Instantiated bivector planes: Double Slit vs. EPR

[Bryan Sanctuary]

Dear All,

I have been, mostly, occupied and not had a chance to reply. I posted the simulation that uses instantiated planes that are present in bivectors but not in usual Dirac spin.  There is more to come, the program and some notes, and will soon.

Why am I on this forum? I was asked. It is quite simple: I believe this question is so important, I just accept the agro as part of it. I believe the bivector provides a lot that is missing, and until I am proven wrong, I will push it.

The Bet

The bet was recently raised again by Richard: I will bet you any time, but the goals must be clear.  I do not want a recipe telling me what to do. You must tell me what to show in a simulation.  This time, to avoid the confusion about what winning means, I suggest we have 5 impartial judges, and a majority wins.  Anyway, it is up to you. 

The question

But my only focus here is science. I will show how the violation can be explained.  First, however, my paper. The Double Slit Experiment in the Bivector Standard Model."  has been accepted. The resolution of the Double Slit experiment using bivectors is very similar to EPR violation. So once the paper is out, I will send you a link. 

There is something else: in a double slit experiment, I show that each particle hits the screen one-by-one that seems random. The interference is only seen at the end of the experiment, when the bin populations are counted: that is where the coherence is manifest, AFTER the collection of many experiments, not from  one click.

• double slit: interference phase appears statistically in spatial bins 
• EPR:  coherences appears statistically in coincidence bins.

Bell only considers Boolean pairs.  They cannot give the statistical coherence of the bins. Geometry is needed to restrict the pairs.

A similar macroscopic collective motion is observed is superconductivity, superfluidity, coherent lasers, Bose-Einstein Condensates, etc. 

Looking forward to interesting discussions

Best wishes

Bryan

[Mark Hadley]

Bryan,

You lost the bet. You said you would convince the majority of physicists that you had a local explanation of epr. You even claimed that people would hand back Nobel prizes. And the vet had a date. One year.

You did not do this. Nobody thinks you did this. Not 3 adjudicators not 5.

You missed the deadline and lost.

You are dishonest not to admit this and pay up.

Mark

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[Richard Gill]

Dear Bryan, dear all, especially Parker and Ghenadie,

Regarding EPR, I’m just waiting to see the code Bryan used to create the right hand picture of the pair of images he sent us recently. The second is certainly a big improvement on the first.

Regarding challenges, my longstanding challenge remains open, the rules are very clear, it does not require a jury. If anyone thinks they can win my challenge they simply must make their code publicly available. See Section 9 of https://arxiv.org/pdf/1207.5103 on Quantum Randi Challenges.

I think it is clear from Bryan’s latest email that he ran Bell’s simple LHV model, collected the data, and post-processed it in his own way using bivectors.

As I said, I’m waiting to see the code. We can send it to Zeilinger, or the folk at Delft or at NIST, or to Gisin, and ask them to reprocess their data using his bivector algorithm.

Yours

Richard

PS my paper was published here: https://projecteuclid.org/journals/statistical-science/volume-29/issue-4/Statistics-Causality-and-Bells-Theorem/10.1214/14-STS490.full

Statistics, Causality and Bell’s Theorem

Richard D. Gill

Statist. Sci. 29(4): 512-528 (November 2014). DOI: 10.1214/14-STS490

It has been cited 126 times according to Google scholar, mostly not by myself. And by Bell-deniers as well as Bellists.

Sent from my iPad

On 23 May 2026, at 02:22, Bryan Sanctuary <bryancs...@gmail.com> wrote:



[Richard Gill]

Bryan, let’s turn it around. Why don’t you write the recipe? Then I’ll write the code.

It could be “the task is to come up with post-processing of the data generated by a simulation of Bell’s LHV in order to create a graph like panel 2 of the pair of graphs Bryan sent us the other day”. 

I’ll do it without a quaternion rotor! I think my code will be simpler than yours.

Sent from my iPad

On 23 May 2026, at 02:22, Bryan Sanctuary <bryancs...@gmail.com> wrote:

[Richard Gill]

Dear all

I wrote the following short R program, to explain what I mean. I draw the triangle wave by simulating Bell's simple model. Then I apply what I call "Gill's cosine rotor" to transform the correlations obtained from the raw data into the theoretical negative cosine. 

set.seed(12345)

alpha <- 0

gamma <- runif(10000, 0, 2 * pi)

results <- rep(0, 361)

for (i in 1:361){

    beta <- (i - 1) * pi / 180

    x <- 2 * ((gamma - alpha) %% (2 * pi) < pi / 2 | (alpha - gamma) %% (2 * pi) < pi / 2) - 1

    y <- - (2 * ((gamma - beta) %% (2 * pi) < pi / 2 | (beta - gamma) %% (2 * pi) < pi / 2) - 1)

results[i] <- mean(x * y)

}

plot(0:360, results, type = "p", pch = 3, cex = 0.2,

      main = "EPR correlations using a Gill-cosine rotor", xlab = "(a - b)", col = "blue")

points(0:360, cos(-pi/2 + results * pi/2), pch = 3, cex = 0.2, col = "red")

text(300, 0.7, "Bell's Boolean pairs", col = "blue")

text(300, 0.8, "Gill's cosine phase", col = "red")

Yours

Richard

[Richard Gill]

This RPubs report of the results of a simple R program shows how to tweak the data coming out of Bell's very simple local hidden variables model so as to reproduce the negative cosine predicted by quantum mechanics. Bryan Sanctury has a similare trick using Geometric Algebra. I prefer to keep it simpler: I just plug in the cosine, and hey presto, out it comes!

As you can see, all we need to know is to enlarge correlations close to -1 or +1 and to shrink correlations near zero so they become closer to zero.

A very simple post data-collection transformation does the trick. Kind of “data massage”.

No need to do this with bivector rotors. A cosine transformation is much easier.

On 23 May 2026, at 02:22, Bryan Sanctuary <bryancs...@gmail.com> wrote:

[Austin Fearnley]

Hi Richard

I have not followed you in RPubs but simply assume you are correct.

When averaging correlation coefficients using of the Fisher's z transformation, the problem with r is that it gets notionally blocked by the barriers at +1 and -1 correlation as one cannot get, say, correlations of +1.2 or -1.3.

So Fisher's z transformation counteracts the compression of r at the barriers.  This sounds like you could try using a Fisher's z transformation instead of the cos formula?

Austin

[Parker Emmerson]

Check.

Bell locality is not the same as microcausal locality, and Richard-compliance is not Bell's original language. If a model has Bell-local scalar response functions with one unconditional ensemble, the Richard spreadsheet follows. Richard-compliance is a later finite protocol, not Bell's original wording, but it is not arbitrary goalpost-moving for Bell-local LHV models; it is the finite spreadsheet form of their CHSH counterfactual structure, PV can evade it only by becoming selection-contextual or noncommutative, Richard's additional caveats and refinement of Bell's theorem may indeed illustrate he understands where its purview stopped. Your spreadsheet challenge tests global Booleanization. These programs test the Bell-only algebraic event law. PV passes the latter and deliberately rejects the former. These programs complete the Bell-only diagram task, not the Gill spreadsheet task. The issue is that if the task were Bell-only, it would be fair, but the Gill-spreadsheet requirement makes it unfair. Bell's theorem did not originally say: “Assume a Gill spreadsheet.” Bell's theorem did not originally present itself as merely a theorem about “Kolmogorov/global-Boolean spreadsheets.”

Richard’s spreadsheet is a valid test of Bell-factorizable hidden-variable programs, but it is not Bell’s original theorem itself. It is a finite global-Boolean operationalization of one normal form of Bell locality. PV does not claim that the pre-Boolean event structure is a table of simultaneous scalar values (A_0,A_1,B_0,B_1). PV lifts the Lorentz coefficient into a branch/fiber rotor or into holomorphic/saddle event geometry. The resulting model has cross-wing microcausality ([A(a),B(b)]=0), locally noncommuting alternatives, and the singlet law (P(x,y|a,b)=\frac14(1-xy\cos(a-b))). Thus it reproduces the Bell/EPR graph while rejecting the Gill spreadsheet ontology. The spreadsheet proves that global Boolean shadows cannot violate CHSH; it does not prove that PV event algebra cannot reproduce the EPR law.

PV need not be described as “abandoning a Bell-locality premise” unless Gill first establishes that Bell’s foundational criterion legitimately requires PV’s event structure to be represented by his factorizing/global-counterfactual format. Bell’s theorem is a theorem about locality as Bell formulated it; Gill’s spreadsheet is a particular executable formalization of that locality criterion. If PV contends that Gill’s formalization has added a Boolean counterfactual requirement not warranted by Bell’s more general foundational logic, then the issue is not which premise PV abandons, but whether Gill’s protocol has faithfully represented Bell’s premise for the PV case at all. Bell’s own later definition of local causality refers to probabilities for local beables being unaffected by sufficiently specified spacelike-separated beables and relevant past causes; the disputed move is turning that causal requirement into a four-column Boolean outcome table for a non-Boolean event model.

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/96229dc5-0d18-465f-9a93-1d688fd50ffdn%40googlegroups.com.

[Richard Gill]

Dear Parker

I am under no obligation whatsoever. I promote the notion of irreducible randomness and I promote Belavkin’s solution of the measurement problem. But I have no “programme” of how to go further. I do combat nonsense where I see it.

The obligation is on you, Parker, to show that PV makes exciting and testable predictions. I’m not qualified to judge. For that purpose you’ll have to learn to present your ideas in language which people understand instead of in what appears to be an extensive and impenetrable private jargon. You can hope to get someone else excited and do that job. Good luck. I recognise originality but I’m sceptical.

My spreadsheet challenge is a didactic tool and a joke. It is literally a fool’s quest. Please study my writing on quantum Randi challenges in the last section of my 2014 “Statistical Science” paper https://arxiv.org/abs/1207.5103 

“ Statistics, causality, and Bell’s theorem “.

Since then I’ve been retired and primarily working on miscarriages of justice, and especially the Lucy Letby case.

Sent from my iPhone

On 24 May 2026, at 07:30, Parker Emmerson <powerin...@gmail.com> wrote:



Check.

Bell locality is not the same as microcausal locality, and Richard-compliance is not Bell's original language. If a model has Bell-local scalar response functions with one unconditional ensemble, the Richard spreadsheet follows. Richard-compliance is a later finite protocol, not Bell's original wording, but it is not arbitrary goalpost-moving for Bell-local LHV models; it is the finite spreadsheet form of their CHSH counterfactual structure, PV can evade it only by becoming selection-contextual or noncommutative, Richard's additional caveats and refinement of Bell's theorem may indeed illustrate he understands where its purview stopped. Your spreadsheet challenge tests global Booleanization. These programs test the Bell-only algebraic event law. PV passes the latter and deliberately rejects the former. These programs complete the Bell-only diagram task, not the Gill spreadsheet task. The issue is that if the task were Bell-only, it would be fair, but the Gill-spreadsheet requirement makes it unfair. Bell's theorem did not originally say: “Assume a Gill spreadsheet.” Bell's theorem did not originally present itself as merely a theorem about “Kolmogorov/global-Boolean spreadsheets.”

Richard’s spreadsheet is a valid test of Bell-factorizable hidden-variable programs, but it is not Bell’s original theorem itself. It is a finite global-Boolean operationalization of one normal form of Bell locality. PV does not claim that the pre-Boolean event structure is a table of simultaneous scalar values (A_0,A_1,B_0,B_1). PV lifts the Lorentz coefficient into a branch/fiber rotor or into holomorphic/saddle event geometry. The resulting model has cross-wing microcausality ([A(a),B(b)]=0), locally noncommuting alternatives, and the singlet law (P(x,y|a,b)=\frac14(1-xy\cos(a-b))). Thus it reproduces the Bell/EPR graph while rejecting the Gill spreadsheet ontology. The spreadsheet proves that global Boolean shadows cannot violate CHSH; it does not prove that PV event algebra cannot reproduce the EPR law.

PV need not be described as “abandoning a Bell-locality premise” unless Gill first establishes that Bell’s foundational criterion legitimately requires PV’s event structure to be represented by his factorizing/global-counterfactual format. Bell’s theorem is a theorem about locality as Bell formulated it; Gill’s spreadsheet is a particular executable formalization of that locality criterion. If PV contends that Gill’s formalization has added a Boolean counterfactual requirement not warranted by Bell’s more general foundational logic, then the issue is not which premise PV abandons, but whether Gill’s protocol has faithfully represented Bell’s premise for the PV case at all. Bell’s own later definition of local causality refers to probabilities for local beables being unaffected by sufficiently specified spacelike-separated beables and relevant past causes; the disputed move is turning that causal requirement into a four-column Boolean outcome table for a non-Boolean event model.

<03_holomorphic_phase_fiber.png>

<02_holomorphic_saddle_diagram.png>

<01_pv_lorentz_rotor_diagram.png>

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CANitqNkvXXYaoOz%3DRC2_e7%2B56XFgQieLMD2oM114ChzGabeH%2Bg%40mail.gmail.com.

<Bell_only_PV_Holomorphic_Saddle_Challenge_Diagrams.ipynb>

[Richard Gill]

Austin, why use arc tangent when my cosine transformation does the job exactly? It’s a smooth transformation of [-1, +1] to itself.

Fusher’s z-transformation had the purpose of stabilizing the variable of an empirical correlation thereby improving the normal approximation (hence the name “z”) used in creating a confidence interval for the true correlation based on sample data. Bryan’s purpose is to replace the observed correlation with one predicted by quantum theory. 

If the experimenters did their job well and QM is true they certainly don’t want to distort their statistics to show different results from what they observed.

Bryan seems to be interested in experiments which at first sight show Bell’s saw tooth (aka triangle wave, or zigzag) correlation.

Sent from my iPhone

On 23 May 2026, at 19:54, Austin Fearnley <ben...@hotmail.com> wrote:

Hi Richard

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/96229dc5-0d18-465f-9a93-1d688fd50ffdn%40googlegroups.com.

[Richard Gill]

Simple way to massage Bell LHV correlations to look like quantum correlations.

[Austin Fearnley]

Hi Richard

I withdraw my comment.

