ChatGPT analysing Diether and Sanctuary

[anton vrba]

Dear Fred, Dear Bryan

Enough is enough, stop bickering like Kindergarteners.  Once both of you have cleared the chatCPT critique summarised as  "your logic and your interpretation is inconsistent to Bell's theorem" you be better off not say anything at all. Looking forward to new papers that can pass the chatGPT review.

I asked chatGPT to review: 

Bryan Sanctuary:
1) Please forget whatever is in other projects and chats: 2) can you critique https://www.mdpi.com/2624-960X/6/3/28 not from accepted physics but purely mathematically and application of Bell's theorem

here is the full reply: https://chatgpt.com/share/695413ca-80e0-8011-98bc-0f5dae164a68  

Final Formal Conclusion

The specific equations used in the paper—operator traces for correlations (Eqns (8) and (14)), and algebraic helicity constructs (Eqn (12))—do not satisfy the mathematical assumptions required to derive or test Bell’s inequalities within classical probability theory. As a result:

• The model does not constitute a counterexample to Bell’s theorem,

• It does not define the necessary probability structure,

• It uses algebraic methods incompatible with the core premises of Bell’s inequality derivation. MDPI

Fred Diether III

please comprehensively review Diether paper https://www.scirp.org/journal/paperinformation?paperid=147271 together with reference Christian reference https://doi.org/10.1098/rsos.180526 and R.Gill comment https://doi.org/10.1098/rsos.201909 The comprehensive review is based solely on the mathematics and theorems of Bell and not subject to general opinion on seriousness and reputation of authors and journals

here is the full reply https://chatgpt.com/share/695414c6-2518-8011-80ee-dd5c0b772d02

7. Final Mathematical Verdict

What Diether successfully does

• Constructs an algebraic averaging procedure yielding the quantum correlation function

• Uses correct geometric algebra identities

• Produces numerically correct simulations

What Diether does not do

• Define scalar ±1-valued random variables satisfying Bell locality

• Provide a valid probability-theoretic expectation

• Evade the CHSH inequality within its domain of applicability

---

8. Precise Conclusion

Mathematical conclusion (strict):

Diether’s derivation does not refute Bell’s theorem because it does not instantiate the mathematical hypotheses of Bell’s theorem.

The result

E(a,b)=−a⋅b

is obtained by changing the mathematical object whose expectation is taken, not by violating a Bell inequality.

Bell’s theorem therefore remains intact.

Joy Christian: 
Here we continue the Mathematical Review Bell's Theorem: Can you do the same analysis on Christians paper

here is the full reply https://chatgpt.com/share/695415c0-c7a4-8011-bcad-f953d6ab4152

Final conclusion

Christian’s paper does not refute Bell’s theorem.
It presents a mathematically consistent non-Bell model that reproduces quantum correlations by abandoning Bell’s assumptions, particularly scalar outcomes and commutativity.

This is a change of axioms, not a disproof.

[Fred Diether]

LOL!  How wonderful!  More nonsense from a Bell fanatic.  We already know BS's papers are a pile of junk.  You have any papers AI can review? 

Your chatGPT missed the mark on my paper.  My paper is a prediction that quantum mechanics is local for EPR-Bohm.  The AI didn't say anything about that.  And I am not going to click on any links from a Bell fanatic for security reasons.  Post the whole thing here or shut the F up!

[Bryan Sanctuary]

Dear Anton

Thank you for taking the time to obtain independent ChatGPT reviews.

However, you have not framed the question to ChatGPT which is relevant here.

My present paper is about Fred’s errors. It is not a philosophical challenge to Bell’s theorem, nor does it rely on my spin–helicity paper. Its sole purpose is to identify specific algebraic errors in Diether’s derivation, Eqs. (20)–(27), which are inherited from Christian.

The issue under discussion is therefore not “whether Bell survives”, but whether Diether’s equations are internally correct. Deflecting this into philosophy, subjective comments, or my other papers misses the point entirely.

