Re: [Bell_quantum_foundations] Bell's biggest mistake

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Richard Gill

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5:01 AM (18 hours ago) 5:01 AM
to Mark Hadley, Bryan Sanctuary, Diether Fred, Bell_quantum...@googlegroups.com
Very good, Mark! I missed this one.


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On 13 Jan 2026, at 23:37, Mark Hadley <sunshine...@googlemail.com> wrote:


Dear Bryan,
Here is one explanation given to you back in October..

On Sun, Oct 12, 2025 at 10:49 PM Mark Hadley <sunshine...@googlemail.com> wrote:
Dear Btyan,
That's a great post. An excellent contribution. Very constructive.
It has the right details in it.
I say with confidence that I (we) agree with each equation for the correlations and the totals (except E_bivector)
And N^tot is correct

The point is that given the equation for E(a.b) which is true. It is what we measure and it is what we need to derive.
Do you agree that we need to derive an expression for E(a,b) in terms of the v and b distributions???

Once we substitute the equation for N^even etc then it is still true.
And what you call E_bellist, which is identically E(a,b), is achieved by algebra. 
There is no alternative result. It is a set of algebraic steps that are correct and offer no alternatives.

Your N^tot is correct.
You can rearrange the terms of E(a,b) in different ways perhaps, but no maths will get from the E(a,b) definition to the expression for E_biector

Or to put it another way what you call E_bellist is derived mathematically.
As far as I can see E_bivecor is just written done as a convenient(for you) result.

There are other ways to see that E_bivector is wrong. It does not depend on the relative number of b and v events.

So if there were a million b events and only 1 v event. Then E(a,b)_bivector would be just the same as if there were a 50:50 mix.
The E_bellist in contrast moves smoothly from one to the other as their contributions change.

Secondly, take a special case of b = -a so that E(a,b) = 1
Presumably E_v and E_b also have values of 1 otherwise they would disagree with experiment and with the BI assumptions.
The E_Bell says that the expected value is 1 which is sort of obvious.

E_bivector gives an expected value of 2 
Note that the maximum possible value in any experiment is 1 yet your expression says the average becomes 2 
which is clearly impossible.

Cheers
Mark








On Sun, Oct 12, 2025 at 10:05 PM Bryan Sanctuary <bryancs...@gmail.com> wrote:
Dear All,

Judging by the acrimonious replies I got from Richard, Jan-Ake and Mark, my assessment of them as hostile and sink to personal attacks appears to be spot on. I seek a clear academic solution to a problem that might be of interest to others.  What do EPR experiments give when there are two sources of correlation that the experiment cannot distinguish?  I want them to explain their objection to adding them.  I paste below a clear delineation of the issue so we have common notation and expressions to discuss.  I seek objective clarity, and collegial engagement.  
Bryan
<image.png>


On Sun, Oct 12, 2025 at 10:23 AM Bryan Sanctuary <bryancs...@gmail.com> wrote:

Dear Richard and others:

I took a respite from commenting, but still followed some interesting discussions.  I note there are two types of discussions: those who seek a collegial interaction to present their ideas, listen to responses, and hear about new ideas.  This is what the forum is about in my view.  Recently someone in this group, who followed the interactions with me and a few others, found it amusing, but suggested such aggravation is not the way to proceed. I fully agree.

There is a group of people, led by Richard Gill, who I first met in about 2002. He is the gatekeeper of Bell. He will talk with deep knowledge and engage cordially with anyone who does not threaten Bell.  Anyone who challenges Bell is attacked: first, if he can, to point out errors, and second, if he cannot, to simply discredit the challenger and obfuscate the problem.  That is where it becomes acrimonious.

Richard likes to propose a Bell bet (impossible to win because it is not possible to violate the inequalities with a local model. )  Richard recently said:  “have done this bet before. Luigi Accardi thought he could do it. He violated the conditions by using the detection loophole. Joy Christian thought he could do it. Fred Diether thought he could do it. Nobody has won the challenge yet.” Richard left out my bet with him, why? Because I made no errors and Richard seems reluctant or nervous to put his objections into press. So I can claim to have won, but I agreed with Richard to drop the bet.  I knew he would never capitulate.