I was simply pointing out that Fisher's Z had a track record for use with transforming  r.  Of course, one needs to use the inverse z at the end of any manipulations.

Further, it is dark arts to manipulate Bell outcomes in this manner and I do not condone that.  I withdraw my comment as I don't want it thought that I agree with this approach.

When our paths first crossed on Fred's website I was trying to obtain the cos curve on one of JCs models in a simulation I was writing in Excel VB.  I couldn't get the cos curve while others were obtaining what seemed to be close.  You entered the scene and asked for all pairs to be counted for input and than output.  It then came out that others were not using all pairs as output.  I had been worrying that my VB was somehow inferior, but no, I was simply using all data pairs.  I still do not understand how folks were writing their code to allow that.

Austin

[Parker Emmerson]

Dear Richard,

On the contrary, the code speaks for itself. If you yourself are not qualified to judge objections to your own challenge, then why host a challenge? Meta-logical and mathematical realities aren't jargon for those who are literate in them. It seems you've encountered a higher order logic to deprogram your proposed goose chase. Indeed, the power of meta-mathematics and mathematical semantics is that it changes what people perceive as possible. If that's not exciting to you, I'm not sure why you are in the sciences. I think you really are hooked on phenomenological velocity now actually.

The major issue is this: If your challenge admits only classical scalar local-response programs whose four counterfactual outputs coexist on a single Boolean sample space, then its no-win conclusion inside that class is mathematically valid. Parker’s own Rung-0 analysis agrees with it.

But excluding the PV microcausal model on the ground that it is not a member of that scalar Boolean class is not a test of the PV model. It is a tautological admission rule: a noncommutative event model is rejected because the challenge was defined to accept only commutative scalar models. Now to be fair, diagnosing this tautology of yours was time intensive and complex, so it would indeed get the better of most.

The updated program addresses your challenge in the form that actually matters operationally: it generates run-by-run binary outputs at Alice and Bob, chooses the measurement settings independently after source preparation and separation, scores every run unconditionally in the PV lane, and produces the singlet correlation table with CHSH value approaching (2\sqrt{2}).

The program is not merely plotting (-\cos(a-b)), and it is not substituting a precomputed correlation curve for trial outcomes. It now produces explicit event records:

[
(a_i,b_j,A_i,B_j,A_iB_j)
]

for every run, with (A_i,B_j\in{\pm1}). The PV microcausal lane then computes the CHSH statistic from those recorded outcomes exactly as an experimental run log would.

The crucial point is that the program contains three separate lanes and does not conflate them.

The first lane is the ordinary Bell/Gill scalar-output model:

[
A(a,\lambda)=\operatorname{sgn}(\cos(\lambda-a)),\qquad
B(b,\lambda)=-\operatorname{sgn}(\cos(\lambda-b)).
]

It satisfies the classical Bell premises and produces the expected triangular correlation with (S\approx2). Parker’s mathematics agrees with this. There is no claim that a Gill-admissible classical scalar table reproduces (2\sqrt2).

The second lane implements the setting-dependent acceptance construction. It also uses run-by-run local scalar outputs, but the accepted sample is setting dependent. It reproduces (-\cos(a-b)) on accepted data, while explicitly recording that unconditional all-run scoring has been abandoned. That lane is included as a diagnostic control, not as the unconditional PV result.

The third lane is the actual unconditional PV construction. It uses the phenomenological-velocity parameter through

[
\kappa(v)=\sqrt{1-\frac{v^2}{c^2}},\qquad
\vartheta(v)=\arccos(v/c),
]

and the associated local rotor

[
U(v)=\exp!\left(-\frac{i}{2}\vartheta(v)\sigma_y\right).
]

The Alice and Bob observables are

[
A_v(a)=\bigl(U(v)^\ast\sigma(a)U(v)\bigr)\otimes I,
\qquad
B_v(b)=I\otimes\bigl(U(v)^\ast\sigma(b)U(v)\bigr).
]

These are local in the microcausal sense:

[
[A_v(a),B_v(b)]=0.
]

The program verifies this directly. It also verifies that the within-wing alternative observables do not commute, which is precisely why the model is not reducible to the classical Boolean counterfactual spreadsheet assumed by the scalar Bell program class.

In the singlet state, the common PV frame shift cancels relationally:

\langle\psi^-|A_v(a)B_v(b)|\psi^-\rangle

-\cos(a-b).
]

The run-by-run simulator samples actual (\pm1) event outcomes from this joint event law, with unbiased local marginals and the required pair correlations. On the standard CHSH quartet,

[
a_0=0,\quad a_1=\frac{\pi}{2},\quad
b_0=\frac{\pi}{4},\quad b_1=-\frac{\pi}{4},
]

the all-run PV output converges to

[
S=2\sqrt2.
]

Thus the PV lane preserves:

1. binary outcomes on every run;
2. independently chosen settings after preparation and separation;
3. measurement independence of the prepared source/state;
4. no postselection or rejected trials;
5. no cross-wing communication;
6. unconditional CHSH scoring;
7. local cross-wing commutation.

What it does not assume is the extra classical premise that all four counterfactual outcomes must already coexist as scalar functions on a single Kolmogorov sample space:

[
A_0(\lambda),A_1(\lambda),B_0(\lambda),B_1(\lambda).
]

That is exactly the premise your scalar Bell program tests. It is not a rule that prohibits phenomenological velocity, nor is it a consequence of spacelike separation alone.

Therefore the issue is straightforward. If your challenge requires only run-by-run local outputs, later independent settings, unconditional scoring, and no communication, then the PV program meets those requirements and produces the singlet CHSH value.

If you instead require every submitted mechanism to reduce in advance to a single Boolean scalar counterfactual table, then you have imposed the disputed Bell premise as an admission rule. In that case, the challenge does not refute Parker’s PV construction; it excludes the construction by definition before testing it.

Bell did not independently prove that every locally microcausal event mechanism, including a PV-indexed one, must possess a faithful scalar Boolean reduction of that kind. That reduction is precisely what would need to be established before failure of a scalar-table test could answer the PV theorem.

The updated program makes this distinction executable rather than rhetorical. It includes the scalar Bell lane, the selection lane, and the unconditional PV microcausal lane; it records the premises preserved or abandoned by each; and it produces run-by-run outputs for direct audit.

So the relevant question is no longer whether I can supply actual runs. I have. The question is whether you are willing to test the submitted local event mechanism on its stated premises, or only a substituted scalar model that my theorem never claimed to be. Just be glad we don't have a running bet. I'm not a betting man. I prefer code and certainty. 

\code,

Parker

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/6f58216e-11cb-4ff1-b539-e6ccc8c78f34n%40googlegroups.com.

[Mark Hadley]

Parker,

you talk nonsense. Long answers with lots of homemade jargon will not save you.

Richards test is superb, exactly because it makes no assumptions about your model. same as Bell.

if you think you have a model that predicts the outcomes at A and B without sharing the angles a, b then you don't need to explain your model or even share it. Just out the code into Richard's program and out will come a judgement.

I kept asking simple questions like "can your model give the result if individual measurements?" if not then you can't use Richard's test, and to be honest our interest is limited.

and "can you do it at B without knowing setting a and vice versa?"

Cheers

mark

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CANitqNnMeuBZ7j-eQcUvtaFvfVja22hLtwJaX4GKQCsM7k%3DqTg%40mail.gmail.com.

[Richard Gill]

Dear Parker

You wrote “It is a tautological admission rule: a noncommutative event model is rejected because the challenge was defined to accept only commutative scalar models. Now to be fair, diagnosing this tautology of yours was time intensive and complex, so it would indeed get the better of most.

Exactly! You got it.

I like the look of your “solution”. You exploit the “move the goalposts” loophole. You effectively redefine “correlation”. Bryan Sanctuary might appreciate your solution, since he seems to be trying to do something similar. I don’t give prizes for people who solve a modified challenge. But I recommend you publish it. It seems rather elegant, much more elegant than any of this type that I saw before.

But I didn’t check the maths yet. I’d also be interested to see the code, in R or Python.

Richard

Sent from my iPad

On 25 May 2026, at 17:13, Parker Emmerson <powerin...@gmail.com> wrote:



To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CANitqNnMeuBZ7j-eQcUvtaFvfVja22hLtwJaX4GKQCsM7k%3DqTg%40mail.gmail.com.

[Parker Emmerson]

Richard - Does your challenge permit a submitted source object whose separated local measurement maps return ±1 outcomes from local settings alone, but whose shared pre-measurement event state is represented by a noncommutative microcausal algebra rather than a joint scalar counterfactual table? Or is admissibility restricted in advance to a single Kolmogorov space carrying A0,A1,B0,B1 simultaneously?

[Mark Hadley]

Parker,

as a contribution to Bell discussion, you need to ask. If you can calculate the +/- results for an angle a at A, can you calculate tha come without knowing the setting at B. 

No fancy words. I don't care how you do it, I don't care about states microstates topology or anything. can you deliver the outcome without knowing the setting at B.

if you need to use B at some point, then your work seems unremarkable. I you don't use B then your correlation will satisfy Bell.

Mark

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CANitqNkwtpigZusnU%3Dx1acn0G422WzVgTUAhGYCDxrYp_JmGSQ%40mail.gmail.com.

[Parker Emmerson]

Please let Richard address the actual question, Mark, without distracting from the issue at hand: "Richard - Does your challenge permit a submitted source object whose separated local measurement maps return ±1 outcomes from local settings alone, but whose shared pre-measurement event state is represented by a noncommutative microcausal algebra rather than a joint scalar counterfactual table? Or is admissibility restricted in advance to a single Kolmogorov space carrying A0,A1,B0,B1 simultaneously?"

[Parker Emmerson]

By the way, Mark. Here's simplicity for you:

You are conflating:

1. Failure to be a Bell-local scalar-output model, with
2. Failure to be relevant to the scope and premises of Bell’s theorem.

[Richard Gill]

The challenge is explicitly restricted in advance. It seems I need to say this again:  it’s a practical joke. Designed to send Bell-deniers into a rabbit hole so that they discover Bell’s theorem for themselves. It’s a pedagogical challenge. A class-room impossible assignment.

You’d be surprised how many people have fallen for it. In particular, Joy Christian supporters.

Sent from my iPad

On 25 May 2026, at 19:00, Parker Emmerson <powerin...@gmail.com> wrote:



[Richard Gill]

Dear Mark

Since Parker manages to reproduce the singlet correlations, his program has non-locality (or worse) built in somewhere. I’m looking forward to seeing the code.

Incidentally, the idea of the impossible computer assignment is not just mine. Steve Gull, one of the founders of Geometric Algebra, used it as a Cambridge University physics exam question. And built an original proof of Bell’s theorem on it, using Fourier analysis. I tidied up his solution for him. See link below.

Excuse me as I take some steps down memory lane.

Joy Christian challenged me to prove Bell’s theorem without using statistics or probability theory. A bit crazy, since QM predicts probabilities and statistics.

Professors Hess and Philip (Illinois), members of respectively the US and the Austrian Academy of Sciences, were dismayed by my use of martingale theory to disarm the memory loophole. They asked their colleague Joe Doob, founder of martingale theory, if he knew my work. Obviously, he didn’t. I’m a statistician, not a probabilist, so rather low in the pure maths pecking order. Hess and Philip told Christian. So they wrote on internet for all to read “Hess told me that Doob says Gill is not even a mathematician. He’s merely a statistician”. They were so pissed off that Marek Zukowski, Jan Åke Larsson and I had discovered the tiny slip-up in their magnum opus 60 page disproof of Bell’s theorem, published in PNAS. As members, they could publish some papers despite negative referee reviews.

The Austrian pro Bell team were particularly annoyed by Hess and Philip, whose disproof of Bell’s theorem was announced in newspapers all over the world. (I read about it in my daily Dutch newspaper.) Clearly it was wrong but where was the mistake?

David Mermin was delighted with our work and by the transparent, elegant and polite way we destroyed their life’s work in our PNAS published critique.

Yes, the life of a dedicated fighter against quantum crackpots has its rewarding moments. [I only fight wrong maths. I’m not against crazy ideas. On the contrary, I love them].

Richard

Sent from my iPad

On 25 May 2026, at 19:58, Mark Hadley <sunshine...@googlemail.com> wrote:



[Richard Gill]

Dear Parker

Thanks for the Python notebook. 

If you are a good programmer, the code will indeed speak for itself!

Richard

Sent from my iPad

On 25 May 2026, at 17:13, Parker Emmerson <powerin...@gmail.com> wrote:



To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CANitqNnMeuBZ7j-eQcUvtaFvfVja22hLtwJaX4GKQCsM7k%3DqTg%40mail.gmail.com.

[Richard Gill]

Dear Parker

My challenge makes no restrictions whatsoever. I think you still haven’t carefully read section 9 “Quantum Randi Challenges” of my magnum opus "Statistics, Causality and Bell's Theorem”.

https://arxiv.org/abs/1207.5103

In the meantime I have installed Anaconda and your Jupyler Notebook is loaded. It’s been a while since I used it and in the meantime I got a new MacBook Pro.

I’m looking for a friendly user interface.

I want facilities to set and reset the random seed so that I can do controlled replicable experiments.

I want the facility to choose the number of trials and to supply the settings myself, and output the generated data,

The point is that one can objectively verify whether or not the model used both settings to get both outcomes from some simple experiments. No need to study the code.

Richard

[Richard Gill]

Dear Parker

I discovered where I can set the random seed and the number of runs per lane, The program works fine with N = 1.

But it chooses whether the settings pair will be 00, 01, 10 or 11

I want to set it myself. 

I hope I can find out where you generate the settings.

Richard

[Austin Fearnley]

Hi Richard

I remember online comments years ago about 'mere' statisticians daring to tackle QM issues.

Ironic ...  because .... QM is a statistical method as fundamental level 1 data are not available and QM gives only probability outcomes based on aggregated level 2 data (eg quantum states).

Trying to solve fundamental Level 1 issues using only level 2 data inevitably leads to more and more complicated maths.  Which partly explains one of the current difficulties in physics.