If you wish to rely on ChatGPT, the appropriate question is not a general Bell critique, but a direct comparison of Diether’s Eqs. (20)–(27) with my explicit correction. That is where the disagreement lies.

I suggest we keep the discussion focused on that concrete mathematical issue.  Moreover, you might note that I have not responded to Diether for some time and his latest reply represents an ad hominem response of no interest.  I will send the forum the reviewers’ comments as they come in.  I rely on those more than the Chat GPT.

Best regards,
Bryan

[Fred Diether]

Triple LOL!  BS really is a clueless sociopath and a traitor.  Anton does not care about your idiotic paper about my paper.

[anton vrba]

Dear Bryan, I let chatGTP loose on you old paper “Spin Helicity and the Disproof of Bell’s Theorem” (Sanctuary, MDPI Quantum Reports 2024) and it highlights exactly where you go wrong.

But now by your request, I asked chatGPT: Please review Sanctuary's critique to Diether's paper The Diether and Christian papers are available in the other threads as internet links.

Here is the full reply: https://chatgpt.com/share/6954391e-d3c4-8011-ae9b-f9ff973aab80

Generally chatGPT confirms your critique of Eqs. (20)–(27) , and this should please you: yours and R.Gill comment https://doi.org/10.1098/rsos.201909  on Christian reference paper concur .

9. Final synthesis

Gill provides the general impossibility proof. [for Christians paper]
Sanctuary provides the forensic reconstruction. [for Diether paper]

They differ in language, but not in substance.

If Gill is correct, no Christian-style model can work.
If Sanctuary is correct, Diether’s specific implementation fails exactly in the way Gill predicts.

Taken together, they form a mutually reinforcing refutation:

• Gill: This class of models cannot produce Bell correlations locally.

• Sanctuary: Here is precisely how this one fails.

From a strictly mathematical standpoint, there is no tension between the two critiques; Sanctuary’s analysis sits squarely within Gill’s framework and makes its abstract objections explicit at the level of equations.

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

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

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

Cc "Bell Inequalities and quantum foundations" <bell_quantum...@googlegroups.com>

Date 12/30/2025 6:58:50 PM

Subject Re: ChatGPT analysing Diether and Sanctuary

[Fred Diether]

Oh, so Anton is going to continue with his Bell fanatic nonsense.  How wonderful is that?  LOL!  Your stupid AI still hasn't addressed the main point of my paper.

But thanks anyways for drawing attention to it.

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

[anton vrba]

Fred, stop acting like a spoiled child ! You do not post your papers as the whole thing, so why the fuck should I click on a scrip.org link in the future to read your papers?  Stop spamming us, how many times have we seen it. Same logic applies!

The real question to ask both Fred and Bryan, what physical realities has your model. Can it model a photon with it properties like polarisation, orbital angular momentum OAM, Berry phase rates under cyclic evolution in polarisation, etc.  If not then all your mathematical wizardry is just mental masturbation.

[anton vrba]

Fred claims:  My paper is a prediction that quantum mechanics is local for EPR-Bohm.  The AI didn't say anything about that.  And I am not going to click on any links from a Bell fanatic for security reasons.

so I asked chatGPT:

The reply is appended to the previous reply  https://chatgpt.com/share/695414c6-2518-8011-80ee-dd5c0b772d02

 

But to satisfy Fred's clicking links phobia here is chatGPT answer to Fred's claim

Diether’s criticism hinges on a category distinction that is important to make explicit. His statement—

“My paper is a prediction that quantum mechanics is local for EPR–Bohm. The AI didn’t say anything about that.”

—can be addressed cleanly within the mathematics of Bell’s theorem, without invoking reputation, intent, or interpretation.

The short answer is:
the review did address locality, but at the level at which Bell’s theorem defines and constrains it. Diether’s notion of “local” is not the same mathematical notion of locality used in Bell’s theorem, and this difference is decisive.

Below is a precise clarification.