Richard has attacked a lot more people than those above.  His biggest bet,  however, was 5,000 euros with me.  I did not take his above condition, I just said that I would show the violation with a local model and prove it with a simulation.  I did.  In the BiSM, coincidences have two sources: polarization and coherence.   Bell used one set, I used two. Here is my simulation:

<image.png>
 

Richard and other Bellists reject this. I will come to that. Note that there are two contributions to the correlation: between two vectors, (the triangle) and between two bivectors (the mustache).  Richard, and others, like Jan-Ake and Mark Hadley, say I lost the bet because I didn't do it in the two year limit but NOTE THIS: the paper sat with the Foundations of Physics for 9 months, the one REVIEWER WAS RICHARD GILL and the paper was rejected without allowing me a rebuttal.   That is why it was beyond the two years. Subsequently I published four papers on this. Even so the bellists say I am wrong, but they will not commit to explaining why.

They only say without justification,  I must average the correlations (vector and bivector) and not sum them.  They insist this means I do not violate BI,  and Jan-Ake concludes I fail Probability 101.

Any discussion about this is an exercise in futility.  Richard's goal is to discredit my work and save Bell.  Then, in response to my explanation, Richard and his other gatekeepers come out with sarcasm, leading questions to try to trip me, state I don't understand, and call into question my findings without any cogent explanation. Unlike with  Acardi, Christian and others, Richard is silent about me in the press but not in public or private. On forums like this, and behind my back, he tells everyone "Sanctuary does not understand Bell's work.".  That is his fall back position to save Bell.

I want to suggest a way out in my next email that hopefully allows us to resolve this issue once and for all. 

I am interested in Science and new ideas. Richard and some others want to gatekeep because if I am right, his legacy, and that of many others, is jeopardized. That is unwittingly done on my part. I simply could not accept quantum weirdness, and Bell's theorem stood in the way.  If  I am right, then Quantum information theory, as we know it, will end, and billions of research funding will find other projects  

So, from my perspective, the acrimony on this forum is due to the Gatekeepers of Bell, rather than trying to understand something entirely different. Richard admits he has not read my work and does not understand it, yet he says I am wrong.

I will soon send a proposal with the goal of settling the "add vs. average" issue.

Bryan

 

 

 

 


On Fri, Oct 10, 2025 at 11:57 PM Richard Gill <gill...@gmail.com> wrote:
Mark, if you want to *use* BI (1964, three correlations inequality) you’ll have to do experiments with four pairs of orientations (including one pair with equal orientations)

Under local realism, CHSH is *true* for any four orientations, including a = b = c = d. 

But watch out: BI is about theoretical expectation values. About mean values in the limit of infinitely many repetitions. In small samples there is statistical variation.

Fred has never understood the difference between  theoretical mean value and an experimentally found mean value.


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On 10 Oct 2025, at 22:40, 'Mark Hadley' via Bell inequalities and quantum foundations <Bell_quantum...@googlegroups.com> wrote:


No. a =b means the polarisers are both pointing the same way. That's a very special case and not interesting. BI requires at least three different orientations.



On Fri, 10 Oct 2025, 17:37 Fred Diether, <fredi...@gmail.com> wrote:
But for Bell's derivation, a = b always.  It's nonsense.

On Friday, October 10, 2025 at 12:06:23 PM UTC-7 sunshine...@googlemail.com wrote:
Dear Fred,

Yes, I agree with you. -1 always in that situation.

So if a =b then each arm of the experiment measures in the same direction.  Then if it's -1 on one side then it's +1 on the other side. And the product is always -1

P(a,b) is the expected value  the product of the results, or in other words it's the correlation. As Richard says it's poor notation P is the expected value of the product, not a probability.

So your analysis of equation 14 is correct,  if both arms measure in the same direction then the correlation is -1

I've downloaded the paper, so I should be more responsive going forwards.

Cheers
Mark


On Fri, 10 Oct 2025, 15:28 Fred Diether, <fredi...@gmail.com> wrote:
Your explanation was also a redirect.  I'll continue without your redirects.

If "a" = "b" then we have (A(a, lambda))^2 = 1 so, P(a, b) = -1  The right hand side of the equation is - 1 ALWAYS!

Now, you should be able to figure out what that does to the rest of Bell's calculation for the inequality.  It's nonsense.

On Friday, October 10, 2025 at 9:49:21 AM UTC-7 sunshine...@googlemail.com wrote:
Except I didn't redirect. I gave you a detailed answer to the equation you presented.

And then it was clear that you were struggling with the concepts and basic formalism of Bells original paper I offered you an easier route. But it's up to you. If you you want to ask about bells original paper by all means continue.