I did not realise any of this when I began to develop my (level 1?)  preon model.  I simply wanted to understand fundamental particles better.

Austin

[Richard Gill]

Dear all: 

Parkers PV simulation program uses action at a distance.

The program is of course a deterministic hidden variables model. The hidden variable is the (current state of the) random seed

I used the same initial seed four times, asked for a a run of length 1, and arranged for the settings to be each of the following four combinations

(by editing the two vectors A_SETTINGS and B_SETTINGS)

seed: 110951

0, pi/4     1, -1

0, -pi/4    1, -1

pi/2, pi/4  1, -1

pi/2, -pi/4 1,  1

These are: setting Alice, setting Bob, outcome Alice, outcome Bob

Comparing the second and the fourth row you see that Alice's setting has changed, Bob’s is the same; but Bob’s outcome has changed!

I hit lucky first time! Well, the random seed was my birthday, so that figures.

Richard

PS the trick is to use non-locality sparingly enough in order to hit exactly 2 sort 2. It’s beautiful work, Parker!

[Bryan Sanctuary]

I agree that Richard's bet is unwinnable.  That is why I changed our bet a few years ago.  I bet him that I could resolve EPR by including a bivector, and I did, it was published, but Richard and the bellists refused it over them not accepting spin has more than a vector \sigma, but needs a bivector i\sigma.  This led to a debate, a tough one, and I then was able to remove their objection.  I am writing that up now.

So most of what Richard does in Bell is to send people down Rabbit Holes. But there was a misunderstanding in our particular bet:  to me winning was getting published , and to them, it was convincing everyone, including them.  

The bet is not serious Richard's way.  I suggest we ignore it.  Simply stated Bell is Boolean, Nature is not. Richard's bet is Boolean.

Bryan

Left: Old:  I took the bivector correlation, projected out a vector (triangle) and bivector (mustache) and simulated each separately. The sum works being cosine like:  Bellists say avaerage them, not add, and reject this.

Right New:  I removed the projection, and programmed a product of two quaternions, and this avoids the add\average issue.  I have not presented the program yet, but will soon

Left

[Richard Gill]

Dear Bryan

You keep trying to rewrite history. Unfortunately, there were witnesses, and they know what you actually bet.

You bet that you would convince the majority of our peers within one year (later increased at your request to two) that your resolution of EPR was correct and that Bell was wrong. You fantasised that Zeilinger and others would start to withdraw their papers. You still haven’t achieved your goal. I won our bet, whether you pay up or not, and the fact that you don’t pay up increases the magnitude of the victory.

I am looking forward to seeing your new simulation program so that I can exhibit its non-local character. Which I will do, whether you like it or not. You wanted me to give your research publicity by publishing a critique of your work. You seem to see me as an influential spokesman for the pro Bell maffia. But so far I did not find your works interesting or influential enough to warrant writing a paper about them. 

What does interest me however is a certain similarity between your ideas and Parker’s. There is some interesting method to Parker’s madness.

Yours

Richard

[Richard Gill]

I hear there are still a few places free at this year’s Vaxjo conference. Is anybody here going there?

[Bryan Sanctuary]

Richard,

I agree to forget the bet, but YOU keep bringing it up, and still propose it to others.

You are also well known for using probability to find women innocent of crib deaths.  You must then know of  Ignaz Semmelweis the 19th century physician who recommended washing hands. It reduced delivery deaths by TEN times.  His ideas, and data, were rejected by the medical profession and Semmelwies was pilloried.  

You, and Bellists, are guilty of what is called the Semmelweis effect: "The tendency to favour information that is consistent with prior beliefs or values" . "The Semmelweis proposal was met with unanimous rejection and hostility from the medical community in the 19th century, exemplifying the phenomenon of groupthink, where consensus overrides consideration of alternatives" 

I point to the famous work by Dirac in 1928-30, with his celebrated matter-antimatter solution.  That was 100 years ago and has dominated groupthink since.  From that QFT emerged and the SM.  It is so firmly entrenched in physics, people cannot change. But, as I have pointed out, there is a second way to linearize the KG equation.  It is my view that we should use the bivector solution and not the matter-antimatter solution. Then we have simple geometric algebra, Nature is real, and spin really is spin:  it is a quaternion.

Bryan

[Mark Hadley]

you lost the first bet pay up.

you produced a paper too late for the vet and largely ignored. It had two fundamental errors in it that were explained to you.

you never correct the errors in the high school maths.

but you continue with the work. Presumably hoping that the volume of writing will cover the uncorrected mistakes.

Mark

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[Bryan Sanctuary]

Mark,

Please write a rebuttal to my paper and I will respond in the press.

Bryan

[Richard Gill]

Bryan, YOU brought it up. Your short-term memory is getting very bad!

I was not talking about your bet with me, but about the general computer challenge which I described in my 2014 paper. It’s still open.

You are going to show us your computer program and I will evaluate it using the techniques which I described in 2014. I’m looking forward to getting the code. It would be nice if you paid up, but I do not expect that. Semmelweis effect?

The simulation which produces the right hand image uses a quaternion rotor to implement action at a distance. As my analysis of your code will establish without a doubt.

Richard

[Mark Hadley]

I've already made a rebuttal. Several times. You have already offered several times to consider matters and reply. But when you saw how strong my maths and logic was you went quiet.

you have had my criticisms before. in detail.

Do I have to send them yet again?

If I do send them what assurances do I have that you will follow up

Mark

[Richard Gill]

The outcome of our bet did not depend on whether or not you got a paper published, Bryan. It depended on a majority of our peers endorsing it. 

After your paper was rejected by some serious main stream journals you succeeded at last with two papers in the MDPI journal “Quantum Reports:

https://www.mdpi.com/2624-960X/6/3/26

EPR Correlations Using Quaternion Spin

https://www.mdpi.com/2624-960X/6/3/28

Spin Helicity and the Disproof of Bell’s Theorem

Both were submitted mid July 2024 and accepted within one month. Just one has by now been cited by someone apart from yourself:

"Nevertheless, there is an alternative interpretation of Bell's inequality. Some scholars argue that nonlocality is unphysical and should be avoided, asserting that any theory aimed at achieving physical realism must preserve its causality and locality [90]”, that’s from:

[90] Interaction Wave Functions for Interaction-Based Coherence and Entanglement in Complex Adaptive Systems

Shi, Leilei; Guo, Xinshuai; Zhang, Wei; Wang, Bing-Hong

International journal of theoretical physics, 2025-11, Vol.64 (12), p.323, Article 323

It does not appear that you are gaining a huge amount of traction. 

[Richard Gill]

Mark, you can post your rebuttal on PubPeer.

[Richard Gill]

I just posted on PubPeer, twice:

EPR Correlations Using Quaternion Spin

The author writes the correlations in the EPR-B model as the sum of two terms. He shows that each part separately can be modelled by a local-hidden variables model and gives them names "polarization" and "coherence". This leads him to conjecture that the entanglement between two particles leaving a source in the singlet state and heading towards two measurement devices breaks down. As the particles approach the measurement devices, somehow both devices detect the same one of the two components of "spin" (sometimes one, sometimes the other). He fails to provide full (locally operating) mechanistic details. If he could, it is clear that this would be a model of the local hidden variables type. So if the measurement outcomes are binary, the resulting correlations would satisfy Bell's inequalities. However, he reproduces the negative cosine. So something must be wrong. Now, if the two detectors always both respond to polarization, or both respond to coherence, they must have to "know" one another's setting in advance. The model is incompletely specified. Since it does reproduce the negative cosine, any fully "mechanistic" specification would have to be non-local.

and

Spin Helicity and the Disproof of Bell’s Theorem

Sanctuary writes "His [Bell's] mistake is assuming that classical and quantum variables are the same. Whereas classical variables are real, commute, and form one convex set, quantum variables are complex, do not commute, and form two convex sets." The author seems to completely misunderstand Bell's logic. Bell asks the question, could quantum-like correlations also arise under the assumption of local causality, which he describes in Chapter 24 of "Speakable and Unspeakable" (under the title "La Nouvelle Cuisine"). Sanctury does not disprove Bell's theorem because he does not show that his model cannot be written in the required format. Note: there is no restriction on the kind of mathematical description of hidden variables in Bell's "local causality". The abstract of the paper claims that Bell's theorem is disproved by a counterexample, but the paper contains no counterexample. Sanctuary talks about convex sets but never says what sets he is talking about. A convex combination of quantum observables is another quantum observable.

My comments are awaiting moderation. More comments can be placed by others, and of course, Bryan himself should respond. He will be informed by PubPeer provide my comments pass the moderation phase.

On 26 May 2026, at 15:02, Richard Gill <gill...@gmail.com> wrote:

Mark, you can post your rebuttal on PubPeer.

[Leo]

Richard, 

I have absolutely zero knowledge of what Bryan is doing and Im probably not going to read his paper in the short term. But from your description "EPR Correlation Usong Quaternion Spin",  where you say "Now, if the two detectors always both respond to polarization, or both respond to coherence, they must have to "know" one another's setting in advance. The model is incompletely specified. Since it does reproduce the negative cosine, any fully "mechanistic" specification would have to be non-local." an obvious reply would be to assign the role of the choice to lambda. So maybe you might want to expand your comment with sufficient details.

"

[Bryan Sanctuary]

Mark,

You need not resend them. You should write a paper and submit it as a comment to the Journal. I will respond.

Bryan

[Parker Emmerson]

Dear Richard, Bryan, Mark, and all,

Apologies to Mark in advance for the length. Occam’s razor is a useful heuristic, but it is not a logical premise, and it cannot replace distinguishing the assumptions in a complex issue.

I hope you will enjoy the exact semantic assertions provided by the ipynb notebook attached. Thank you for your feedback on the first version, Richard. This is even more precise and true to the conception of phenomenological velocity's response to Einstein's concerns. Please read the following analysis of the problem at your own pace. 

I want to separate several claims that are being run together.

First, I accept the strict scalar-output conclusion. If a submitted program has the form

[ A(a,\lambda)\in{\pm1},\qquad B(b,\lambda)\in{\pm1}, ]

with one source law for (\lambda), late user-supplied settings, no communication, and all runs scored, then on a CHSH quartet each source record fixes one of the sixteen deterministic rows

[ (A_0,A_1,B_0,B_1)\in{\pm1}^4. ]

Each such row has pointwise CHSH score (\pm2). Therefore no PV formula inserted inside separated scalar methods alice(a, source) and bob(b, source) can yield (S=2\sqrt2). I have no disagreement with that theorem. The executable notebook confirms it.

But that is exactly why the scope of the test must be stated carefully.

Bell was responding to Einstein. Einstein’s concern was not merely whether one can write down a classical spreadsheet of scalar counterfactuals. The deeper issue was whether quantum mechanics is incomplete because there is an underlying causal reality not captured by the wavefunction. The question is therefore:

[ \text{Does Einstein’s demand for an underlying causal reality necessarily require one classical scalar Kolmogorov space carrying }A_0,A_1,B_0,B_1\text{ simultaneously?} ]

That is the point at issue.

PV is treated as an automorphism acting on commuting local observable algebras, and a common PV action is gauge-like in the singlet correlator because only relative action can matter.

In Bell’s 1964 deterministic theorem, the relevant mathematical object is indeed a separated scalar form,

[ A(a,\lambda),\qquad B(b,\lambda), ]

with the remote magnet setting absent from the local outcome. In later Bell-local-causality and CHSH/Fine formulations this becomes the factorization or screening-off condition

[ P(x,y\mid a,b,\lambda)

P_A(x\mid a,\lambda)P_B(y\mid b,\lambda), ]

or equivalently the existence of a joint scalar distribution for

[ A_0,A_1,B_0,B_1. ]

But that stochastic factorization formula is not literally the wording of Bell’s original 1964 theorem. It is the later local-causality/scalarization formalization of the same classical family. Gill’s challenge operationalizes this family as an executable replay test.

That distinction matters.

My PV claim is not that a classical scalar instruction table beats Bell. It does not. The notebook already acknowledges that.

My claim is that PV proposes an underlying realist event mechanism whose locality is microcausal and noncommutative, rather than Bell-factorizable and Boolean. In the PV operator construction, Alice’s and Bob’s local observables belong to commuting cross-wing algebras:

[ [A_v(a),B_v(b)]=0. ]

The singlet law is reproduced by the noncommutative event algebra:

[ E(a,b)=-\cos(a-b), \qquad S=2\sqrt2. ]

This is local in the microcausal/operator-algebraic sense, but it is not local in Bell’s scalar-factorizable sense. That distinction is not evasion; it is precisely the mathematical issue.

So if the claim is:

“PV supplies a strict classical shared-randomness local-output simulator that passes Gill’s interface and reaches (2\sqrt2),”

then the claim is false. I agree.

But if the claim is:

“PV supplies an underlying microcausal, noncommutative event algebra reproducing the singlet statistics without cross-wing operator noncommutation,”

then failure in Gill’s scalar-output challenge does not refute it. The challenge tests whether the model admits a faithful scalar reduction of the form (A(a,\lambda),B(b,\lambda)). The PV operator construction is explicitly not such a reduction.

Richard, this is also why I need clarification about the phrase “no restrictions whatsoever.” Earlier the challenge was described as explicitly restricted in advance, but later as imposing no restrictions. Those cannot both be literally true unless the distinction is this:

• there is no restriction on the internal vocabulary of the submitted model; it may contain PV phases, bivectors, spinors, matrices, branches, or whatever else;
• but there is a strong restriction on the observable interface: the model must output separated run-by-run scalars (A(a,\lambda)) and (B(b,\lambda)), with same-source replay under all four setting pairs.

If that is the intended meaning, then I agree. But then the test decides only whether a classical Bell/Fine/Gill scalar adapter exists. It does not decide whether a noncommutative microcausal event theory exists, which is not necessarily, "quantum mechanics."

The binary singlet sampler in the notebook makes the distinction visible. It reproduces the singlet joint law, but it fails the strict replay test because the sampled event uses the setting pair. The notebook even finds a remote-setting witness. Good. That sampler is not a strict Bell/Gill adapter.