---

1. What “Local” Means in Bell’s Theorem (Mathematically)

In Bell’s framework, locality is not a philosophical slogan. It is a factorization condition on random variables:

P(A,B∣a,b,λ)=P(A∣a,λ)P(B∣b,λ)

Equivalently, for deterministic models:

A=A(a,λ),B=B(b,λ)

This definition has three non-negotiable mathematical consequences:

1. Outcomes are scalar random variables (±1)

2. They are jointly defined for all settings

3. Their correlations are expectations of pointwise products

Bell’s theorem states:

No theory satisfying this definition of locality can reproduce the EPR–Bohm correlations of quantum mechanics.

This is a theorem in probability theory.

---

2. What Diether Means by “Local”

Diether uses “local” in a different sense, closer to:

• No superluminal signalling

• No explicit dependence of one wing’s algebraic expression on the distant setting

• Local generation of geometric algebra elements

All of these statements may be true of his construction.

However:

They are not sufficient to establish Bell locality.

Bell locality is stronger and more specific than “no signalling” or “no explicit dependence”.

This distinction is standard and mathematically precise:

• Quantum mechanics itself is no-signalling

• Yet quantum mechanics is not Bell-local

Thus, claiming locality in the no-signalling or geometric sense does not contradict Bell’s theorem.

---

3. Why the Review Did Not Accept the “Local QM” Claim

The review did not ignore Diether’s claim; it evaluated whether his construction satisfies Bell locality.

The conclusion was:

Diether’s model does not define scalar, jointly measurable, ±1-valued random variables whose expectations reproduce the correlations.

Once that is established, the following implication is unavoidable:

• Either the model is not Bell-local

• Or it is not a hidden-variable model in Bell’s sense

• Or it abandons joint definability / realism

Diether’s construction falls into the second and third categories.

Therefore, the claim
“quantum mechanics is local for EPR–Bohm”
does not hold in the mathematical sense relevant to Bell’s theorem, even if the model is “local” in a weaker or different sense.

---

4. Where Diether’s Claim Overreaches

Diether’s result can be stated accurately as:

“There exists a geometric-algebraic averaging procedure, using locally generated objects, whose scalar projection reproduces the quantum correlation.”

What cannot be stated (mathematically) is:

“Therefore quantum mechanics satisfies Bell locality.”

That inference fails because:

• Bell locality is a property of probability measures on scalar random variables

• Diether’s correlations are ensemble-level algebraic scalars, not expectations of pointwise outcomes

This is exactly the same gap identified by Gill in relation to Christian, and it applies regardless of whether the construction is elegant, deterministic, or local in a geometric sense.

---

5. Why Bell’s Theorem Still Applies

If quantum mechanics were Bell-local for EPR–Bohm, then:

• A CHSH inequality derivation would go through

• The inequality would not be violated

But experimentally and mathematically:

∣S∣=2√2  ​>2

Diether’s model reproduces this value only by stepping outside the mathematical domain in which the inequality is derived.

That does not refute Bell’s theorem; it confirms its scope.

---

6. Final, Precise Response to Diether’s Criticism

A mathematically accurate reply to Diether’s statement would be:

Your paper demonstrates a local geometric-algebra construction that reproduces quantum correlations, but it does not demonstrate Bell locality as defined in Bell’s theorem. Therefore it does not establish that quantum mechanics is local in the sense ruled out by Bell.

The original review did not omit this point; it implicitly addressed it by showing that Bell locality is not satisfied, even if “locality” in another sense is preserved.

---

Bottom line (strictly mathematical):

• Diether may correctly claim no signalling and local algebraic generation

• He may not claim Bell locality for EPR–Bohm

• The review evaluated locality at the only level where Bell’s theorem applies

If you want, I can next:

• Formalize Diether’s model as a contextual hidden-variable theory

• Show explicitly which Bell axiom fails (Outcome realism vs joint measurability)

• Or contrast Bell locality with parameter independence / outcome independence in Diether’s framework

Do all three

I. Formal Rewriting of Diether’s Model as a Contextual Hidden-Variable Theory

I.1 Bell’s Non-Contextual Hidden-Variable Structure

A Bell-local hidden-variable (HV) model requires a single probability space

(Λ,F,ρ)

and four jointly defined random variables

A(a,λ),A(a′,λ),B(b,λ),B(b′,λ)∈{±1}

such that for all λ:

E(a,b)=∫Λ​A(a,λ)B(b,λ)ρ(dλ)

The crucial property is joint definability: all four variables exist simultaneously for the same λ.