I've explained that equation 14. If it's still puzzling you, then write down the classical expression for the outcomes of throwing two dice. Expressed as a function of the unknown throwing parameters. You will get something very similar.

Cheers
Mark


On Fri, 10 Oct 2025, 13:14 Fred Diether, <fredi...@gmail.com> wrote:
Typical Bell fanatic procedure;  redirect the conversation to something else.

On Friday, October 10, 2025 at 3:35:48 AM UTC-7 sunshine...@googlemail.com wrote:
A more recent derivation of CHSH is easier to follow.

 It's admirable to look at the original papers, of course I had to do that when preparing my course. But Ishams book gave a much clearer treatment.

Cheers
Mark

On Thu, 9 Oct 2025, 22:31 Fred Diether, <fredi...@gmail.com> wrote:
LOL!  It's Bell 1964 equation (14).   I'm surprised you didn't know that. 

On Thursday, October 9, 2025 at 4:34:57 PM UTC-7 sunshine...@googlemail.com wrote:
Great,
Thanks for engaging and sharing with us.

I'll probably give a better answer if I know where it has come from and what the previous equations were.

But it looks to me like a classical equation for probability. Classically ALL probabilities can be expressed as a weighted volume element. It's practically the definition of classical probabilities. Where you sum or integrate over all possibilities. Here lambda is a catch all for the different possibilities ( the hidden variables ) and rho is the weighting, because some will be more likely than others.

By symmetry it's using the same function for a and b, I'm not certain of the context here.

So for example it's what you need if you threw two dice and a , b were the possible values. P(1,3) would be the probability that the first dice was 1 and the second was 3. Lambda would be all possible throwing parameters. rho would be needed because some throw speeds or spins would be more likely than others.

Does that make sense.

Cheers 
Mark





On Thu, 9 Oct 2025, 20:15 Fred Diether, <fredi...@gmail.com> wrote:
bell14.jpgeq.(14)
That is Bell's first mistake.  It is only good for when "a" = "b".  And it is not a probability; it is an average.

On Thursday, October 9, 2025 at 11:51:35 AM UTC-7 Fred Diether wrote:
You are so brainwashed that nothing I say is going to change your mind about Bell's nonsense.

I was waiting for you to respond to "local QM theory" but Richard interjected himself there then  Larsson started in with his nonsense.

On Thursday, October 9, 2025 at 10:55:11 AM UTC-7 sunshine...@googlemail.com wrote:
Dear Fred,

I think you are the only person I have come across who thinks there is a mathematical error in BI. It is high school maths.

Jan does a great teaching job on BI on this forum. He has helped me and I try to do the same to others.

I'm quite interested in how people respond to BI because I think one such result will lead to an explanation of QM.

I don't think the term indoctrination really applies to BI. It's not much more than the triangle inequality. Derived from the axioms of field theory.

As I said, pick a CHSH proof that's publicly available and tell us where you have an issue. That's where this forum can help.

Cheers
Mark

On Thu, 9 Oct 2025, 14:17 Fred Diether, <fredi...@gmail.com> wrote:
Hmm... I guess that is a NO.  You are not going to ignore my posts.  Ugh!

Educate?  That is BS!  You are trying to indoctrinate people to Bell's nonsense.  A real scientist wouldn't be that stupid.

Ok, time to get back to physics and not nonsense.

On Wednesday, October 8, 2025 at 10:18:28 PM UTC-7 Jan-Åke Larsson wrote:

A real scientist would attempt to understand.

A real scientist has a role in society to educate others.

An internet troll has the role to use up other peoples time for no good.

I am attempting to educate others here.

On 10/9/25 01:25, Fred Diether wrote:
If you don't know what you did wrong, I'm not going to tell you.  And if I see any actual scientists here, I will let you know.

A real scientist would never believe in Bell's nonsense and certainly wouldn't be wasting their time on this crummy Google group.  LOL!

BTW, I thought you were going to ignore my posts.  Please do; I'm pretty tired of your nonsense already.

On Wednesday, October 8, 2025 at 1:43:08 PM UTC-7 Jan-Åke Larsson wrote:

If you do not want to understand, why are you here?

To ridicule actual scientists?


On 10/8/25 22:41, Fred Diether wrote:
Oh double jeez, out of context nonsense piled on top of nonsense.

On Wednesday, October 8, 2025 at 10:52:29 AM UTC-7 Jan-Åke Larsson wrote:

Who said anything about action?

The statement is that you cannot reproduce quantum predictions using a local realist model. 