The PV operator theorem is different again. It does not submit scalar run records. It gives an operator-algebraic event mechanism with cross-wing commutation. To refute that theorem, one must show either that the operator calculation is wrong, or that any acceptable Einstein-complete causal event mechanism must reduce to Bell’s scalar local-causal form. That second claim is substantive. It cannot simply be assumed by imposing Gill’s scalar interface and then declaring non-passage a refutation.

So I propose the following clean separation.

1. Classical scalar adapter claim: PV cannot pass Gill’s strict challenge while retaining (S=2\sqrt2). This is settled by the sixteen-row CHSH certificate.

2. Microcausal PV event-algebra claim: PV supplies a noncommutative local event mechanism, with cross-wing commutation, reproducing the singlet law. Gill’s scalar challenge does not decide this claim unless a theorem is added showing that such a microcausal event algebra must reduce faithfully to a scalar Bell/Fine joint distribution.

3. Bell-local-causality claim: If “locality” is defined to mean Bell factorization or scalar screening-off, then the PV operator model is not local in that sense. But that is not the same as saying it has remote-setting operator influence, because it satisfies ([A_v(a),B_v(b)]=0). It means Bell locality and microcausal locality are different mathematical notions.

Please do not substitute the slogan “local hidden-variable model” for the actual logical issue. The question is not whether PV can be squeezed into the exact classical scalar form Bell ruled out. It cannot. The question is whether Einstein’s incompleteness concern forces that scalar form, or whether an underlying noncommutative microcausal event algebra is a legitimate alternative notion of causal completion.

If Richard’s claim is only:

“My test decides whether a classical shared-randomness separated scalar-output implementation exists,”

then I agree. PV cannot win that test while keeping (2\sqrt2).

If the stronger claim is:

“Therefore the PV microcausal operator theorem itself is refuted,”

then that overreaches. It replaces microcausal locality by classical run-by-run factorization and then rules out the replacement.

That is not a refutation of the PV claim. It is a refutation of a scalar reduction of the PV claim.

Best, Parker

[Parker Emmerson]

There's also one more: 

[Richard Gill]

Sent from my iPad

On 26 May 2026, at 21:14, Parker Emmerson <powerin...@gmail.com> wrote:



<PV_Microcausal_Ontology_RH_Control_and_Gill_Interface_Audit_FINAL_EXECUTED.ipynb>

[Richard Gill]

Dear Parker

From my experimental approach to your PV Jupyler notebook, I was able to deduce that your PV model can be seen as a non-local hidden variables model, ie of the form x = A(lambda; a, b), y = B(lambda; a, b) where lambda is a uniform(0, 1) pseudo random number. 

You believe that “PV supplies an underlying microcausal, noncommutative event algebra reproducing the singlet statistics without cross-wing operator noncommutation” and that your approach contributes to the EPR discussion. Your sentence is a concise technical description of your particular functions A and B. I may or may not get around to studying them. 

Your task is to interest theoretical physicists and philosophers of science in your approach. You say that the real metaphysical question is “does Einstein’s demand for an underlying causal reality necessarily require one classical scalar Kolmogorov space carrying A_0, A_1, B_0, B_1 simultaneously?”. That’s a good question for philosophers of science. I’m just a mathematical statistician.

We could ask the question: would Einstein have liked Parker’s model? I suggest we consult Einstein on that question. My feeling is that he would have been impressed but unconvinced. I think he was looking for something else. But maybe present day theoretical physicists will see something in it. They’ve been stuck down their own rabbit holes for decades chasing string theories and desperate for something new. They’re talking seriously about superdeterminism now.

Gerard ‘t Hooft helped get Dutch nurse Lucia de Berk out of jail. I’m hoping someone like him will speak out for Lucy Letby.

I will look at the new notebook later today.

Richard

[Leo]

Dear Parker, Dear Richard, dear all,
I don't think we should shy away from philosophical discussion. Bell's theorem is clearly not simply a mathematical theorem, it provides a direct bridge from mathematical truths to what is assumed to be real about the world.  
Philosophy does not merely consist of vague metaphysical speculation, but is also the engine that drives scientific thought itself: the analysis of concepts, assumptions, and meanings that ultimately guides how mathematical structures are connected to physical reality.

With that said, I would like to offer two thoughts. On the issue that Parker raises (whether a scalar algebra is implied by EPR realism), I have many times considered whether this is even an objectionable thing in classical mechanics.
The main consideration here is that probabilistic frameworks classically are constructed on phase space, whathever observable quantity you deal with can be embedded into a phase space through parametrizations.
Koopman and von Neumann already showed in the 30s that the structure of Hilbert spaces, with linear operators, superposition, and so on, are not at all exclusive descriptions of quantum mechanics; in particular, Koopman constructed a classical wavefunction by linearizing the non-linear phase space flows of observables through functions of the observables themselves, which composed linearly.
The crucial distinction between Koopman's construction and QM then becomes that in QM these operators are matrices, which need not commute. In contrast, in Koopman's construction the non-commuting object is not the observable itself, but the Liouville operator associated with Hamiltonian evolution, [ L f = {f,H}, ] which generates the phase-space flow through the Poisson bracket. Multiplication operators corresponding to ordinary functions on phase space still commute pointwise: [ f(x,p)g(x,p)=g(x,p)f(x,p). ]
In quantum mechanics, by contrast, observables themselves become non-commuting operators. Position and momentum are no longer merely functions on an underlying phase space, but operators whose algebra already contains the dynamical structure through the commutator relations. In this sense, the kinematical observables and the generators of transformations become deeply intertwined. What this ultimately means physically is still, in my opinion, not entirely understood.

I also want to mention under this topic 2 interesting facts: Wigner's quasiprobability function, which essentially is the inverse of the Koopman construction; Wigner forces the quantum state representation into phase space, but the noncommutativity gives rise to negative probability densities.
The other is something I've seen Gabriele Carcassi talk about, namely the same stuff in terms of entropy. Classical mechanics predicts that, given hbar as a coarse graining choice (the size of the smallest cell in a coarse grained phase space representation), the product of uncertainties of the phase space variables satisfies:
DxDp >= hbar/e

Where e is Euler's number. This comes straight from gaussian distributions.

In quantum mechanics, the relationship that holds is instead

DxDp >= hbar/2

The smaller denominator essentially comes directly from the non trivial correlations in entangled states, which is again ultimately due to non commutativity of observables.

The last thing i want to mention, which is more relevant to Parker's question, is that it's not entirely clear to me how scalar functions can encode all the relevant information in EPR tests specifically. The obervable, even though it can be compressed to a yes no question, physically appears as a dot on the screen (for stern gerlach apparatuses, but this consideration can be generalized). Bell introduces geometric dependence through the parameters a,b and so on. But when we move across context, we use and compare only the final output of the function: a scalar. This does not encode the fact that geometrically a dot on the screen assigned to +1 for a is not the same dot assigned to +1 for a'. In fact, all such dots form a circle on the screen. One might think that the relative geometric disposition of the outcomes would constitute a variable to be predicted. In principle, moving away from stern gerlach magnets and spin deflections, there is no reason to think a system that outputs contextual outcomes would necessarily also geometrically separate them. I can imagine some kind of machine that correlates the outcomes across wings depending on the relative directions of the two apparatuses, yet outputs dots on the screen always in the same exact two positions, irrespective of the local orientation of the machine.


Now on to the second thought.
My daily job is as a colorist; i build and test programs to predict, given some combinations of coloring pastes, the final color of the mixture. The mathematics of color theory are a bit out of the scope of the present comment, but some aspects of it deeply remind me of QM features.
When you try to predict the final result of a mixture there is no global concept of a coefficient you can use to predict with certainty the result of adding a certain paste. Theoretically, one would wish for a table of numbers that said, given a certain combination of additives, what their effects will be on the final color. But that is not practically possibile: non-linearities of paste interactions, together with the rules of perception of our eyes, makes it so that the final outcome depends on the starting tint that you are modifying and the final result that you want to achieve. For a very simple practical example, adding black to to white will result in a huge drop in brightness; but adding the same pigment on an alrrady very dark tint will result in a much more quenched effect, in some cases the final color might even by brighter.
Another well known example is adding blue to yellow: by themselves, the additives would only change the Blue/Yellow axis of your tint; but together they actually change the Red/Green axis as well.
This is a form of contextuality; there are no global parameters that you can find that fit all outcomes for all possible combinations of inputs. Of course, everyone assumes that the underlying mechanisms are completely deterministic; its just that there is no representation of such dynamics in terms of the relevant observables (spectral information).

Quite a long post, sorry. I would love to hear your thoughts.

[Richard Gill]

Dear Parker

Please tell us what “RH” means?

You say that PV makes use of an underlying realist event mechanism whose locality is microcausal and noncommutative. Yet your program runs on a classical computer and what you see as “non commutative” are merely operations on arrays of complex numbers. Which are just pairs of arrays of real numbers, Behind your "micro-causal noncommutativity" there is just addition, subtraction, multiplication and division of ordinary scalars. There is no non-locality since all the numbers are in one physical location (my laptop). The non-locality is in your imagination. You see it when you look at it (ie, try to visualise it) at one particular level

The actual mechanism is non-local since Alice’s outcome often depends on Bob’s setting or vice versa or both. You can give it fancy names and get into learned scholarly discussions about ontology but I think that these are just words to provide a comfort blanket for things which we don’t understand and can’t understand. Feynman believed that any theory behind QM would be even crazier. I think that Parker’s theory illustrates that. Actually this is rather like medieval scholars seriously competing how many angels could dance on the head of a pin. I don’t wish to belittle them. They were extremely intelligent, learned, and probably also wise,

I switch off when people start throwing the word “ontic” about. It’s fine by me that for some people this is their academic bread and butter but it is not for me. Wittgenstein famously said: “Whereof one cannot speak, thereof one must be silent” . The most interesting and meaningful things in life need to be expressed in art and culture (poetry, rituals). 

Richard

On 26 May 2026, at 21:14, Parker Emmerson <powerin...@gmail.com> wrote:

<PV_Microcausal_Ontology_RH_Control_and_Gill_Interface_Audit_FINAL_EXECUTED.ipynb>

[Austin Fearnley]

Leo

Your interesting comment on colour theory...

I am an amateur artist (in addition to being an amateur physicist). Spend more time painting now than on physics. I remember a long and very interesting TV program by Land on colour theory.  Also I read about Chevreul's work on colour theory.  Problems are that painting and light use different primaries; any light frequency stimulates all three primary receptors; the brain has complicated functions wrt vision. Land explained that in fading intensity of background light the brain maintains our perception of hue (colour) despite (eg) red normally seeming to be brown in reduced intensity. Chevreul famously explained that receptors can become over-saturated such that colour complements can de-saturate receptors.

At the moment I am painting in 'reduced palette' using a pair of complementary colours.  Crimson with veridian in some  paintings, and burnt sienna with ultramarine in other paintings.  Colour complements are on a diagonal across the colour circle.  It is always tempting to add into the mix a colour not on that diagonal so as to use 'local' colour.  But doing so can reduce harmony and it is well known that adding a new colour in a painting can change all the colours around it.  I explain this as any colour stimulates all three receptors and hence will affect all the colours because of changes in saturation levels in receptors.  But there is also the mysterious brain functions at work too. 

[Parker Emmerson]

Dear Richard,

Thank you. Your feedback has been extremely helpful in advancing the phenomenological velocity program, which has gone through several evolutions. Your reply is useful because it brings the issue to its sharpest point.

First, a small clarification of terminology. By PV-REC I mean Phenomenological-Velocity Relational Event Completion. This is the proposed event-completion lane, not merely the operator-control lane and not the contextual singlet sampler.

Also, by “RH” I mean the Riemann Hypothesis. In the present Bell notebook, the RH/PV material is not a Bell-run output mechanism. It supplies no functions

A(a, λ),    B(b, λ),

and no Bell event records. It is a semantic/source-fiber annotation layer, not the mechanism by which PV-REC produces outcomes.

Now to the Bell issue.

I agree with your statistical audit of the scalar event sampler. If a notebook lane produces binary event records and, after all random seeds are included in the source record λ, the outputs have the form

x = A(a, b, λ),
y = B(a, b, λ),

then that lane is not Bell-local in the 1964 separated-result sense. If it could instead be written as

x = A_A(a, λ),
y = B_B(b, λ),

with a setting-independent preparation law, then the CHSH proof applies and gives

S ≤ 2.

So I am not claiming that a strict separated scalar PV adapter can pass your same-source replay test and reach 2√2. It cannot. The strict scalar lane of the notebook confirms this.

But this is exactly why I object to letting the phrase “local hidden variables” do all the work. The real issue is not whether PV can be squeezed into Bell’s scalar replay interface. It cannot. The real issue is whether that scalar replay interface is a faithful mathematical rendering of Einstein’s demand for an underlying local and realist mechanics.

I do not think it is.

Bell’s theorem is exact. What is not exact is the common slogan that Bell has ruled out Einstein’s whole vision of locality and reality. Bell ruled out a particular scalarization of that vision.

The crucial distinction is this:

ACTUAL SCALAR READOUTS IN A CHOSEN EXPERIMENT

are not the same as

ONE GLOBAL SCALAR COUNTERFACTUAL TABLE
FOR ALL UNCHOSEN EXPERIMENTS.

Every Bell experiment ultimately reports scalar outcomes,

x, y ∈ {−1, +1},

because the laboratory scoring interface is scalar. In that sense, scalar readouts are not some alien classical imposition. They are also how quantum experiments are recorded: detector clicks, signs, eigenvalue labels, binary scores.

The questionable move is different. Bell takes the scalar reporting layer and asks whether there exists one underlying scalar ledger

(A₀, A₁, B₀, B₁) ∈ {−1, +1}⁴

attached to the same source record. That is a much stronger demand. It is not merely the demand that actual experiments have actual outcomes. It is the demand that all possible local measurement alternatives be jointly scalarized on one Boolean sample space.

That is the mathematical compression I am challenging.

Einstein asked whether quantum mechanics is incomplete: whether there is an underlying real state of affairs behind the statistical wavefunction. Bell reformulated that question into a test of whether the underlying account can be represented as separated scalar functions

A = A_A(a, λ),
B = B_B(b, λ),

or, in stochastic form,

P(x, y | a, b, λ)
  = P_A(x | a, λ) P_B(y | b, λ).