---

I.2 Diether’s Actual Mathematical Objects

Diether does not define four scalar random variables. Instead, he defines setting-dependent algebraic maps:

A(a,λ),B(b,λ)

where:

• A,B are geometric algebra elements

• Scalar outcomes emerge only after averaging and projection

• Different settings require different algebraic contexts

Thus, for a fixed λ:

• A(a,λ) and A(a′,λ) are not jointly defined scalar objects

• Their scalar reductions depend on which measurement context is chosen

---

I.3 Formal Contextuality Statement

Diether’s model satisfies:

A(a,λ) exists only relative to context a

There is no function

λ↦(A(a),A(a′),B(b),B(b′))

defined on a single probability space.

This is the definition of contextuality in the Kochen–Specker / Bell sense.

Therefore, Diether’s model is mathematically a contextual hidden-variable theory.

Contextual hidden-variable models are explicitly excluded from Bell’s theorem.

---

II. Explicit Identification of the Bell Axiom That Fails

Bell’s assumptions can be decomposed as follows:

Bell Assumption	Status in Diether’s Model
Measurement independence	Satisfied
Parameter independence (no signalling)	Satisfied
Outcome independence	Violated
Joint definability	Violated
Scalar random variables	Violated

Let us be precise.

---

II.1 Parameter Independence (Satisfied)

Diether ensures:

A(a,λ) does not depend on b B(b,λ) does not depend on a

This guarantees no superluminal signalling.

Quantum mechanics itself satisfies this.

---

II.2 Outcome Independence (Violated)

Outcome independence requires:

P(A∣a,b,λ)=P(A∣a,λ)

But in Diether’s model:

• The scalar outcome does not exist prior to averaging

• The value depends on algebraic cancellation with the partner wing

Hence:

A is not a function of (a,λ) alone

This violates outcome independence.

---

II.3 Joint Measurability (Decisive Failure)

Bell’s derivation requires:

A(a,λ),A(a′,λ) both exist

Diether’s algebraic objects do not permit this:

• Each measurement setting defines its own algebraic reduction

• There is no common refinement

Mathematically:

A(a,λ)&A(a′,λ)cannot be jointly assigned

This single fact is sufficient to block Bell’s inequality.

---

III. Why Diether’s Model Cannot Satisfy the CHSH Inequality

III.1 Algebraic Identity Behind CHSH

For scalar variables:

A(a)B(b)+A(a)B(b′)+A(a′)B(b)−A(a′)B(b′)=±2

This identity holds pointwise, before averaging.

---

III.2 Why It Cannot Be Written in Diether’s Model

In Diether’s construction:

• Each term lives in a different algebraic context

• The four terms cannot be summed as scalars

• No pointwise identity exists

Therefore:

• The CHSH inequality is not violated

• It is undefined

This is not a loophole; it is a change of axioms.

---

IV. Relation Between Bell Locality and Other Notions of Locality

This resolves Diether’s complaint directly.

IV.1 Three Distinct Notions of Locality

Notion	Meaning	Status in Diether
Relativistic locality	No superluminal signals	✔
Parameter independence	No dependence on remote setting	✔
Bell locality	Factorization + joint realism	✘

Bell’s theorem concerns only the third.

Thus, the statement:

“Quantum mechanics is local for EPR–Bohm”

is true in the first two senses and false in the third.

Bell’s theorem addresses only the third.

---

V. Why the Original Review Was Correct but Implicit

The earlier review did not explicitly repeat Diether’s locality claim because:

• The mathematical test for Bell locality was applied

• The model failed that test

• Therefore the claim was already negated by implication

Stated explicitly:

Diether demonstrates locality in the no-signalling sense, but not locality in the Bell sense required to evade Bell’s theorem.

