Re: Local hidden variables.

[Bryan Sanctuary]

Mark,

That "proof" was answered before.  I will answer again:

  Your High School proof is mathematically correct for Bell's assumptions. My paper argues that one of those assumptions, joint definability of the Bell observables, is not satisfied by the bivector construction.  

Bryan

On Sat, Jun 27, 2026 at 3:22 AM Mark Hadley <drmark...@gmail.com> wrote:

This was sent three years ago...

---------- Forwarded message ---------
From: Mark Hadley <drmark...@gmail.com>
Date: Thu, 23 Feb 2023, 09:30
Subject: Re: Local hidden variables.
To: Richard Gill <gill...@gmail.com>
Cc: Bryan Sanctuary <bryancs...@gmail.com>

Dear Richard and Bryan,

Yes a trivial error on equation 3. I've corrected that.

And I have changed the result to deal with cases where the p and e populations are unequal. 

It's straightforward algebra. And gives a sensible result. Bryan was right to start with a definition of correlation. That is what I have done. 

Bryan, 

Can you follow and agree with this derivation? 

Thanks 

Mark

On Thu, 23 Feb 2023, 04:56 Richard Gill, <gill...@gmail.com> wrote:

Dear Bryan,  Mark

Sorry, I first sent this to Udi and Bryan, by mistake. Another try.

Bryan: When we calculate correlations we divide by the number of pairs of particles, not the number of particles.

Mark: your handwritten note contains an obvious misprint on line 3 I think, but I agree with your conclusion

To Bryan again, all of Mark’s “N”s are numbers of particle pairs. In his line 1, N_tot is the total number of particle pairs.

A particle pair can be of type pol, or of type coh

The two particles of a pair either lead to the same outcome or they lead to opposite outcomes.

Mark: do you agree that your line 3 is wrong? Perhaps you should correct it for Bryan.

Richard

PS I’m not sending this email to Jarek’s group because Jarek and other members of his group are getting annoyed by all the messages about Bell’s theorem. Jarek’s group is not about Bell’s theorem, it is about the nature of time.

Sent from my iPad

[Richard Gill]

I think Bryan is saying that quantum mechanics is correct, and local realism (local hidden variables) is not true.

He has slowly realised that Bell’s theorem is true, but hasn’t realised that he has changed his position.

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[Bryan Sanctuary]

Richard,

Total nonsense.  You cannot paraphrase me as to what I might think when you do  not understand what I say.  

I am NOT saying QM is correct!!!!!!!!!  You missed the big point.  I am saying fermions are not fundamental and bosons are.  I am saying that Dirac chose matter-antimatter and I chose a bivector.  The two are totally different, yet you say you THINK I agree with QM.  WRONG as always. I disagree with spin.

And "slowly coming to accept Bell" is nonescence too.  Bell, mathwise, is trivial. I accepted his inequalities 25 years ago.  I say now that Bell forgot the bivector and that is fatal to ALL Bell's work.  I mean ALL of Bell's work. (GIve me a paper on EPR by Bell that is not based on quantum weirdness.

So if you wish to speculate about my work, understand it first, or say nothing.  But you are simply playing the role you have embraced: gatekeeping Bell.  

"Bell will be fine" will be your demise.

Bryan

[Richard Gill]

Bryan, you claim that the singlet state correlations predicted by QM are correct.

[Richard Gill]

I don’t have to understand your work at all, in order to discern contradictions in your logic.

On 27 Jun 2026, at 12:37, Bryan Sanctuary <bryancs...@gmail.com> wrote:

[Bryan Sanctuary]

Spoken like a true gatekeeper.

Bryan

[Bryan Sanctuary]

Richard, 

Gimme a contradiction you discern in my work. Just one, or more if you wish.

Really you have nothing I cannot answer.  

Bryan

[Bryan Sanctuary]

Mark,

Like I said, no errors, just not applicable to spin when treated as a bivector.  You assume a single space for counterfactual events.  

Bryan

On Sat, Jun 27, 2026 at 6:58 AM Mark Hadley <drmark...@gmail.com> wrote:

I didn't use bells assumptions I used the definition of correlation and high school maths.

If you aren't sure how to combine correlations from different distributions then you have to go back the definitions. 

The definition of correlation coefficients in this context is well known. Do you accept the definition.

Is any line if my proof wrong. You have not found an error in it.

Mark

[Bryan Sanctuary]

Mark

There are no errors in Bell's derivation or yours. It is just that your derivation, giving |S| = 2, rests on an assumption that makes that inapplicable. 

Recall Bell said in 66  that von Neumann made the linear assumption which he rejected,  I say the single prob space does not exist for spin, so Bell is not applicable to spin

Clear?

Bryan

On Sat, Jun 27, 2026 at 9:00 AM Mark Hadley <drmark...@gmail.com> wrote:

If there are no errors then your work is faulty. The correlation combination only required the definition of correlation coefficient. 