That is a brilliant theorem about that formalization. But it is not innocent to identify that formalization with Einstein’s entire physical demand.

Einstein’s concern was mechanical and realist. Bell’s tested object is scalar and counterfactual. Those are not the same thing.

The PV program is intended to expose precisely that gap.

1. The strict Bell/Gill scalar lane

The strict scalar lane has one setting-independent source law,

ρ(λ | a, b) = ρ(λ),

and separated scalar response maps,

A_A(a, λ),    B_B(b, λ).

The correlations are

E(a, b) = ∫ A_A(a, λ) B_B(b, λ) ρ(dλ).

Then the CHSH proof is pointwise. For each λ,

A₀B₀ + A₀B₁ + A₁B₀ − A₁B₁ = ±2,

so

S ≤ 2.

No PV formula inside this lane can evade Bell. I accept this completely.

But notice what this lane assumes: it assumes that the complete source record λ supports simultaneous scalar values for mutually exclusive local measurement contexts. That is not “realism” by itself. That is a particular scalar counterfactual representation of realism.

Or, put differently:

actual scalar readout
  ≠ global scalar counterfactual ledger.

Bell’s theorem begins after that ledger has been admitted.

2. The selection / exceptional-locus lane

There is another PV-related issue: exceptional-locus or “defined-only” semantics.

If a radical expression, branch convention, detector rule, coincidence window, or validity condition changes which trials are counted, then the reported law is no longer the emission law ρ. It is the accepted law

                   γ(a, b, λ) ρ(dλ)
ν_ab(dλ) = ─────────────────────────────── .
             ∫ γ(a, b, λ) ρ(dλ)

Then the observed correlator is

E_obs(a, b)
  = ∫ A_A(a, λ) B_B(b, λ) ν_ab(dλ).

The four CHSH terms are now evaluated under

ν₀₀, ν₀₁, ν₁₀, ν₁₁,

not one common measure. The usual CHSH integration step no longer applies.

This is not a loophole-free local explanation. It is selection/contextual conditioning. But it is mathematically explicit. It can be audited by total-variation geometry, for example with

S_obs ≤ 2 + 2Δ_Q.

So if PV appears through exceptional-locus semantics, it is not mystical. It is a change of ensemble:

ρ  →  ν_ab.

That is one possible PV semantics, but it is not the final PV-REC claim.

3. The PV operator-control lane

The operator-control lane introduces PV as a common local action:

A_v(a) = U_v† σ(a) U_v ⊗ I,

B_v(b) = I ⊗ U_v† σ(b) U_v.

The cross-wing commutator vanishes:

[A_v(a), B_v(b)] = 0.

In the singlet pairing,

ω(A_v(a) B_v(b)) = −cos(a − b).

This lane is important because the common PV action cancels from the singlet correlator. It shows that PV can be represented as a shared relational action without introducing cross-wing operator noncommutation.

But this lane alone is not an event ontology. It supplies expectation values, not actual binary event records. Therefore it is not a Gill replay adapter.

The implementation substrate is secondary. The calculation may be represented on paper, in NumPy, in a symbolic algebra system, or eventually on IBM quantum hardware. The substrate does not decide the Bell question. The Bell question is whether the represented model supplies separated scalar maps

X = X_A(a, λ),
Y = Y_B(b, λ).

The operator-control lane does not supply such maps.

This is also why I do not want the discussion reduced to “your laptop only manipulates numbers.” Any implementation has a substrate. A classical computer may represent a PV multiplication rule using arrays of scalar entries; a quantum backend may represent the same structure differently. Neither fact settles the Bell question. The Bell question is not the machine. The Bell question is the event interface.

4. PV-REC: the actual event-completion lane

PV-REC, the Phenomenological-Velocity Relational Event Completion, is the event-completion proposal. This is the part that is not merely standard singlet quantum mechanics.

The compatibility weights are

m_xy(a, b) = ¼[1 − xy cos(a − b)],

with

x, y ∈ {−1, +1}.

PV-REC does not simply identify these weights with Born probabilities. It converts them into event-channel intensities:

Γ_xy^PV(a, b; λ)
  = Γ₀ [m_xy(a, b)]^κ(v),

where

             v²
κ(v) = √(1 − ──).
             c²

The actual event is selected by a competing-threshold rule:

                     ξ_xy
(X, Y) = arg min  ────────────────── .
          x,y∈{±1} Γ_xy^PV(a, b; λ)

Under the exponential-threshold ensemble, this gives

                     [m_xy(a, b)]^κ(v)
P_PV(x, y | a, b, v) = ──────────────────────────────── .
                        Σ_x′,y′ [m_x′y′(a, b)]^κ(v)

Therefore,

E_PV(a, b | v)
  = −tanh{κ(v) artanh[cos(a − b)]}.

At

v = 0,    κ(v) = 1,

this becomes

E_PV(a, b | 0) = −cos(a − b).

But for

v ≠ 0,

PV-REC is empirically distinct from ordinary singlet predictions.

On the standard CHSH quartet,

S_PV(v)
  = 4 tanh{κ(v) artanh(1/√2)}.

For the illustrative notebook value

v/c = 0.37,

one has

κ(v) = √(1 − 0.37²) ≈ 0.9290,

and hence

S_PV(0.37c) ≈ 2.697717.

The Monte Carlo simulation gives approximately

S ≈ 2.700.

That value is a theoretical/simulation output, not experimental evidence for PV. A laboratory Bell experiment can produce values near 2.7, but that alone would not prove PV, because ordinary singlet predictions plus visibility, loss, detector effects, and source imperfections can also produce values in that range.

The real empirical test would be the full angle-dependent deformation

−cos(a − b)

changing to

−tanh{κ(v) artanh[cos(a − b)]}.

PV is introduced at the level of event formation, not merely at the level of probability assignment. Whatever one calls the orthodox formalism, it gives a probability calculus for scalar readouts. It does not by itself supply the PV event-mechanical ontology or the phenomenological-velocity actualization law above.

That is precisely the level PV-REC is trying to address.

5. Why your replay criticism is correct but not exhaustive

PV-REC is not Bell-local in the scalar separated-result sense. I accept that.

The actualization map is generally

(X, Y) = K_ab(λ),

or equivalently,

X = X(a, b, λ),
Y = Y(a, b, λ).

It is not generally of the form

X = X_A(a, λ),
Y = Y_B(b, λ).

So the same-source replay audit fails. The notebook now shows this explicitly.

But this failure means:

PV-REC is not a Bell scalar hidden-instruction model.

It does not mean:

PV-REC has been refuted as an event-mechanical proposal.

That second conclusion would require an additional theorem saying that any acceptable underlying realist event mechanics must reduce to Bell scalar separability. That is precisely the bridge I deny.

In symbols, Bell proves

BellScalarSep  ⇒  S ≤ 2.

But what would be needed to dismiss PV-REC on purely Bell grounds is

RealEvent ∩ Microcausal ∩ NoSignal
  ⇒ BellScalarSep.

That implication is not Bell’s theorem. It is an extra philosophical and mathematical identification.

PV-REC is designed to occupy the difference:

PV-REC ∈ RealEvent ∩ Microcausal ∩ NoSignal,

but

PV-REC ∉ BellScalarSep.

Here,

RealEvent

means that each run has a definite actualized outcome pair

(X, Y) ∈ {−1, +1}².

Microcausal

means that the separated event structures commute across wings:

[𝔄_A, 𝔄_B] = 0.

NoSignal

means the operational marginals do not depend on the distant setting:

P_A(x | a, b) = P_A(x | a),

P_B(y | a, b) = P_B(y | b).

And

BellScalarSep

means the much stronger condition

X = X_A(a, λ),
Y = Y_B(b, λ),

or equivalently,

P(x, y | a, b, λ)
  = P_A(x | a, λ) P_B(y | b, λ).

These are not the same mathematical requirement.

If one calls PV-REC “nonlocal” because K_ab(λ) depends on the full setting context, then I accept that in the Bell-factorization sense. But that is not the same as operational signalling, and it is not the same as cross-wing operator noncommutation. The whole purpose of the construction is to distinguish those notions rather than collapse them under the slogan “local hidden variables.”

6. The Einstein point

You asked whether Einstein would have liked this. I cannot claim Einstein would have endorsed PV. But I can say what Bell did and did not prove about Einstein’s program.

If Einstein’s locality is defined as emission-time scalar separability, then Bell rules it out for CHSH-violating correlations. That is the theorem.

But Einstein’s deeper demand was not obviously “give me a single spreadsheet of scalar answers to all possible unperformed experiments.” His demand was for an underlying reality in which physical events are not created by a merely epistemic wavefunction update and in which no mechanical influence is sent superluminally between separated systems.

Bell’s move was to translate that demand into scalar counterfactual form. Again, the theorem is brilliant. But the translation is not neutral.

The PV objection is that the scalar translation confuses the actual scalar score of a performed measurement with a global scalar ontology of all unperformed measurements.

That is the point.

An actual experiment produces one scalar result. Bell asks for four scalar counterfactuals on the same source record:

A₀, A₁, B₀, B₁.

PV-REC refuses that move. It says: actual events are real, but mutually exclusive measurement contexts need not be jointly scalarized before actualization.

So the precise claim is:

Bell rules out Einstein only after Einstein is translated
into Bell scalar separability.

It does not prove that every realist, no-signalling, microcausal event mechanics is impossible.

Equivalently:

actual scalar readouts
  ≠ global scalar counterfactual table.

Bell assumes the latter in the separated hidden-variable form

X = X_A(a, λ),
Y = Y_B(b, λ).

For a CHSH quartet, this entails the existence, for each λ, of

A₀(λ), A₁(λ), B₀(λ), B₁(λ).

Then Bell follows.

PV-REC accepts actual scalar readouts

(X, Y) ∈ {−1, +1}²

for the performed context (a, b), but denies the global table

(A₀, A₁, B₀, B₁)

as an emission-time scalar object.

Instead,

(X, Y) = K_ab(λ).

That is contextual actualization, not scalar counterfactual separability.

So the formal distinction is

K_ab(λ) ≢ [X_A(a, λ), Y_B(b, λ)].

That is the core of the argument.

If PV-REC were physically demonstrated — not by a single S ≈ 2.7, but by the full angle-dependent PV correlation law and by exclusion of ordinary singlet and experimental-imperfection explanations — Bell’s theorem would remain correct. What would change is the interpretation of its scope. It would mean that Bell conquered the scalar-counterfactual territory, not the whole territory of possible Einsteinian event mechanics.

To put it compactly:

Bell did not defeat realism.

Bell defeated scalarized counterfactual realism.

PV asks whether Einstein’s deeper mechanical intuition survives outside that scalarization.

That is the question I am trying to make mathematically precise.

So I agree that your challenge refutes a separated scalar PV hidden-variable adapter. It does not by itself refute a contextual, no-signalling, microcausal event-completion with its own empirically testable correlation law.

Bell’s proof is not wrong. The overreach is treating Bell’s scalar ledger as if it were Einstein’s whole concept of physical reality. PV-REC is not trying to fill the ledger. It is denying that the ledger is the right mechanical object.

You said that my task is to interest theoretical physicists and philosophers of science in the approach. I accept that. The first step is to be clear about what has and has not been refuted:

Gill replay refutes separated scalar PV adapters.

It does not refute, by itself,

PV-REC as a contextual, no-signalling, microcausal
event-mechanical proposal.

That proposal has to be judged by its own mathematics and, ultimately, by its empirical angle-dependent predictions.

All my Best,

Parker

Parker

[Parker Emmerson]

[Richard Gill]

Dear Leo

Very interesting comments.

(1) Even if we use all the mathematical apparatus of Hilbert spaces, non commuting “observables” et al, all that maths can be expressed in terms of real numbers. If you can compute things on an ordinary computer you are doing that with scalar arithmetic. In fact, with binary arithmetic.

(2) What is the relevant information in an EPR test? It depends what the purpose of the test is. A Bell-CHSH experiment has a very narrow focus. The experimenter is allowed to collect whatever data they like during the local measurement processes and to process that data however they like, but the final experiment will report the statistics of binary functions of whatever data was collected in the short time interval allowed. Naturally, an experimenter hoping to publish the first loop-hole free successful violation of Bell inequalities (with a really impressive p-value) will do lots of test runs in order to find the functional of available data which does the job best. In other words, to optimise the power of the test, to use a statistical term; ie , the probability of rejecting the null hypothesis in the case that that the null hypothesis is not actually true. The null hypothesis is local realism. (More precisely: Bell’s classical local causality).  Once plenty of independent experiments have confirmed that local realism is not true, there is no more need for the Bell-CHSH experiment. I’m not sure if we’ve reached that stage yet. The Delft and Munich style experiments have large effect sizes but huge standard errors too. The Vienna and NIST experiments have good statistical significance but a tiny effect size. 

Anyway, once there is not much to be gained by improving past experiments, ambitious experimenters will be looking for new hypotheses which can be tested by innovative new experiments.

Richard

[Richard Gill]

Dear Parker

Unfortunately, the word “contextual” is a bit dishonest. The context is the set of entire conditions of a single (N = 1) trial. Thus, it includes both settings “a” and “b”. PV-REC is a nonlocal (globally contextual) no-signalling, microcausal event-mechanical proposal.

I don’t think Einstein would have liked it. You have simply adopted Bohr’s not very convincing excuse.

Since the model reproduces QM predictions, its empirical angle-dependent predictions are beyond reproach. Because QM satisfies no-signalling, your model does too.

To get back on topic, I do feel that your model is very similar to Bryan Sanctuary’s approach. A dream converted into difficult maths. But the dream is a fantasy. This is not science, it is science-fantasy. It is art.

Richard

[Parker Emmerson]

Yes, it's state of the art.

[Parker Emmerson]

Oh... looks like Einstein refuses to lose. lolzz

[Richard Gill]

Dear all, dear Bryan

My two PubPeer comments on Bryan’s two recent papers claiming he has resolved Bell’s theorem are now public.

Richard

Sent from my iPad

On 29 May 2026, at 02:25, Parker Emmerson <powerin...@gmail.com> wrote:



[Richard Gill]

Brian Einstein will never admit defeat.

But I will defeat him. All that needs to be done is to locate the point in his program at which settings a and b (angles in degrees) together with the current state of a pseudo random number generator are used to produce outcomes x, y.

O course this happens many, many times.

The first question will be: do x, y take values +/-1 and is the correlation calculated as the average of the product x times y for many replicates with the same a, b (or a, b in the same bins)?

If not, Bryan is not simulating EPR-B correlations

But if he is, then we finally need a few times to generate outcomes x, y ; x, y’; x’, y; x’, y’ for settings a, b; a, b’; a’, b; a’, b’ ; and the *same initial state* lambda of the pseudo random number generator.

Bell-CHSH says that if he does get -cos(a - b) by a legitimate calculation from legitimately generated data, then his model must be non-local for a fairly large proportion of trials. Ie, after a few tests I’ll find a set a, a’, b, b’, x, x’, y , y’ which violate locality.

It’s a simple exercise in forensic auditing of Bryan’s program.

I hope his computer program is reasonably transparent.

> On 29 May 2026, at 02:25, Parker Emmerson <powerin...@gmail.com> wrote:
>

[Leo]

Dear Richard,

I've seen in many of your replies you stating something to the effect of: "Bell-CHSH says that if one obtains (-cos(a-b)) by a legitimate calculation from legitimately generated data, then the model must be non-local."

Aside from the fact that this seems to make the conclusion depend rather strongly on what is meant by "legitimate" in the first place, it made me curious. If "legitimate" here means a model satisfying Bell's premises, then it would appear that any model reproducing the quantum correlations while remaining within that class would necessarily fall under Bell's conclusion by construction.

In the paper with Inge and Bart you specifically mention that your own way of finding closure with the Bell issue is to abandon the Aristotelian notion of "prior" cause. However, I don't think I have seen a paper of yours specifically modeling the EPR setup from that premise.

Given that notion as a modeling assumption, are you able to derive the quantum correlations, through any method you would consider physically satisfactory?

The EPR correlations obey a very well defined structure, they are not merely arbitrary correlations. I am asking because many times when I discussed with proponents of superdeterminism (and even in papers by Hossenfelder, who is one of its most notable proponents), I found that while the mathematical premise itself is proposed as a way around Bell, it is often less clear how the exact quantum correlation structure emerges event-by-event. To my knowledge, nobody has yet provided a generally accepted derivation of the full quantum correlation function from such premises alone.

Best regards,
Leo

[Richard Gill]

Dear Leo

I explained exactly what I meant by a legitimate calculation from legitimately generated data. You just had to keep on reading the same email.

It means firstly that x, y take values +/-1 and the correlation is calculated as the average of the product x times y for many replicates with the same a, b (or a, b in the same bins).

Secondly It must be possible to generate outcomes x, y ; x, y’; x’, y; x’, y’ for settings a, b; a, b’; a’, b; a’, b’ ; and the *same initial state* lambda of the pseudo random number generator.

I think these are very modest requirements. If anyone thinks they are unreasonable, I would welcome discussion and alternative constraints.

It is easy to simulate the EPR-B setup if you allow me to use nonlocal randomness. That means randomness which depends on a and b. Given a and b, calculate the probabilities of getting outcomes +/-1, +/-1. They are four probabilities which add up to one, of the form (1 - r x y) / 4. “r” will be the correlation. Split a circle of circumference 1 into 4 segments of those lengths. They can be formed by the intersections of two semicircles and their complements.  The length of the intersection of the two semicircles is determined by r. Pick a point uniformly distributed on the circle. It falls into one of the four segments. Define x, y according to which segment.

I don’t think this is physically natural. But if you believe in superdeterminism or retrocausality or action at a distance you could dream up a physics story.

Richard

Sent from my iPad

On 30 May 2026, at 20:18, Leo <leo_...@hotmail.it> wrote:



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[Parker Emmerson]

There is a separate issue in the other thread being discussed: absolute mathematical truth. Now, for me, and Richard, you mentioned Buddhism - while I wouldn't deny that there are maybe some analogies between Christianity and Buddhsim, they essentially are extremely different. Buddhism teaches cessation -- the cessation of actual existence (people can argue, but that's essentially what it states), while Christianity teaches eternal life forever with Yeshua in heaven. Not sure about you, but I'll take the latter. Anyway, besides all that (Yeshua's being the incarnate truth in reality) --- the absolute truth purported by mathematics is not really as absolute as most people think. The premise that mathematics hasn't evolved, developed and advanced since John S. Bell's time is very flawed. Mathematics is essentially, a language. The rigidity of arithmetic is not absolute as absolute as people think it is, especially when it comes to functors, a priori numeric energy, etc. These mathematical methods are more flexible than people realize, and that makes them adaptable as well for a variety of applications. I'm not sure if you read the previously attached paper or saw the open problems in it. They have since been solved. The updated paper is attached. I'm going to try to get this published somewhere. If you have any recommendations, let me know. Otherwise, I'll go for IJQF at some point. Also, someone else is trying to join the group who designed some experiment for testing my other paper's propositions. - just a heads up. It's always a delight to hear your thoughts on Bell's Theorem. Let me know what you think about this most updated version if you have any time to find it interesting. It's not science fiction!

All my best,

Parker

P.S. - Einstein refuse to lose. Who do you think you are arguing with Albert Einstein? Sheesh.

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/0430A199-6238-49BF-AB6D-9943892736DF%40gmail.com.

[Richard Gill]

Dear Parker

The attached paper by yourself in your last posting is too long for me. I need to start writing a new paper myself, today. It will be short but it will take me a long time, rewriting every sentence numerous times, and getting new ideas as I write, causing the abstract and introduction and conclusion to be rewritten completely many times over. Maybe I will take a look this evening. 

I have no interest whatsoever in “eternal life with Yeshua in heaven”. The words are meaningless. It’s not clear Jesus ever existed. It’s a comfort blanket. If he did exist, it seems his teachings on how to live the life we have now coincide with the Buddha’s and those of all the other world religions. I have other ways of finding motivation to get out of bed in the morning. I write this at six a.m. on Sunday morning. I have a lot of cleaning up to do before the cleaning lady comes this afternoon (she’s Muslim).

I have had a lot of interest in the foundations of mathematics all my professional life. More than 50 years ago I had lectures at Cambridge from John Horton Conway and he took us through Gödel’s theorems. I corresponded with Douglas Hofstädter about a Beetles song which he alleged was pure nonsense. I showed him it was a biting critique of the British upper classes, Monty Puthon avant la lettre. As an American, he hadn’t realised that.

I spent all my career as the token statistician in pure maths dominated maths departments. The best maths departments at the best universities in the Netherlands. I had some exceptionally good students! I think category theory has taken the soul out of pure mathematics. However, Klaas Landsmann at Nijmegen university is doing interesting stuff with it in the foundations of physics.

I don’t argue with Albert Einstein. I am arguing a lot with Bryan Einstein Sanctuary. 

Richard

Sent from my iPad

On 31 May 2026, at 04:04, Parker Emmerson <powerin...@gmail.com> wrote:



<PV_REC__A_Phenomenological_Velocity_Relational_Event_Completion__Copy_ (2).pdf>

[Richard Gill]

They should contact the group’s owner and manager Alexandre de Castro


Sent from my iPad

> On 31 May 2026, at 04:04, Parker Emmerson <powerin...@gmail.com> wrote:
>

[Richard Gill]

Dear Leo

Indeed. Nobody has done it yet and IMHO no one ever will. But there are people who try, such as my friend Engel Wichmann. He derives the EPR-B correlations from some structural premises. He rejects reductionalism.

Superdeterminism requires finding a mechanism which determines the settings chosen outside the measurement apparatus, and the physical variables inside, at the same time. This entangles physical processes which seem to have nothing whatever to do with one another. 

Richard

Sent from my iPad

On 30 May 2026, at 20:18, Leo <leo_...@hotmail.it> wrote:

[Leo]

Dear Richard,

Thanks for the paper. It reminds me a lot of Christian's papers to be honest. Its not entirely clear to me where he introduces statistical dependence, as from the formulas it would seem we are still free to ask "what if chose b instead of a?". But I only gave it a superficial reading.

As for your requirements: those are exactly Bell's requirements, meaning any program following those rules can't hope to evade Bell. That's the circularity i was referring to, what is considered legitimate is something that sets one up to failure. Progress (if at all possible) can only be made by relaxing these requirements of Bell, hopefully in a way that is still reconducible to a notion of locality. Many in the past have suspected for.example that Bell's mathematical notion of realism might be too strong. 

[Leo]

Richard:

"
That means randomness which depends on a and b. Given a and b, calculate the probabilities of getting outcomes +/-1, +/-1. They are four probabilities which add up to one, of the form (1 - r x y) / 4. “r” will be the correlation. Split a circle of circumference 1 into 4 segments of those lengths. They can be formed by the intersections of two semicircles and their complements.  The length of the intersection of the two semicircles is determined by r. Pick a point uniformly distributed on the circle. It falls into one of the four segments. Define x, y according to which segment."

Yes, its easy to come up with a distribution obeying setting dependence. My point is that it is much harder to explain how that dependence arises. 

[Richard Gill]

Dear Leo

That is the whole point. My method enables one to evaluate claims that people have disproved Bell’s theorem by means of a computer simulation. I’m looking forward to using it to show that Bryan Sanctuary has been foolish himself and that his papers should never have been published.

Richard

Sent from my iPhone

On 31 May 2026, at 10:10, Leo <leo_...@hotmail.it> wrote:

Dear Richard,

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[Richard Gill]

I know. That’s obvious. And so far no-one has done it. I think it never will be done.

Engel Wichmann thinks he will do it. I think he won’t succeed. But I encourage you to study his preprint and learn about his ideas. He is not stupid. There’s some very clever and original maths in his work. The maths seems to be correct.

I am not convinced by his premises.

Sent from my iPhone

On 31 May 2026, at 10:12, Leo <leo_...@hotmail.it> wrote:

Richard:

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/68158fcf-7b3b-4b23-adf7-87184e8bbfa6n%40googlegroups.com.

[Richard Gill]

PS. The point is that there is no need to study the complex mathematics which many people use to disprove Bell’s theorem. I like to use Bell’s theorem to show that their accompanying and illustrative simulation experiment is fundamentally flawed. Most disproofs of Bell’s theorem are constructed by persons who have not understood the proof.

Bryan Sanctuary’s next paper, with a new simulation experiment, is going to be an interesting test case for me.

Sent from my iPhone

On 31 May 2026, at 10:31, Richard Gill <gill...@gmail.com> wrote:

Dear Leo

[Mark Hadley]

We need a way to screen long complicated papers that claim to explain epr correlations.

Richard gives his computer test.

I look forward a clear coherent description of how non locality is introduced or avoided.

if it can't pass those tests it's not worth reading.

mark

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/221F6FC0-98E2-467E-9583-999ED98F7560%40gmail.com.

[Inge Svein Helland]

Dear Mark,

In my opinion we can avoid nonlocality by assuming that we all are limited as observers.

See the description of Charlie in my joint paper with Richard and Bart. As I see it, Charlie can be any of us.

Inge

Sendt fra Outlook for iOS

---

From: 'Mark Hadley' via Bell inequalities and quantum foundations <Bell_quantum...@googlegroups.com>
Sent: Sunday, May 31, 2026 11:03:54 AM
To: Richard Gill <gill...@gmail.com>
Cc: Leo <leo_...@hotmail.it>; Bell inequalities and quantum foundations <Bell_quantum...@googlegroups.com>
Subject: Re: [Bell_quantum_foundations] Instantiated bivector planes: Double Slit vs. EPR

 

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CAN%3D2%2Bo0LR4S0HLxf6E0Q9e4_NE59uGwLL2_MskXQ-J2%3DX82hOg%40mail.gmail.com.

[Bryan Sanctuary]

Dear Parker, Leo and others,

Since I posted this thread, there have been over 60 replies and discussions.  So I will try to summarize a bit:

You are encountering Richard who is completely closed minded on Bell.  He will argue black is white and confuse people's arguments.  If that fails, he attacks and discredits.  His attacks are first to obfuscate with different math, and gets off topic, If you still persist, his attacks become personal.  At first I was a quantum crackpot, I lost my marbles, failed probability 101, and now I am called Brian (Bryan) Einstein!   In the course of this tread, Richard mentions several people : Joy Chirstian, Karl Hess, W. Phillipp, Han Geurdes, and Marian Kupczynski. These physicists will no longer communicate with Richard, and you can surmise why.  I state this, because this dishonesty holds up science. Richard is the gatekeeper of Bell, and by his own admission does not understand QM, only probability theory.  

I am here because I have something to say, and, like most, I like a forum.  This question is important, so I stand up to Gill and the other Bellists. 

As I said, I will soon post my Double Slit paper using bivectors, and then a short paper for  the group that answers Gill.  The bivector resolution of the Double Slit is closely related to EPR violation.

Here is a concise statement:

• Bell's theorem begins with Boolean detector values that exist throughout the experiment, allowing all correlations to be constructed from a common set of pre-existing binary variables. 
• In contrast, the BiSM begins with a continuous quaternionic rotor state carrying a common Lorentz-invariant phase relation established at the source. 
• This phase is not a signal exchanged between Alice and Bob, but a geometric property of the pair that persists during free flight, much as phase coherence persists in lasers, superconductors, Bose-Einstein condensates, and other coherent systems. 
• The analyzer settings act locally on the incoming rotors, instantiating local measurement planes from the underlying phase structure. Only at detection is the rotor converted into a Boolean outcome. 
• The observed cosine correlation therefore arises from the geometric relation between two locally instantiated rotor states sharing a common phase coherence, rather than from pre-existing Boolean assignments or nonlocal influences. 
• In this view, EPR correlations are not evidence for superluminal communication, but a statistical manifestation of transported geometric phase coherence.  

Richard's off -handed comments include that there is no need for me to invent new math!  What a joke!! I have NOT.  Rather I replace QFT with classical physics and Geometric Algebra. 

I will soon post my response, but like us all, I must be careful when I write, line by line.  It takes time.

EPR is the simplest example of long range coherence (only between a single pair of particles) whereas coherence between, say lasers, involves a complete ensemble of collective motion.  The long range EPR coherence is simply a product of two quaternions: Q_{ab} =Q_(a,\lambda)Q*_(b,-lanbda) where the quaternions are rotors, Q_(a,\lambda) =exp(i(a-\lambda)Y) and the instantiated plane is (a-\lambda). Product states have no non-locality.  There is only one channel of clicks, not two.

I predict, with high probability, that Richard will dismiss my explanation as a non-local application of Bell. Wanna bet?$ 

Bryan

[Richard Gill]

Hi Bryan

You promised to show us the computer program that you used to draw this graphic:

I’m looking forward to reporting here what I find. Does the code faithfully follow your concise description?

Richard

Sent from my iPad

On 31 May 2026, at 13:12, Bryan Sanctuary <bryancs...@gmail.com> wrote:



[Bryan Sanctuary]

Hi Richard,

You asked 

I’m looking forward to reporting here what I find. Does the code faithfully follow your concise description?

Answer: Yes

Bryan

[Richard Gill]

Great, that’s very exciting, I’m looking forward to test-running it!

Richard

Sent from my iPad

On 31 May 2026, at 13:52, Bryan Sanctuary <bryancs...@gmail.com> wrote:



Hi Richard,

You asked 

I’m looking forward to reporting here what I find. Does the code faithfully follow your concise description?

Answer: Yes

Bryan

On Sun, May 31, 2026 at 7:34 AM Richard Gill <gill...@gmail.com> wrote:

Hi Bryan

You promised to show us the computer program that you used to draw this graphic:

[Mark Hadley]

so what part of Bells inequalities does it bypass?

[Bryan Sanctuary]

Mark,

It means Bell's polytope, the 4-cube of counterfactual ponts, cannot be formed. So Bell is not applicable.

Bryan

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CAN%3D2%2Bo1re%3D-d-UkCrVkirP4gr4-Ve0a-xX5nGAoTdjmW%3DOLfgw%40mail.gmail.com.

[Inge Svein Helland]

The CHSH inequality may be violated because there is no joint distribution of the four products.

Sendt fra Outlook for iOS

---

From: Bryan Sanctuary <bryancs...@gmail.com>
Sent: Sunday, May 31, 2026 3:11:45 PM
To: Mark Hadley <sunshine...@googlemail.com>
Cc: Inge Svein Helland <in...@math.uio.no>; Richard Gill <gill...@gmail.com>; Leo <leo_...@hotmail.it>; Bell inequalities and quantum foundations <Bell_quantum...@googlegroups.com>

[Mark Hadley]

you mean the A( a lambda) functions don't exist?

the theory does not predict the outcomes at all?

Or it needs a an b to predict outcomes.

[Mark Hadley]

CSHS never required that. it needed the A(a lambda) functions

[Bryan Sanctuary]

Inge,

Exactly, and that is my point.

Bryan

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/OS6P279MB06993D5BF89CB250A4B890E7F5142%40OS6P279MB0699.NORP279.PROD.OUTLOOK.COM.

[Mark Hadley]

That is not required to derive Bell. it is a consequence of the A functions existing.

1) If the A exist then it is a realistic theory

2) 

If they only depend on one detector it is local realist

And yes, in that case the probability structure is classical.

if you want to communicate with us clearly then say if 1 or 2 is true at the outset.

On Sun, 31 May 2026, 15:11 Bryan Sanctuary, <bryancs...@gmail.com> wrote:

[Bryan Sanctuary]

Hi Mark,

You forgot the third condition, Fine's theorem,

Bryan

[Richard Gill]

Fine’s theorem is not a further condition. It’s a converse to Bell’s theorem.

Fine says that if the 16 probabilities p(x, y|a, b) satisfy no-signaling (four linear equalities) and also satisfy all 8 one-sided CHSH inequalities, then there exist functions A(a, lambda), B(b, lambda), and a probability distribution over a set of values of a hidden variable lambda, such that etc etc etc.

Richard

Sent from my iPhone

On 31 May 2026, at 18:14, Bryan Sanctuary <bryancs...@gmail.com> wrote:



[Mark Hadley]

No there is no third condition.

I think Fines theorem derives the probability structure from 1 and 2

Certainly CSHS can be derived without invoking Fines theorem.

Bryan, you are trying to add complications to distract us from your ridiculous mistakes.

[Inge Svein Helland]

Bryan. I agree that the 4 products have no joint distribution, but my explanation of this is different than yours. Call the products X_1Y_1, X_1Y_2, X_2Y_1 and X_2Y_2. Then the first two products are related through a common X_1. Then I have a mathematically derived theorem implying the following for Charlie during his modelling attempts: Assume that Charlie can have a model containing two related variables, and that these are maximal in a welldefined way. Then he cannot have in his model a third maximal one which is related to the first variable, but not to the second one. Here, the third product is related to the first one through a common Y_1, but not to the second one. So Charlie is unable to form a joint probability model of the three first products.

The notion of maximality is what I call maximal accessibility. When making his model, Charlie must look at one run at the time, then one response from Alice and one from Bob.

Mark. I refer to Bryan's recent response. I agree with 1 and 2, but not with what Bryan would call 3.

Richard. I agree with you on most of what you say, but my reasoning is what I would call local: It is just one local observer Charlie.

Inge

---

Fra: Mark Hadley <sunshine...@googlemail.com>
Sendt: søndag 31. mai 2026 17:00
Til: Bryan Sanctuary <bryancs...@gmail.com>
Kopi: Inge Svein Helland <in...@math.uio.no>; Richard Gill <gill...@gmail.com>; Leo <leo_...@hotmail.it>; Bell inequalities and quantum foundations <Bell_quantum...@googlegroups.com>
Emne: Re: [Bell_quantum_foundations] Instantiated bivector planes: Double Slit vs. EPR

 

[Inge Svein Helland]

Dear Richard,

Disregarding this discussion and disregarding Fine's theorem, I think that we agree that there are three conditions in Bell's theorem: locality, counterfactual definiteness an non-conspiracy. So, Mark's list of two is incomplete.

Inge

---

Fra: Richard Gill <gill...@gmail.com>
Sendt: søndag 31. mai 2026 18:38
Til: Inge Svein Helland <in...@math.uio.no>
Emne: Re: [Bell_quantum_foundations] Instantiated bivector planes: Double Slit vs. EPR

 

Dear Inge

The singlet state EPR-B correlations violate Bell-CHSH for suitably chosen setting pairs for Alice and Bob. So either Bryan’s math is wrong, or Bell’s math is wrong.

When we see his math and/or his computer simulation program, we’ll be able to decide which is the case

Richard

Sent from my iPhone

On 31 May 2026, at 15:22, Inge Svein Helland <in...@math.uio.no> wrote:



[Richard Gill]

Dear Bryan

On 31 May 2026, at 13:12, Bryan Sanctuary <bryancs...@gmail.com> wrote:

Here is a concise statement:

• Bell's theorem begins with Boolean detector values that exist throughout the experiment, allowing all correlations to be constructed from a common set of pre-existing binary variables. 

That is not true. Bryan is thinking of Bell (1964). Bell later abandoned that thinking completely.

• In contrast, the BiSM begins with a continuous quaternionic rotor state carrying a common Lorentz-invariant phase relation established at the source. 
• This phase is not a signal exchanged between Alice and Bob, but a geometric property of the pair that persists during free flight, much as phase coherence persists in lasers, superconductors, Bose-Einstein condensates, and other coherent systems. 
• The analyzer settings act locally on the incoming rotors, instantiating local measurement planes from the underlying phase structure. Only at detection is the rotor converted into a Boolean outcome. 

This looks like x = A(a, lambda), y = B(b, lambda), where lambda is a complete description of the two rotors just before they interact with the two analyzers. In particular, their “common phase coherence” at any moment during their flights from source to analyzers is part of the hidden variable lambda.

• The observed cosine correlation therefore arises from the geometric relation between two locally instantiated rotor states sharing a common phase coherence, rather than from pre-existing Boolean assignments or nonlocal influences. 
• In this view, EPR correlations are not evidence for superluminal communication, but a statistical manifestation of transported geometric phase coherence.  

Looks like a local hidden variable model

[Richard Gill]

Mark took the no-conspiracy condition for granted.

Bryan does too.

That’s quite OK. 

It has a completely different status to locality and realism. It’s a metaphysical loophole to the theorem that QM contradicts local realism.

Sent from my iPhone

On 31 May 2026, at 18:45, Inge Svein Helland <in...@math.uio.no> wrote:



[Bryan Sanctuary]

Mark

Bell assumes that all correlations can be represented by a single probability distribution over shared hidden variables λ, with each measurement outcome being a local function of λ and the local setting.    Fine's theorem states that the Bell–CHSH inequalities hold if and only if all four possible measurement outcomes can be described by a single joint probability distribution.

My theory shows that such a single joint probability space cannot be constructed. Therefore, Fine's theorem is not applicable, and Bell-CHSH inequalities cannot be constructed.

Bryan

[Bryan Sanctuary]

Mark,

Maybe you can derive CHSH with 1 and 2 only, but it is only an equation.  The derivation, however,  requires counterfactual definiteness: outcomes for all four CHSH settings are assumed to be simultaneously well-defined, including those corresponding to measurements that were not performed. Fine's theorem shows that the CHSH inequalities are equivalent to assuming a single joint probability distribution for all four actual and counterfactual measurement outcomes.

I argue that a single probability space cannot be formed for spin.

Bryan

On Sun, May 31, 2026 at 12:33 PM Mark Hadley <sunshine...@googlemail.com> wrote:

[Mark Hadley]

I have obtained that. QM correlation from super determinism or retro causality.

see my webpage for published papers DrMarkHadley.com

these are basically the steps...

1) recognise that we are dealing with probabilities 

2) How do we know the probabilities of classical dice tossing? We apply the same principles

3) we recognise that it is structurally context dependent. ( that's different to dice)

4) Established result is that the only way to represent probabilities in a context dependent system is using spaces and subspaces if a vector space. ( for dice we always use weighted volume elements)

5) The only probability measure on the vector spaces is a quadratic form ( scalar product or Trace ) ( for dice it is an integral over the volume elements)

6) Given the quadratic form, if we assume symmetry and continuity we obtain Schroedinger's equation etc ( that's in quantum text books, Balentine and Weinberg)

If you think about it that's how you get the probability of a 4 on the dice. etc.

And that's it. It's a proof but can't be any other way. ( just as with dice probabilities) My Maths supervisor does not like those sorts of proof because while valid they give little insight.

I hope that helps.

I find Richards inclinations sound but unappealing.

Mark

On Sat, 30 May 2026, 19:18 Leo, <leo_...@hotmail.it> wrote:

Dear Richard,

I've seen in many of your replies you stating something to the effect of: "Bell-CHSH says that if one obtains (-cos(a-b)) by a legitimate calculation from legitimately generated data, then the model must be non-local."

Aside from the fact that this seems to make the conclusion depend rather strongly on what is meant by "legitimate" in the first place, it made me curious. If "legitimate" here means a model satisfying Bell's premises, then it would appear that any model reproducing the quantum correlations while remaining within that class would necessarily fall under Bell's conclusion by construction.

In the paper with Inge and Bart you specifically mention that your own way of finding closure with the Bell issue is to abandon the Aristotelian notion of "prior" cause. However, I don't think I have seen a paper of yours specifically modeling the EPR setup from that premise.

Given that notion as a modeling assumption, are you able to derive the quantum correlations, through any method you would consider physically satisfactory?

The EPR correlations obey a very well defined structure, they are not merely arbitrary correlations. I am asking because many times when I discussed with proponents of superdeterminism (and even in papers by Hossenfelder, who is one of its most notable proponents), I found that while the mathematical premise itself is proposed as a way around Bell, it is often less clear how the exact quantum correlation structure emerges event-by-event. To my knowledge, nobody has yet provided a generally accepted derivation of the full quantum correlation function from such premises alone.

Best regards,
Leo

Il giorno sabato 30 maggio 2026 alle 11:33:52 UTC+2 gill...@gmail.com ha scritto:

Brian Einstein will never admit defeat.

But I will defeat him. All that needs to be done is to locate the point in his program at which settings a and b (angles in degrees) together with the current state of a pseudo random number generator are used to produce outcomes x, y.

O course this happens many, many times.

The first question will be: do x, y take values +/-1 and is the correlation calculated as the average of the product x times y for many replicates with the same a, b (or a, b in the same bins)?

If not, Bryan is not simulating EPR-B correlations

But if he is, then we finally need a few times to generate outcomes x, y ; x, y’; x’, y; x’, y’ for settings a, b; a, b’; a’, b; a’, b’ ; and the *same initial state* lambda of the pseudo random number generator.

Bell-CHSH says that if he does get -cos(a - b) by a legitimate calculation from legitimately generated data, then his model must be non-local for a fairly large proportion of trials. Ie, after a few tests I’ll find a set a, a’, b, b’, x, x’, y , y’ which violate locality.

It’s a simple exercise in forensic auditing of Bryan’s program.

I hope his computer program is reasonably transparent.


> On 29 May 2026, at 02:25, Parker Emmerson <powerin...@gmail.com> wrote:
>
> Oh... looks like Einstein refuses to lose. lolzz

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[Leo]

Dear Bryan,

Unfortunately time is not plentiful for me to dive into multiple papers. Could you summarize the central concept which makes ypu conclude that "spin has no joint distribution" in simple terms and how that saves local realism? If I find that convincing, I might dive into your work.

[Bryan Sanctuary]

Hi Leo,

Thanks,  I will soon post my double slit paper and then a discussion of just your point.  So coming soon.

Best wishes

Bryan

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/011500b1-66a8-40e6-9d90-bec7df617245n%40googlegroups.com.

[Bryan Sanctuary]

Mark,

Here is my (standard) derivation of CHSH  

Bryan 

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CAN%3D2%2Bo1ScFUfrs0-XW_fvEnN24c2Hgn_etvC3SgjKBvrj91c5g%40mail.gmail.com.

[Mark Hadley]

you used if and only if in Fines theorem

so you are claiming  that your variables cannot be used to construct the A functions. Do you agree that is your claim?

so either you offer no explanation for the +/- results, or your theory is non local.

neither of which is remarkable.

Mark

[Bryan Sanctuary]

Mark,

My variables can and do construct A(a) and B(b) with outcomes of \pm 1.  If they exist then A(a') and B(b') do not exist. So no single prob space describes all four experiments as Bell requires.

You will see when I send my program details.

Bryan

[Mark Hadley]

No.

you are misunderstanding Bells theorem.

The amazing result can be used in two quite different ways.

1) is quantum theory compatible with a local hidden variable theorem. This is an entirely theoretical result. It is meaning full without an experiment. It can apply to an ideal thought experiment. Obviously with no conspiracy.

I think QM makes correct predictions so this interests me.

2) is the real world compatible with a local hidden variable theory. This question is completely independent if quantum theory. It can be determined by experiment. if the experiments allow a conspiracy then they can be convincing but not overwhelming proof.

Mark

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/OS6P279MB0699D0550450BC605BC051C2F5142%40OS6P279MB0699.NORP279.PROD.OUTLOOK.COM.

[Parker Emmerson]

Bell-locality is being treated as if it were locality itself, when it may only be a condition on one particular mathematical representation of locality. Why should we have to keep apologizing with “not Bell-local” every three sentences? 

PV-REC is not BellLocal. But PV-REC claims a different locality notion:

EventLocal=locally registered outcomes + no operational signalling + no occupied global Bell table.

The dependence is not a concealed message between wings. It is the refusal of the model to decompose one completed joint event into four pre-existing scalar counterfactuals. Bell replay fails, but signalling does not follow. PV-REC is not a Bell-scalar replay theory. It does not assign a pre-existing four-setting table (A1,A2,B1,B2) to the source record. Instead, it assigns one definite outcome pair only to the completed measurement context (a,b). The joint event law depends on the completed context, but the local marginal statistics do not. Therefore the model denies that locality requires Bell-scalar replay; it does not introduce operational signalling.

PV-REC can be interpreted as satisfying the physical ethos of Bell’s conditions, but not the later Bell-scalar replay formalization of those conditions.

PV-REC says:

No conspiratorial source-setting dependence, no negative probabilities, no missing detections, no controllable superluminal signalling, definite performed outcomes.

That is a very strong sense in which it preserves the spirit of the Bell premises.

So Richard is kind of right that replay captures Bell’s formal assumption. But “replay” is a later operational packaging, not Bell’s original philosophical wording. "Give me a theory that violates Bell while already being formatted as the kind of theory Bell proves cannot violate Bell."

Bell’s theorem is decisive against theories whose complete state supports separated scalar counterfactual replay. PV-REC denies that this replay object is physically present. Therefore Gill’s programming challenge is fair as a test of Bell-scalar replay models, but not fair as a test of PV-REC’s actual claim. PV-REC is arguing that Bell’s assumptions are not the right formalization of local realist event completion. Richard, the issue is that your interpretive framing preselects the formal object under dispute, then treats failure to supply that object as failure of the theory. Gill asks PV-REC to enter the debate only after accepting Bell’s scalar ledger.

Your programming challenge is mathematically clean, but it is not interpretively neutral. It requires the model to present itself as two separated scalar replay functions on a common source record. That already installs the Bell/Fine global-counterfactual ledger. PV-REC’s claim is precisely that this ledger is not physically occupied before measurement. The actual experiment produces one definite local outcome pair, not four jointly defined scalar answers for mutually exclusive settings. Therefore, when PV-REC fails your replay interface, that is not an accidental computational failure; it is the predicted failure of Bell-scalar representability. The challenge proves that PV-REC is not a Bell-replay model. It does not prove that PV-REC is not a realist, no-signalling, contextual event-completion model. The disagreement is not inside the CHSH algebra; it is over whether your replay interface is the only legitimate mathematical rendering of locality and realism. 

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CALLw9YyZdyLKexneXuacX_CdAJMT__1eQoemGGshYZ1QqFGs_w%40mail.gmail.com.

[Mark Hadley]

if the probability space condition can be derived from Bells condition, as per Fines theorem, then it is not a separate assumption.

That's simple logic.

mark

[Mark Hadley]

You idiot.

A(a) is a function of the detector angle. It takes a value 0 to 360 and gives +/- as a result.

you can label the angles with a or a' or call them Bryan and Fred. you feed an angle in and get a result.

suggesting the the result friends upon the name if an angle is stupidity.

Mark

[Parker Emmerson]

Dear Richard, 

I hope you are well. Your challenge is mathematically fair if the target is Bell-scalar separability: if one assumes a single setting-independent source record λ and separated response functions X = X_A(a, λ), Y = Y_B(b, λ), then CHSH follows by the usual pointwise identity A₀B₀ + A₀B₁ + A₁B₀ − A₁B₁ = A₀(B₀ + B₁) + A₁(B₀ − B₁), whose value is always ±2, so averaging gives S ≤ 2. I do not dispute that theorem. The issue is that this “locality” condition already contains a very specific resolution of the physical question: it requires emission-time scalar screening-off, namely that the same source record λ must support all counterfactual replays A₀, A₁, B₀, B₁. That is stronger than no signalling, stronger than preparation independence, and stronger than definite local records. PV-REC keeps preparation independence, P(λ₀ | a,b) = P(λ₀), and keeps operational no-signalling, P_A(x | a,b) = P_A(x | a) and P_B(y | a,b) = P_B(y | b). In the singlet sector it uses m_xy(a,b) = ¼(1 − xy cos(a − b)) and P_PV(x,y | a,b,v) = m_xy(a,b)^κ(v) / Σ_x′y′ m_x′y′(a,b)^κ(v). Since m_++ = m_-- and m_+- = m_-+, the marginals are exactly balanced: P_A(+ | a,b,v) = P_A(− | a,b,v) = ½, and likewise for Bob. So the model is not smuggling in an observable signal. What it denies is the extra claim that λ₀ is the complete Bell screening variable. In PV-REC the completed event is Λᶜᵒᵐᵖ_ab = (λ₀, 𝔅_A(a), 𝔅_B(b)), and the actualization law is (X,Y) = K_ab(λ₀), not X = X_A(a,λ₀), Y = Y_B(b,λ₀). That is the whole logical distinction: replay captures Bell’s formal scalar assumption, but replay is not identical to every coherent notion of locality, realism, or no-signalling event mechanics. If “local” is defined to mean “Bell-scalar replay-admissible,” then PV-REC is not local by definition. But that definition has already built the desired theorem into the admissible class. PV-REC’s point is that a time-symmetric boundary-event theory can have local records, no controllable wing-to-wing signal, preparation independence, constant total flux, and exact operational no-signalling, while still failing scalar replay. Therefore the real disagreement is not over the CHSH algebra; it is over whether Bell-scalar separability has a privileged right to exhaust the meaning of physical locality.

All my best,

Parker

[Parker Emmerson]

Richard’s challenge is a very good test of what it is designed to test, and a very poor test of what it pretends to test. It does not test whether PV-REC permits signalling. It does not test whether the source distribution depends on future settings. It does not test whether Alice sends a physical influence to Bob. It tests whether PV-REC can be rewritten as a Bell-scalar hidden-instruction model. But PV-REC’s whole mathematical point is that completed events are not source-only hidden instructions. So the replay challenge refutes only a straw version of the theory: the version obtained by first deleting its boundary-event ontology and then complaining that what remains does not fit Bell’s spreadsheet.

[Richard Gill]

Dear Parker

My challenge does not “pretend” to test PV-REC.

I did test your PV-REC computer simulation and I found it to be non-local.

I don’t subscribe to your ontology. Those who do are obviously uninterested in my challenge.

Richard

Sent from my iPad

On 1 Jun 2026, at 04:42, Parker Emmerson <powerin...@gmail.com> wrote:



Richard’s challenge is a very good test of what it is designed to test, and a very poor test of what it pretends to test. It does not test whether PV-REC permits signalling. It does not test whether the source distribution depends on future settings. It does not test whether Alice sends a physical influence to Bob. It tests whether PV-REC can be rewritten as a Bell-scalar hidden-instruction model. But PV-REC’s whole mathematical point is that completed events are not source-only hidden instructions. So the replay challenge refutes only a straw version of the theory: the version obtained by first deleting its boundary-event ontology and then complaining that what remains does not fit Bell’s spreadsheet.

On Sun, May 31, 2026 at 8:21 PM Parker Emmerson <powerin...@gmail.com> wrote:

Dear Richard, 

I hope you are well. Your challenge is mathematically fair if the target is Bell-scalar separability: if one assumes a single setting-independent source record λ and separated response functions X = X_A(a, λ), Y = Y_B(b, λ), then CHSH follows by the usual pointwise identity A₀B₀ + A₀B₁ + A₁B₀ − A₁B₁ = A₀(B₀ + B₁) + A₁(B₀ − B₁), whose value is always ±2, so averaging gives S ≤ 2. I do not dispute that theorem. The issue is that this “locality” condition already contains a very specific resolution of the physical question: it requires emission-time scalar screening-off, namely that the same source record λ must support all counterfactual replays A₀, A₁, B₀, B₁. That is stronger than no signalling, stronger than preparation independence, and stronger than definite local records. PV-REC keeps preparation independence, P(λ₀ | a,b) = P(λ₀), and keeps operational no-signalling, P_A(x | a,b) = P_A(x | a) and P_B(y | a,b) = P_B(y | b). In the singlet sector it uses m_xy(a,b) = ¼(1 − xy cos(a − b)) and P_PV(x,y | a,b,v) = m_xy(a,b)^κ(v) / Σ_x′y′ m_x′y′(a,b)^κ(v). Since m_++ = m_-- and m_+- = m_-+, the marginals are exactly balanced: P_A(+ | a,b,v) = P_A(− | a,b,v) = ½, and likewise for Bob. So the model is not smuggling in an observable signal. What it denies is the extra claim that λ₀ is the complete Bell screening variable. In PV-REC the completed event is Λᶜᵒᵐᵖ_ab = (λ₀, 𝔅_A(a), 𝔅_B(b)), and the actualization law is (X,Y) = K_ab(λ₀), not X = X_A(a,λ₀), Y = Y_B(b,λ₀). That is the whole logical distinction: replay captures Bell’s formal scalar assumption, but replay is not identical to every coherent notion of locality, realism, or no-signalling event mechanics. If “local” is defined to mean “Bell-scalar replay-admissible,” then PV-REC is not local by definition. But that definition has already built the desired theorem into the admissible class. PV-REC’s point is that a time-symmetric boundary-event theory can have local records, no controllable wing-to-wing signal, preparation independence, constant total flux, and exact operational no-signalling, while still failing scalar replay. Therefore the real disagreement is not over the CHSH algebra; it is over whether Bell-scalar separability has a privileged right to exhaust the meaning of physical locality.

All my best,

Parker

On Sun, May 31, 2026 at 4:06 PM Parker Emmerson <powerin...@gmail.com> wrote:

Bell-locality is being treated as if it were locality itself, when it may only be a condition on one particular mathematical representation of locality. Why should we have to keep apologizing with “not Bell-local” every three sentences? 

PV-REC is not BellLocal. But PV-REC claims a different locality notion:

EventLocal=locally registered outcomes + no operational signalling + no occupied global Bell table.

The dependence is not a concealed message between wings. It is the refusal of the model to decompose one completed joint event into four pre-existing scalar counterfactuals. Bell replay fails, but signalling does not follow. PV-REC is not a Bell-scalar replay theory. It does not assign a pre-existing four-setting table (A1,A2,B1,B2) to the source record. Instead, it assigns one definite outcome pair only to the completed measurement context (a,b). The joint event law depends on the completed context, but the local marginal statistics do not. Therefore the model denies that locality requires Bell-scalar replay; it does not introduce operational signalling.

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PV-REC can be interpreted as satisfying the physical ethos of Bell’s conditions, but not the later Bell-scalar replay formalization of those conditions.

PV-REC says:

No conspiratorial source-setting dependence, no negative probabilities, no missing detections, no controllable superluminal signalling, definite performed outcomes.

That is a very strong sense in which it preserves the spirit of the Bell premises.

So Richard is kind of right that replay captures Bell’s formal assumption. But “replay” is a later operational packaging, not Bell’s original philosophical wording. "Give me a theory that violates Bell while already being formatted as the kind of theory Bell proves cannot violate Bell."

Bell’s theorem is decisive against theories whose complete state supports separated scalar counterfactual replay. PV-REC denies that this replay object is physically present. Therefore Gill’s programming challenge is fair as a test of Bell-scalar replay models, but not fair as a test of PV-REC’s actual claim. PV-REC is arguing that Bell’s assumptions are not the right formalization of local realist event completion. Richard, the issue is that your interpretive framing preselects the formal object under dispute, then treats failure to supply that object as failure of the theory. Gill asks PV-REC to enter the debate only after accepting Bell’s scalar ledger.

Your programming challenge is mathematically clean, but it is not interpretively neutral. It requires the model to present itself as two separated scalar replay functions on a common source record. That already installs the Bell/Fine global-counterfactual ledger. PV-REC’s claim is precisely that this ledger is not physically occupied before measurement. The actual experiment produces one definite local outcome pair, not four jointly defined scalar answers for mutually exclusive settings. Therefore, when PV-REC fails your replay interface, that is not an accidental computational failure; it is the predicted failure of Bell-scalar representability. The challenge proves that PV-REC is not a Bell-replay model. It does not prove that PV-REC is not a realist, no-signalling, contextual event-completion model. The disagreement is not inside the CHSH algebra; it is over whether your replay interface is the only legitimate mathematical rendering of locality and realism. 

On Sun, May 31, 2026 at 3:31 PM Bryan Sanctuary <bryancs...@gmail.com> wrote:

Mark,

Here is my (standard) derivation of CHSH  

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Bryan 

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