The claim is not that you need nonlocal action.


On 10/8/25 19:22, Fred Diether wrote:
Oh jeez, more nonsense.  All action in Nature is local.  The rest is just plain nonsense.

On Wednesday, October 8, 2025 at 8:42:27 AM UTC-7 sunshine...@googlemail.com wrote:
Fred,
There are different notions of local:

QT and QFT are both compatible with special relativity, don't allow signalling faster than light and predict probabilities with a local function. Hence a scientist might label the theory as local.

But all classical probabilistic theories ( think roulette) can be described in terms of microscopic deterministic theories.

People interested in foundations of QT and Bell's inequalities,care asking if QT can be described by underlying local deterministic theory. In the sense QT is not local.
Mark

On Wed, 8 Oct 2025, 12:30 Fred Diether, <fredi...@gmail.com> wrote:
You said "Define local QM theory".  

What is it that you don't understand?  local?  QM?  theory?

Well for sure, quantum field theory for particle physics is local.

On Tuesday, October 7, 2025 at 9:26:25 PM UTC-7 Richard Gill wrote:
Define “local QM theory”

Many people in QM consider it to be local. It is compatible with relativity theory. It does not allow action at a distance. 

A few years back it was shown that Tsirelson’s 2 sqrt 2 bound could be derived from an information theoretical principle (without using QM at all).

https://arxiv.org/abs/0905.2292


Sent from my iPad

On 8 Oct 2025, at 03:26, Fred Diether <fredi...@gmail.com> wrote:

That is NOT what I said.  I am talking about described by a local QM theory.

You said, "Strictly, we can't show that QM is not local."  So, how do you know it is non-local?  

On Tuesday, October 7, 2025 at 5:21:01 PM UTC-7 sunshine...@googlemail.com wrote:
We know it is not local. Assuming you mean described by a local realist theory. That's what I just said.

On Tue, 7 Oct 2025, 21:17 Fred Diether, <fredi...@gmail.com> wrote:
Do you think it is possible to show that QM is local?

BTW, Richard and I go way back.  I know all of his stuff.

On Tuesday, October 7, 2025 at 5:01:14 PM UTC-7 sunshine...@googlemail.com wrote:
Strictly, we can't show that QM is not local. We can show, easily, that the results cannot be explained by any local hidden variable theory.

So if you believe there is an underlying explanation for QM events then that explanation needs a non local element to it.

I think that's the current state of play. Jan may be able to say more.

Cheers
Mark

Hmm...  Did you show a proof that quantum mechanics is non-local?  You do a lot more quacking on this group than I do.  Maybe you should shut up.

Weird... now I am getting your messages to my email and not to the group.  ???  
From: Mark Hadley <sunshine...@googlemail.com>
Sent: Tuesday, October 7, 2025 3:46 PM
To: Fred Diether <fredi...@gmail.com>
Subject: Re: [Bell_quantum_foundations] Bell's biggest mistake
 
Fred,
Time to shut up now. I showed you a simple proof of Bell and invited you to identify any step that you didn't understand or didn't agree with. You did not respond. Indeed you could not respond.

Btw Richard has an unemotional computer test for anyone who thinks they have a way round BI.

Cheers
Mark

On Tue, 7 Oct 2025, 18:47 Fred Diether, <fredi...@gmail.com> wrote:
Ok Richard, actually you can disprove Bell.  Demonstrate that quantum mechanics is local.

On Tuesday, October 7, 2025 at 8:56:46 AM UTC-7 Richard Gill wrote:
Dear Eugen

Thanks

But you can’t disprove Bell’s theorem by doing calculations within quantum mechanics. Bell’s theorem is about the limits of classical physics enforced by local causality.

Richard


Sent from my iPhone

On 7 Oct 2025, at 17:25, Eugen Muchowski <eu...@muchowski.de> wrote:

Here is one:

Muchowski, E., What connects entangled photons? International Journal of Quantum Foundations Volume 9, Issue 4, October 2023 

https://ijqf.org/archives/category/all-volumes/volume-9-issue-4-october-2023

Best regards, Eugen



Am 07.10.2025 um 13:11 schrieb Richard Gill <gill...@gmail.com>:

PS There are no local contextual models with hidden variables that reproduce the quantum correlations.



On 7 Oct 2025, at 11:14, Eugen Muchowski <eu...@muchowski.de> wrote:

There are local contextual models with hidden variables that reproduce the quantum correlations.


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