Your correlation summation has nothing to do with the other assumptions 

Mark

DLE Limited

Co. No: 17094634

Reg Address: 4 The Pastures, Dog Lane, Napton, SOUTHAM CV47 8LT

[Mark Hadley]

Clear but wrong.

BI does apply to your variables they are unremarkable, a simple product space.

I proved that for you ages ago.

If you make this extraordinary assertion, have you ever tried to prove it

Mark

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[Richard Gill]

Bell says the single prob space does not exist

Neither theoretically (assuming QM) nor in reality for any well conducted successful  (CHSH violating) loophole free experiments.

[Mark Hadley]

Bryan read my proof. There are no assumptions in it.

I start with the standard definition of a correlation coefficient.

I do high school maths algebra

I end up with a correct equation for the correlation coefficient for two distributions.

Nothing is added. I start with a fact, do algebra and get a result that contradicts your result. ( Despite the criticism, you have never offered a derivation of your correlation addition ).

The equation that is fundamental to your paper is wrong. Plucked from the air and never derived.

Mark

On Sat, 27 Jun 2026, 15:41 Bryan Sanctuary, <bryancs...@gmail.com> wrote:

--

[Mark Hadley]

So in brief, I did not use Bells assumptions. And it does apply to your model.

On Sat, 27 Jun 2026, 11:13 Bryan Sanctuary, <bryancs...@gmail.com> wrote:

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[Richard Gill]

Bryan is in action refuting my comment on PubPeer: https://pubpeer.com/publications/C065FD40CF2C5C36B47C78F1E53385

[Richard Gill]

And here's another: https://pubpeer.com/publications/D77266ADAF36F7DD39BDF8D7514742

[Bryan Sanctuary]

Richard,

If you continue to put up inane and hostile comments on Peerpub, I will continue to call you out as the dishonest gatekeeper of Bell. 

So I suggest you shut up or say something worth reading.

Bryan

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[Richard Gill]

You do that, Bryan! I suggest you try carefully reading what I wrote. Like a real scientist interested in truth.

You have provided no mechanism explaining the actual pair of outcomes in a single shot experiment. N = 1.

You do actually know why you cannot give one: it’s because of Bell’s theorem!

It’s elementary, dear Watson. Elementary logic.

Sent from my iPad

On 28 Jul 2026, at 09:18, Bryan Sanctuary <bryancs...@gmail.com> wrote:



[Mark Hadley]

Richard,

Bryan has bigger problems. He has just found out that his use of CL(2,2) means that the equations are not Lorentz invariant. Or in other words, they are wrong!

 

Mark

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[anton vrba]

The problem is that Bryan uses click-bait titles and continues that click-bait in his text. Following my comment [1] and his reply [2], Bryan explicitly admits:

In particular, we appreciate the recognition that the bivector framework is internally consistent and that Bell’s theorem is not directly applicable to bivector spin because the assumptions underlying Bell’s construction are not satisfied. We agree that this distinction is important. In both cases the individual events are local and Boolean, while the phase relation becomes visible only at the statistical level. Our claim is therefore not that Bell’s theorem is mathematically incorrect. We agree that Bell’s theorem is mathematically valid within its stated assumptions. Our position is that bivector spin does not belong to the class of models Bell considered and therefore lies outside the scope of the theorem.

The issue is that Bryan remains academically dishonest by failing to issue a corrigendum to remove the click-bait from his title, abstract, and text, and to retract all claims of a "Disproof of Bell's Theorem" across his papers.

Once that is done, I presume Richard will no longer have objections, leaving only the discussion on (i) the mathematics and (ii) physical viability — the two precursor steps before any ontological additions to natural philosophy.

 

[1] https://www.mdpi.com/2624-960X/8/2/56

[2] https://www.mdpi.com/2624-960X/8/3/57

Regards
Anton

[Justo Pastor Lambare]

I think that you cannot disprove a theorem by violating its hypotheses. So, perhaps the problem is the way  Bryan expresses the meaning of his results. By the way, I think Bryan the "quaternions", I am curious, isn't that Joy Chritian's method? 

 

      Justo

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[Parker Emmerson]

Dear Justo,

I hope all is well. While there is a contextual reality to what you are saying, I think it's a bit overly relativist. If the theorem or hypothesis is ill-typed, mathematics becomes pretty specific about what it means to be technically correct or a technically correct resolution to a problem vs. what the colloquial description of the findings is. This yields real developments within languages that establish findings relative to different systems (consistent, axiomatic, definitional), not just distinctions of relativism. Where certain theories fit within these precision linguistic forms is the issue. So, when you say, "you cannot disprove a theorem by violating its hypotheses," -- it's kind of loaded, because many hypotheses have to be reforged through semantics to actually be properly typed. The hypotheses in question in such a hypothetical scenario would then be false, but they become participants in the ultimate refinement of the phenomenon with the correct semantics and meta logical structures in place.

All my best,

Parker Emmerson

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