---

VI. Final Mathematical Summary (Unambiguous)

1. Diether’s model is a contextual hidden-variable theory

2. It violates joint definability and outcome independence

3. It preserves no signalling, like standard quantum mechanics

4. It does not satisfy Bell locality

5. Therefore it does not imply that quantum mechanics is Bell-local for EPR–Bohm

---

Final Verdict (Strictly Mathematical)

Diether’s paper does not refute Bell’s theorem.
It reconstructs quantum correlations using a contextual, non-Bell-local framework that preserves relativistic locality.

This is fully consistent with Bell, with quantum mechanics, and with Gill’s critique.

If you want, the next natural step would be:

• A side-by-side symbolic derivation showing exactly where Bell’s inequality collapses when joint measurability is removed, or

• A comparison with explicitly known contextual models (e.g. Fine, Spekkens, Kochen–Specker)

Just indicate your preference.

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

From "Fred Diether" <fredi...@gmail.com>

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

Date 12/30/2025 6:47:13 PM

Subject [Bell_quantum_foundations] Re: ChatGPT analysing Diether and Sanctuary

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[Fred Diether]

Of course!  What can we expect from a Bell fanatic?  More freakin' nonsense.  Eat this,

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

[Fred Diether]

Of course!  What can we expect from a Bell fanatic?  More freakin' nonsense.  Eat this,

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

[Fred Diether]

Oh, BTW please stop spamming the group with your Bell fanatic nonsense.  I think we have had quite enough of the nonsense here.

Here is what Google Gemini had to say about my paper,

"Final Assessment

If you define "local" purely as the absence of instantaneous physical influence between distant points, then yes, this paper successfully demonstrates a mechanism for the EPR-Bohm correlations. It shifts the "mystery" of quantum mechanics away from "non-locality" and onto the geometric structure of physical space itself. It shows that what we perceive as "spooky action at a distance" is actually just the local geometry of the 3-sphere being misinterpreted through the lens of a simpler 3D flat space."

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

On Tuesday, December 30, 2025 at 2:07:42 PM UTC-8 antonvrba wrote:

[Mark Hadley]

Ha ha

That Gemini comment destroys the work doesn't it ??

If, if, you define local that way, then the work is unremarkable. 

And....

If you define local that way, then you cannot engage with a forum where the word means something rather different to everyone else. 

As said repeatedly, you don't know what you are talking about.

Marj

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/09825da2-5618-4635-abd7-c9e55eb6b683n%40googlegroups.com.

[Bryan Sanctuary]

  Thanks, Anton—I appreciate the careful comparison. I’ll be glad if you’re willing to look at the scalar-limit point when you have time.

Bryan  

[Fred Diether]

Well group, what do you think?  Do you think Bell fanatic Mark will ever learn and understand physics?

I don't think he ever will.  In fact, I don't know of any Bell fanatics that actually understand physics.  They are and want to remain stupid idiots.  LOL!

Mark, you can munch on this also,

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

[Fred Diether]

BS, you are an idiot.  The chatbots make mistakes all the time.  Enjoy snacking on the following.  LOL!

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.

[Mark Hadley]

Why don't not you just argue with Gemini and give us all a break.

Your definition of local is not standard

With your definition of local your results are unremarkable 

With the normal definition of local your results are wrong.

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/21ce9aa5-a878-40b1-88af-c94bc815e953n%40googlegroups.com.

[Fred Diether]

Well group, you just heard it from the horse's mouth.  The Bell fanatic Mark doesn't want to learn and understand physics.

Plus..., how do we know Mark is a liar?  We know because he said he was going to ignore my posts.  A liar and a dummy that doesn't want to learn nor understand anything.

Local Quantum Mechanical Prediction of the Singlet State Using Geometric Algebra

https://www.scirp.org/journal/paperinformation?paperid=147271

Bell was wrong big time.