (0)13-28 14 68 Visiting address: Campus Valla, House B, Entr 27, 3A:512

Please visit us at www.liu.se

[Richard Gill]

Dear Bryan

I already knew what you have written and I think I have even told it to you many times in the past.

There is no error in my analysis. It concerns the 2 party, 2 settings, one output channel each, with binary output. We call that the 2x2x2 case.

If two experimenters measure simultaneously in two output channels they can use two Bell inequalities or even a generalised Bell inequality for the 2 parties, 2 settings, four outcomes case, 2x2x4. It’s already be studied. 

But we already know that your model is a local realistic model, so there is no point in testing *your* model.

Richard

Sent from my iPad

On 13 Jan 2026, at 15:35, Bryan C. Sanctuary, Dr. <bryan.s...@mcgill.ca> wrote:



Please see the attached which shows the error in your analysis, therefore EPR correlations must add, not average, and respect locality. 

Bryan

---

From: Richard Gill <gill...@gmail.com>
Sent: January 13, 2026 4:26 AM
To: Bryan C. Sanctuary, Dr. <bryan.s...@mcgill.ca>
Cc: bell_quantum...@googlegroups.com <bell_quantum...@googlegroups.com>; Jan-Åke Larsson <jan-ake...@liu.se>; Mark Hadley <sunshine...@googlemail.com>
Subject: Re: Clarifying the add vs average issue and Irreducible Cartesian Tensors

 

Bryan wrote:

This is a key point, and I raised it in Section 2.4 of my response to Diether. There I show that reproducing the full EPR correlation requires two distinct contributions, not one. That conclusion is not my opinion but follows from a decomposition and an isotropic average. I am certain this was not lost on you.

The question is not whether one can distinguish two different contributions, but whether you can explain Bell experiments in a locally realistic way.

The decomposition is obviously possible in a mathematical sense. I don’t know what Bryan means by “isotropic” average. He seems to think that it corresponds to two distinct physical processes, but as long as we don’t separate them experimentally, this does not prove anything at all. It is speculation.

Bell’s theorem is not a theorem about quantum mechanics. It is not even a theorem about physics. It is a true theorem about distributed (classical) computing.

Bryan: please study my preprint

<arxiv-logo-fb.png>

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

and let me know if there is something you don’t understand. Have you read Judea Pearl’s book on causality? There exist plenty of compact pedagogical presentations focussed on readers from different fields of science. I’m sure some physicists have picked up on this.

Richard 

<Two channels.pdf>

[Bryan Sanctuary]

Dear Richard,

I am long aware of your papers, and also the one you asked me to review.  Your analysis derives CHSH under the assumption of a single binary outcome channel; it does not address, and therefore does not invalidate, my two-channel model in which the additional coherence channel is introduced.

Therefore, your paper supports Bell's single channel analysis.  In the absence of you finding technical errors in my paper, I conclude that you have capitulated and must accept the two channel addition.

Bryan

On Tue, Jan 13, 2026 at 4:01 PM Richard Gill <gill...@gmail.com> wrote:

[Richard Gill]

Dear Bryan

Bell’s single channel analysis is appropriate and correct regarding single channel experiments. We now know that local realism has been experimentally excluded by the findings of some single channel experiments. Your work does not change that.

You’re better encourage experimenters to figure out how to experimentally distinguish helicity from spin, if these two hypothetical quantities are actually physically real. This cannot change the findings from past Bell-type experiments.

The add vs average issue has been settled. Adding makes no sense.

Suppose someone did a two-channel experiment which found CHSH = 2.8. Then I could say - wait, there are actually three components to spin, and 2.8 = 1 + 1 + 0.8. Therefore their wonderful experiment is a waste of time.

That’s your logic, Bryan! I get the impression that you don’t understand Bell’s logic.

Many people have had difficulties with it. They are becoming less common, but I still get one email a month from a new person looking for my blessing on their disproof on Bell’s theorem. They are always pretty intelligent, creative, critical. Good qualities. But till now at least, they’ve always been wrong.

Richard

Sent from my iPad

[Bryan Sanctuary]

Dear Richard,

You are now attempting to obfuscate, which is your tactic when you have no answer.  The paper your quote to refute mine is not incorrect, but rather  has the premise that all physically relevant correlations can be represented as jointly defined binary random variables on a single probability space. That is, you are repeating exactly Christian and Diether's error: conflate polarization and coherence and therefore lose geometric content.

Until you find errors in my paper, you must accept that Bell missed the second channel.  Your comments confirm your capitulation, whether you realize it or not.

Bryan

[Bryan Sanctuary]

Dear Mark,

 I object as strongly as I can that you call me a liar once again. That is totally unacceptable.  You repeatedly suggest that my error is "High School" math without elaboration. If my error is so simple, then show it to me in that two channel paper.  

Find one past email, please do a small search, by anyone who has shown me wrong.  It does not exist. Rather you have no alternative but to admit Bell missed a channel and his non-local inference is shot down in flames.

I do not think you are able to admit your failure.  Nonetheless, your reply confirms your tacit capitulation.  With your and Richard's unable to respond, we are left with Jan-Ake to reply.  

With that, the question is answered: the correlations from two channels disproves Bell's theorem.  It is now time for the 2022 Nobel winners to stand up and defend their positions.  

The challenge is there. The paradigm shift will follow.

Bryan

On Tue, Jan 13, 2026 at 5:47 PM Mark Hadley <sunshine...@googlemail.com> wrote:

[Mark Hadley]

Have you lost all my earlier emails. 

I say again you are simply lying. People have shown you in detail what is wrong. Have you lost the emails?

If I need to find them again I will do and I'll post them to the group again. At which point I'll expect you to apologise or withdraw from the group.

Mark

[Richard Gill]

He didn’t understand them. He’s not lying.

Sent from my iPad

On 13 Jan 2026, at 18:26, Mark Hadley <sunshine...@googlemail.com> wrote:



[Bryan Sanctuary]

Richard,

Say what you want, and speculate all you wish.  The truth is, you cannot respond, your gatekeeping days are over. 

Accept it, and capitulate.  The failure in logic is Bell's not mine.  His work now lies exposed and in ruins.  You have no answer. 

So I leave you with it.

Bryan 

[Bryan Sanctuary]

Mark,

I have no interest in your responses.  Again, you have the  pomposity to continue to insult rather than reply. The ball is in your court, not mine. 

It is you, and the other GateKeepers of Bell, that are in disarray, not me, and your only defense is to insult  rather than expose my "High School" math error.  You are clearly unable to do so, otherwise you would. 

The gates of Bell cannot be revived. That era is over, and the sooner you realize it, the better physics will be.

Bryan

On Tue, Jan 13, 2026 at 8:42 PM Mark Hadley <sunshine...@googlemail.com> wrote:

I disagree, 

Bryan has done some complicated manipulations in his papers. I can't believe he can't calculate a correlation coefficient.

He does not like the result so he switches off.

Mark

[Mark Hadley]

I disagree, 

Bryan has done some complicated manipulations in his papers. I can't believe he can't calculate a correlation coefficient.

He does not like the result so he switches off.

Mark

On Tue, 13 Jan 2026, 18:44 Richard Gill, <gill...@gmail.com> wrote: