Bell experiment with two independent computers

[Ghenadie Mardari]

Dear Friends,

I designed a simulation of a loophole-free Bell experiment using two independent computers. Alternatively, the scripts for Alice and Bob can be run on a single computer, but at different times. (For example, 10,000 measurements by Alice, followed by 10,000 measurements by Bob). There is no communication whatsoever between parties.

The code is simple enough to run on any laptop (and even smartphone), as long as you have access to a Python viewer with standard libraries (locally, or online). Results are available in seconds.

The rules are as follows:

1. Alice and Bob independently generate experiment templates for a predetermined number of iterations (e.g., N=10,000). The mechanism is deterministic and they end up with identical templates. These are the “hidden variables” that explain the correlations.

2. For each iteration, Alice makes a random choice between a1/a2, while Bob makes a random choice between b1/b2. The corresponding values are chosen from the template.

3. Every iteration is retained for analysis, even if some events fall outside the coincidence window. (No iteration is discarded.)

4. Missing events are replaced with random output values ("+" or "-").

 

In short, all the operational constraints of a quantum Bell experiment are obeyed, yet the final result is a very strong Bell violation, despite the underlying deterministic structure.

Such a phenomenon is widely perceived as impossible. This is – of course – the point behind Richard’s bet. Yet, there is an unexpected connection between “quantum monogamy” and “observer free choice” that was not considered before. The mechanism behind this demonstration is quite instructive.

 

The code and other materials can be found here.

The latest version of the manuscript is available at this link.

Let us talk about this.

 

Best wishes,

Ghenadie.

 

[anton vrba]

And when I read "The underlying model is fully deterministic and yields CHSH violations up to S ≈ 3, despite satisfying the operational requirements of loophole-free Bell experiments."  I stop reading and send to bin 13.  No CHSH S>2root2 has ever been reported empirically, so your computer programs are mental masturbation exercises to boost ego and have no value in advancing physical science.

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

From "Ghenadie Mardari" <gmar...@gmail.com>

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

Date 8/4/2026 8:26:30 PM

Subject [Bell_quantum_foundations] Bell experiment with two independent computers

Dear Friends,

I designed a simulation of a loophole-free Bell experiment using two independent computers. Alternatively, the scripts for Alice and Bob can be run on a single computer, but at different times. (For example, 10,000 measurements by Alice, followed by 10,000 measurements by Bob). There is no communication whatsoever between parties.

The code is simple enough to run on any laptop (and even smartphone), as long as you have access to a Python viewer with standard libraries (locally, or online). Results are available in seconds.

The rules are as follows:

1. Alice and Bob independently generate experiment templates for a predetermined number of iterations ( e.g., N=10,000). The mechanism is deterministic and they end up with identical templates. These are the “hidden variables” that explain the correlations.

2. For each iteration, Alice makes a random choice between a1/a2, while Bob makes a random choice between b1/b2. The corresponding values are chosen from the template.

3. Every iteration is retained for analysis, even if some events fall outside the coincidence window. (No iteration is discarded.)

4. Missing events are replaced with random output values ("+" or "-").

 

In short, all the operational constraints of a quantum Bell experiment are obeyed, yet the final result is a very strong Bell violation, despite the underlying deterministic structure.

Such a phenomenon is widely perceived as impossible. This is – of course – the point behind Richard’s bet. Yet, there is an unexpected connection between “quantum monogamy” and “observer free choice” that was not considered before. The mechanism behind this demonstration is quite instructive.

 

The code and other materials can be found here.

The latest version of the manuscript is available at this link.

Let us talk about this.

 

Best wishes,

Ghenadie.

 

--
You received this message because you are subscribed to the Google Groups "Bell inequalities and quantum foundations" group.
To unsubscribe from this group and stop receiving emails from it, send an email to Bell_quantum_found...@googlegroups.com.
To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/fbc4710b-1678-4fdd-988c-0264381c30fdn%40googlegroups.com.

[Ghenadie Mardari]

Dear Anton,

Thank you very much for your reply.

The point of a Bell experiment with two computers is that no amount of "mental masturbation" can fake it.

This is why Richard is using it (as a form of public service, if you will).

Yet, my solution works without "loopholes".

To answer your concern about S=3, this is possible because we start with a system that produces local violations up to S=4.

Tsirelson's bound is just a special case that applies to scenarios with binary energy redistribution. 

See, for example, my latest papers: 

https://www.mdpi.com/2624-960X/7/4/62

https://www.mdpi.com/2624-960X/8/2/35

Best wishes,

Ghenadie.

[Richard Gill]

Dear Ghenadie, dear all

I studied and played with Ghenadie's Python scripts.

He does not simulate a loophole-free Bell experiment. In a loophole-free Bell experiment the settings are chosen externally by Alice and Bob by independent fair coin tosses and fed into the detection devices one by one in synchronised fashion.

His two programs “alice.py" and “bob.py" generate a lot of random data but they do not generate the data from which the four correlations are determined. Your third program “combine.py" processes the two already prepared data files and mixes them up together adding in more randomness which together generate the actual data (10 000 pairs of binary settings and binary outcomes).

Each final set of two settings and two outcomes has been created together, 

This was clever, but a complete waste of time.

By the way, I tried to run the programs with number of trials set to 1. It failed. The reason was that three of the four correlations were not defined, resulting in an attempt to calculate 0/0.

Ghenadie, Please get your programmer to fix this issue. Let us know when the corrected versions are on GitHub.

Yours

Richard

[Richard Gill]

Dear Ghenadie

What you call the rules are ambiguous. Even after reading your paper and studying your code they still seem very inaccurate.

Anyway, in a loophole-free Bell experiment there are no “iterations”. 

There are only repetitions. In each repetition, two new externally and randomly chosen settings go in, two measurement outcomes come out.

Your experiment however is massively loophole-ridden.

You systematically loop through all possible input and output combinations which can contribute to a particular S = 4 without enabling signaling. There are 8 one-sided CHSH inequalities, you target a particular one of the 8. There are 8 patterns of inputs which give your particular S = 4 and they should be occur equally often to avoid signalling.

You chuck in a bit of random noise to reduce S to about 3. You could target any value you like.

Your model is non-local. It is of little mathematical interest (it is kind of amusing, but I’m sure could be presented in a much more transparent way). It has zero physical interest, as far as I can see.

Richard

Sent from my iPhone

On 4 Aug 2026, at 21:26, Ghenadie Mardari <gmar...@gmail.com> wrote:



[Ghenadie Mardari]

Dear Richard,

I see that my explanation of the rules was not clear enough.

So, let me try again, based on your comments:

1. Alice makes a fair coin toss. She chooses a1 or a2, based on the outcome.

2. She then retains the value associated with the chosen setting from the list of instructions.

3. The list of instructions is generated based on a classical system that produces local violations up to S=4.

4. This is repeated 10,000 times (but the number can be increased or decreased at will). Of course, correlations cannot be calculated for N=1.

5. The same process is repeated by Bob, except with choices between b1/b2.

In short, everything is nice and clean.
Random settings go in.
Measurement outcomes come out.
Hidden variables determine the recorded values (and the corresponding correlations).

Next, what does "combine.py" do?
It closes the detection loophole, just like a quantum Bell experiment.

Some events do not fit in the coincidence window.
If I discarded these "repetitions" (as you called them), I would get S=4.
Yet the protocol requires all the “repetitions” to be counted.

For this reason, I treat missing events as real events with randomly assigned values.
This lowers my result to S=3.

In short, there is nothing in my simulation that does not also happen in a loophole-free quantum Bell experiment.
The only difference is that I am using a classical system.

Think of it this way: Aspect did not close the detection loophole, and he got a large violation.
Modern experiments closed this loophole, but achieved smaller violations.

The implication is clear: loophole-free Bell experiments do not falsify locality.
If they did, my simulation would not work.

Best wishes,
Ghenadie.

[Parker Emmerson]

Dear Ghenadie,

Please see the other thread where Richard explicitly states his rigid belief system that local causality means only one specific thing as to whether or not this phenomenon fits in the spreadsheet. "So the disagreement, once located, is not about the bound and not about counterexamples to it. It is about whether "locality" means the preparation-side screen — a completeness postulate about what can be placed on a hypersurface before the event — or the listed boundary conditions (i)–(iv). The theorem says these are inequivalent: the screen is strictly stronger. You may well answer that the screen is what local causality has always meant; that is a defensible position, and arguing it would be a real argument, about the right question."

Then Richard says, "I agree that that is what local causality has always meant.

Remember, it is a concept introduced by John Bell and developed throughout several chapters of “Speakable and Unspeakable”.

Since he is no longer around, we can only guess what he really meant.

I’m not interested in arguing it further." 

The subsequent issues boil down to 1) Does this prove the point simply by winning by definition (more or less - I think yes) 2) Does this actually respond to Einstein's general premise of locality? (and I think no, Bell's theorem does not respond to Einstein). 

Anyway, that's where I see the discussion as it is today. You can dress it up in different language or interchangeable analogies of mathematical terminology, but essentially the cultural interpretation of Bell's theorem provably overreaches. "The

universality inference — that boundary locality places a mechanics in the screening class, so
that the bound governs local physics as such — is not conceded; it is refuted by the exhibited
mechanics of [22, Thm. 2.40], and this refutation is the sense in which the theorem is demoted
from a prohibition to a class characterization."

"The backdating is the mechanism by which a classification theorem is made to carry no-go authority it never earned: the current statement inherits the founding paper’s priority while shedding its refuted scope." 

"The other asserts a true sentence about the asserted statement: the no-go claim, as made, is refuted." 

https://zenodo.org/records/21669459

All my best,

Parker Emmerson

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CADqzJUorQ-y35mH4%2Buip8cQLCAJ5gAP06v59OHVyghUEuzMLWw%40mail.gmail.com.

[Parker Emmerson]

It is about whether "locality" means the preparation-side screen — a completeness postulate about what can be placed on a hypersurface before the event — or the listed boundary conditions (i)–(iv).

[Bryan Sanctuary]

HI Ghenadie

Can you please describe your classical system.  I got CHSH = 3 in my bivector approach

Bryan

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CADqzJUorQ-y35mH4%2Buip8cQLCAJ5gAP06v59OHVyghUEuzMLWw%40mail.gmail.com.

[Richard Gill]

It is very clear that this is not a loophole free Bell experiment.

In a loophole free Bell experiment, N times:

Two random settings are supplied externally

Two outcomes are generated locally

This is repeated N times

At the end of the experiment we have N settings and outcomes at location A; N settings and outcomes at location B.

You do not generate the outcomes locally

You do not allow me to supply settings from “outside”

Instead you generate the settings yourself and you do a massive computation of all the data from both measurement stations before releasing the outcomes.

[Richard Gill]

On 5 Aug 2026, at 19:01, Parker Emmerson <powerin...@gmail.com> wrote:

The subsequent issues boil down to 1) Does this prove the point simply by winning by definition (more or less - I think yes) 2) Does this actually respond to Einstein's general premise of locality? (and I think no, Bell's theorem does not respond to Einstein). 

1) The proof of Bell’s theorem is so elementary that - given the definitions - it is close to a tautology

2) Bell argued that Einstein would have agreed with his (Bell’s) concept of locality. 

Parker has not succeeded in convincing me that “phenomenological velocity” is a useful concept. I hope for his sake that he manages to convince some third person with the pedagogical skills needed to explain it to a wider audience of physicists and mathematicians. I haven’t heard anyone in this group say that they understand it and that it is a great idea. If they exist then maybe they’d like to expound it in their own words sticking to terminology which most physicists and mathematicians are already familiar with.

[Richard Gill]

The loophole free Bell experiments of 2015 followed an experimental protocol described by John Bell in Bertlmann’s socks

Ghenadie apparently does not know the literature, has never read “Bertlmann’s socks”, nor studied the experimental papers of the successful loophole free Bell experiments. 

His work is not about the concept of locality. It is a simple conjuring trick which does not change our understanding of the maths nor the physics. 

He does not allow the experimenter to supply settings at will

The end result depends deterministically on three random seeds for the three programs. They determine the settings and the outcomes. This is super determinism.

On 5 Aug 2026, at 19:01, Parker Emmerson <powerin...@gmail.com> wrote:

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CANitqNm1XJAuedsFSTruxYyammG5Tz47B1923DNdPNg0NhH39w%40mail.gmail.com.

[Mark Hadley]

Bryan's result violating CSHS was a mathematical mistake. He has been shown the mistake, but he needs the mistake to get a non trivial result.

His bivector theory violates Lorentz invariance.

Cheers

Mark

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CALLw9YwQsrR3vX_71vk1wZ4%3DOQBVrRFm1dY2mUGPT5FnAvXYeg%40mail.gmail.com.

[Richard Gill]

Bryan, Ghenadie’s model is very simple. 

Parker, didn’t you recognise what he’s doing?

It is classical in a sense (almost completely deterministic) but seriously nonlocal.

As everyone knows, S = x1y1 + x1y2 + x2y1 - x2y2 always equals +/-2 if all the xi and yi are equal to +/-1. The vector lambda = (x1, x2, y1, y2) takes on 16 different values. 8 of those 16 values of lambda correspond to S = +4, 8 correspond to S = -4. Ghenadie’s hidden variable is essentially lambda, and his probability distribution is the uniform distribution over the 8 values of lambda which give S = +4. A so-called Popescu-Röhrlich box. Non-signalling, marginals are completely random.

In order to reduce S to about 3, Ghenadie randomly mixes this model with the model where the two outcomes are +/-1 independently each with equal probabilities 0.5.

His computer programs elaborately disguise this simple basis idea. He cycles deterministically through the 8 values of lambda starting at a random position in each cycle, instead of using random values.

That’s why his “running instructions” have to generate a whole combined run of settings and outcomes in one go. He needs to hide the nonlocality.

It could have been a very simple non-local model where the user picks the settings themselves. Instead it has to be a complicated super-determinism model in order to disguise the non-locality.

[I might have picked the wrong one-sided CHSH inequality for this exposition. It’s the same story with any of the other 7 choices.]

Sent from my iPad

On 5 Aug 2026, at 22:09, Bryan Sanctuary <bryancs...@gmail.com> wrote:



[Richard Gill]

I think more importantly, Bryan’s model is incomplete. He does not give a local description of the outcomes in a “single shot” experiment. N = 1. He does not resolve the EPR-B paradox. (Assuming locality, QM is incomplete or wrong). Assuming locality, the paradox still holds: two particle quaternion spin is incomplete or wrong. 

Sent from my iPad

On 5 Aug 2026, at 23:20, Mark Hadley <sunshine...@googlemail.com> wrote:



[Richard Gill]

Sorry, I wrote a lot of nonsense late last night. I was mixing up the Popescu-Röhrlich box with the Bell’s simple LHV model.

"The vector lambda = (x1, x2, y1, y2) takes on 16 different values. 8 of those 16 values of lambda correspond to S = +4, 8 correspond to S = -4” Is not true.
Correct is "The vector lambda = (x1, x2, y1, y2) takes on 16 different values. 8 of those 16 values of lambda correspond to S = +2, 8 correspond to S = -2”



Ghenadie, I have a request. Please can you adapt the computer programs so that the user can choose the exact degree of violation of CHSH.

You say that the degree of violation depends on what is done with what you call missing events, events which do not fit in the coincidence window.

Discard them all gets s = 4
Replace half of them at random with completely random outcomes gets S = 3
Replace a bit more gets S = 2
What about S = 0 ?

I find it hard to decipher your python code and understand the explanations in your paper.

it will be easier for me if the programs allow me to choose what S I want to get, so that I can see in the code how this switching operates.

[Richard Gill]

I finally carefully read Ghenadie’s draft paper

https://www.preprints.org/manuscript/202607.1722

Bell Experiment with Two Independent Computers

It is very ingenious, hard to explain in words, it requires words and pictures.

Let me try to explain it only in words. There are two synchronised spinning disks. Each has 8 fields. Bob’s disk is identical to Alice's but is “one field ahead”.

The fields contain a label (A or B) and a setting (1 or 2) and an outcome (+ or -).

8 combinations.

The order of the fields is therefore important, one *trial* corresponds to the sequence of two adjacent fields.

Let me explain the arrangement which gives us the Popescu-Röhrlich box S = 4; other (more elaborate) variations give S = 2 and S = 3.

A1+

B1+

A2+

B2+

A1-

B1-

A2-

B2-

The 8 pairings (Bob’s disk, Alice's disk) are therefore … (A1+, B1+), then (B1+, A2+), ….

This results in settings and outcomes in the format a b x y:  

1 1 + +

2 1 + +

2 2 + +

1 2 - +

1 1 - -

2 1 - -

2 2 - -

1 2 + -

Which means: 1 1 equal, 2 1 equal, 2 2 equal, 1 2 unequal.

and this pattern of four successive measurement setting pairs and equal/unequal pair of outcomes is repeated twice with the signs of the outcomes reversed.

This gives us three correlations of +1 and one of -1 and hence S = 4. There are no missing observations, no random observations.

There is no-signalling. + and - outcomes are perfectly balanced

Various similar but more complicated arrangements give S = 3 or S = 2.

All very ingenious.

My evaluation:

Elementary combinatorics, ingenious trickery. A completely deterministic system which generates settings and outcomes together gives S = 4. Further modifications give S = 2 and S = 3.

Superdeterminism can explain anything you like including strong violation of quantum theory. All it takes is imagination and ingenuity. I don’t think these models have any serious physical meanings but of course they do illustrate the fact that carefully synchronised periodic systems can exhibit all kinds of correlations. The paper underlines the importance of external and random selection of measurement settings. The author misrepresents his results. He has not recognised the key features which allow one to call a particular experiment “loophole free”.

[Richard Gill]

Dear Ghenadie

Your list of “rules” are not satisfied by your computer programs. At best, they are deliberately written to mislead.

I have posted a comment on preprints.org and PubPeer.com. https://www.preprints.org/manuscript/202607.1722

The PubPeer comment has not yet been released. This often takes a week or two. The preprints.org comment passed moderation almost immediately.

At least I can say that your work is very ingenious. You exploit superdeterminism in an amusing way. You exploit the long recognised loophole of periodic deterministic setting choices which was a weak point of Aspect’s first experiment, and which all of the famous recent successful loophole-free experiments have deliberately avoided. 

Richard

Sent from my iPad

On 5 Aug 2026, at 18:51, Ghenadie Mardari <gmar...@gmail.com> wrote:



[Richard Gill]

PS. It is very problematic that your model allows S = 4 and any lower value. If one is going to follow the path of non-locality and/or superdeterminism, the challenge is to show how the empirical predictions of quantum mechanics emerge from your theory, in particular the 2 sqrt 2 Tsirelson bound. Just as for QM, the challenge is to show how a classical world emerges.

Sent from my iPad

[anton vrba]

"Just as for QM, the challenge is to show how a classical world emerges."

Well said Richard,

At least QM was developed from the classical physical models of the time to produce a probable physical model.  The Bryan, Parker, Ghenadie, Joy Christian et al (BPGJ) theories cannot do that, they all use hypotheses based on ego only, no trace of a physical origin.

A worthwhile discussion for this group is how to resolve the question "Is Nature Deterministic or Probabilistic?", BPGJ do not contribute because of non-physicality.
 

Anton

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

From "Richard Gill" <gill...@gmail.com>

To "Ghenadie Mardari" <gmar...@gmail.com>

Cc Bell_quantum...@googlegroups.com

Date 8/6/2026 1:51:09 PM

Subject Re: [Bell_quantum_foundations] Bell experiment with two independent computers

[Parker Emmerson]

Subject: Re: [Bell_quantum_foundations] Bell experiment with two independent computers

Dear Richard, Ghenadie, Anton,

I had this drafted before Anton's message arrived, so I will take all three in turn.

**Ghenadie.** I have now read the manuscript rather than only the thread, and the diagnosis needs adjusting in one respect before I say where I agree. Your rebuttal on settings is correct and Richard's objection there does not hold. In your scheme each station tosses a fair coin per trial and reads the corresponding value from a template indexed by the stopping point T ∈ {0,…,7}, which is setting-independent. That is A(a,λ) and B(b,λ) with a common λ. Outcomes are generated locally, settings are chosen locally and freely, and so far nothing is amiss.

The nonseparability enters at one specific place: the replacement rule. Whether an event counts as displaced depends on which pair (aᵢ, bⱼ) was selected, so the decision to overwrite a recorded outcome with a fresh random bit is a function of both settings. That is where combine.py does its work, and it is why Richard's verdict lands even though his stated reason does not. Worth stressing that this is not the detection loophole you invoke: Pearle, Larsson and Larsson–Gill concern discarded trials, whereas you retain every trial and substitute outcomes instead. Setting-dependent substitution is a distinct mechanism and deserves to be named as such rather than assimilated to coincidence-window analysis.

My physical objection is not that S ≈ 3 exceeds Tsirelson as such. It is that Table 1 makes the model a one-parameter family: replace one eighth of events and S = 3, one sixteenth and S = 2.5, one thirty-second and S = 2.25. I checked the arithmetic and it is internally consistent. The replacement fraction is a free dial spanning S ∈ [2,4] and nothing in the mechanism selects 2√2. Real experiments sit at or below Tsirelson and, more tellingly, reproduce −cos(a−b) across the whole angular range, not merely at four settings. A model that can produce any S on demand, with no principle fixing the dial and no account of the cosine, is not yet in competition with quantum mechanics for those data. That is a request for the missing constraint, not a dismissal.

Where I think you are right, and where I would want to be counted alongside you, is Section 2. Your point that pairwise separability in equations (2)–(4) does not entail global separability in (5), and that (5) is a condition of simultaneous realism rather than of locality, is exactly the distinction I have been pressing under different vocabulary. You reach it through Fine and Vorob'ev; I reach it through a completed boundary event. It is the same fault line.

**Richard.** That brings me to my own model, and to a correction of how it has been described in this thread, including by me. It is not measurement-dependent. Preparation independence holds, and holds as an intervention condition: P(λ₀ | do(a), do(b)) = P(λ₀). Nothing in the source record encodes the later settings. What fails is a different premise, namely Bell-Cauchy screening — the existence of a complete setting-independent variable on a preparation hypersurface whose conditioned responses factor across the wings. I accept BellScreen ⇒ S ≤ 2 without reservation. What I deny is that boundary locality entails the screen. The replay defect is precisely the theorem that excludes a preparation-side screen: same seed, fixed b, fixed λ₀, and Bob's realised outcome differs under a counterfactual change of Alice's setting with probability 0.354. That is an obstruction to completeness, not a demonstration of influence.

Why that is ordinary rather than exotic:

    S[φ] = ½ ∫₀ᴸ (φ')² dx,   φ(0) = a,  φ(L) = b.

The action is local, Euler–Lagrange gives φ'' = 0, and the on-shell action is S(a,b) = (b−a)²/2L with ∂²S/∂a∂b = −1/L ≠ 0. The on-shell boundary functional is irreducibly nonseparable in the boundary data, and there is no influence, no signal and no directed edge anywhere in the system. Boundary-value problems are generically like this. My model has that structure with a completed source–absorber event in place of the string, so the nonseparability sits in the boundary functional rather than in a spacelike message. The absence of a primitive directed A→B or B→A message is a structural theorem about the all-at-once race architecture — and I should say plainly that it is not, and cannot be, inferred from the no-signalling table alone, since any no-signalling table admits simulation by hidden one-way communication.

On terminology your criticism was fair, so here is the result in standard vocabulary. A one-parameter deformation of the singlet correlation,

    E_κ(Δ) = −tanh(κ · artanh(cos Δ)),   0 < κ ≤ 1,

with κ = 1 the Born singlet; equivalently −cos(q_κ(Δ)) with q_κ(Δ) = 2 arctan(tan^κ(Δ/2)), a metric transform of angular distance. Intrinsically, on the positive cone of balanced binary tables with Hilbert projective coordinate Θ, the deformation is the homothety Θ ↦ κΘ, and m ↦ m^κ is the unique positive entrywise map scaling every binary cross-ratio by κ — so the power law is characterised by projective geometry rather than imported from quantum mechanics. Three consequences, all elementary: some CHSH inequality is violated iff κ > 1/2, while the standard quartet detects only κ ≳ 0.623, which is why quartet choice matters; every unbiased two-setting quartet satisfies Tsirelson–Landau–Masanes, so nothing in it is supraquantum; and it is not a visibility-scaled cosine, since F'''(0)/F'(0) = 2(1−κ²) is visibility-independent, so dense angular data bound κ directly.

On the name, I will keep it. "Phenomenological" is meant in something close to Husserl's sense: a bracketing — here effected by an algebraic arrangement rather than an act of reflection — in which a determined quantity is suspended so that one can see what structure survives the suspension. That is the operation the term was coined for, and a computer algebra system performs it faithfully, returning not a value but the report that the parameter is unconstrained, which is what makes the subsequent question well posed. The physicist's sense applies equally, to a fixed sector κ bounded by angular data. Both readings are live. None of the results above depend on the identification κ = √(1−v²/c²); that supplies the covariant reading and the sidereal test, and nothing else.

What is proved rather than tuned: intervention independence, marginals exactly 1/2, an exactly flat coincidence rate in Δ, one definite outcome pair per trial, nothing discarded — γ ≡ 1, so there is no acceptance step and the CHSH value is not accepted-ensemble drift. Ghenadie, the flat rate is worth your attention: your mechanism and mine both retain every trial, for different reasons, and a coincidence-rate profile distinguishes them, since the selection route's acceptance envelope dips to about 0.879 near 46.4° and 133.6°.

**Anton.** Your criterion has a structure worth naming. It is a kafkatrap: a charge constructed so that denial counts as confirmation. If I reply, the reply is ego; if I stay silent, the charge stands unanswered. Stated without the label, P(reply | ego) = P(reply | not ego) = 1, so the observation has likelihood ratio 1 and carries no information about the hypothesis. A claim that no possible behaviour of mine could bear on is not a claim about my work. It is a description of how you have decided to read it, and I mention this only to explain why I am setting that half aside rather than performing indignation about it.

It is also an odd charge to level at mathematics in particular, since motive-independence is the whole point of formalising anything. A derivation is checkable by someone who cannot stand its author. That is what the notation is for.

The other half of your message is a real claim and I would rather answer that one. "No trace of a physical origin" is falsifiable, so: the deformation above is characterised, not posited — the unique positive entrywise map scaling binary cross-ratios by κ on the positive cone, with a second and independent derivation from proper-time action accumulation under a memoryless capacity law. At κ = 1 it reduces exactly to the Born singlet. At κ < 1 it predicts a definite non-Born angular shape whose cubic invariant is visibility-independent, so a dense angular scan bounds κ or destroys the model outright. It cannot be tuned to fit an arbitrary CHSH value, because κ is fixed by the entire angular curve rather than by four settings.

That is also why the grouping fails on your own criterion. The objection I raised to Ghenadie's construction three paragraphs ago is precisely that its dial is free; mine is not. Whatever else you think of my work, the two are not the same kind of object, and you can verify that without reference to anybody's ego.

Finally, on the question you propose as worthwhile — is Nature deterministic or probabilistic — I have a position rather than an abstention. Each trial actualises exactly one outcome pair, definitely, by a threshold race. Probabilities are ordinary Kolmogorov probabilities within each realised context. What does not exist is a single global table of counterfactual answers for all settings at once. Determinate events, ordinary probability, no universal spreadsheet. Whether that is correct is a matter for angular data, which is the only property of a proposal that finally matters.

All my best,

Parker Emmerson

--
You received this message because you are subscribed to the Google Groups "Bell inequalities and quantum foundations" group.
To unsubscribe from this group and stop receiving emails from it, send an email to Bell_quantum_found...@googlegroups.com.

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/em79f0b8a4-653a-448c-b49b-3c294d051474%40gmail.com.

[Richard Gill]

Parker, you haven’t read Ghenadie’s paper well enough. 

Please try again. Focus on the S = 4 case.

No fair coins are tossed to determine settings. Binary setting choices are generated together with binary outcomes. They are cycled through, deterministically.

Richard

Sent from my iPad

On 6 Aug 2026, at 18:56, Parker Emmerson <powerin...@gmail.com> wrote:



[Ghenadie Mardari]

Dear Friends,

Thank you very much for all your comments and questions.
I find it hard to answer everything at once.
So, let us start with the basics.

My solution is based on the properties of a very big object: the “wheel of fortune”.
The values of each sector on the table are fixed in advance.
There is no reshuffling between measurements.
The starting pattern with S=4 is transparently classical.
So, why do we need words like “nonlocal” or “superdeterministic” to describe it?
The answer, in my humble opinion, is that we have a fundamental conceptual problem.

Please allow me to explain.

Bell’s inequality is known to apply to systems with jointly distributed variables (and only to systems with jointly distributed variables). 

This is a well-established mathematical fact.

Yet, classical patterns of correlation can be divided into two groups:
1. We can have classical systems with jointly distributed variables.
2. We can have classical systems without jointly distributed variables.

Accordingly, “Bell Local Realism” is a concept that includes only half of the patterns of classical behavior. When physical properties are expressed at the same time (as part of a single system), they obey Bell’s inequality. When physical properties are mutually exclusive, they naturally violate it.

In short, there is nothing magical about Bell violations.
Seeing a Bell violation is like hearing thunder. We can always jump to supernatural interpretations, but science has straightforward mechanical explanations for it.

As you all know, Bell’s Theorem was formulated in response to an ontological debate.
Quantum theory describes momentum and position as mutually exclusive properties. The question was: how is that possible?
Einstein suggested that quantum momentum and quantum position might be expressed at the same time, even though humans can only observe them one at a time.
Bohr suggested that classical realism is dead.

On closer inspection, this debate was based on a false dichotomy.
It considered only two alternatives:
Either we have properties that exist at the same time, or there is no physical reality at all.
Though, what about classical properties that are mutually exclusive?
Is it impossible for them to have locally causal explanations?

You see, the question was: do non-commuting variables express simultaneous properties?
In this context, Bell provided the perfect solution. We can find the answer with a correlation experiment.
If we get a Bell violation, then quantum momentum and quantum position are not expressed at the same time. Case closed.
 
Unfortunately, this useful discussion about "exist at the same time" had the inherited baggage of "or else nothing else is real".


To sum up, Bell’s inequality is not a marker for ontological Locality (or Realism, or Statistical Independence for that matter). 

It simply does not have the “mathematical chops” for such conclusions.

This is why it is possible to replicate quantum-like correlations in classical systems. 

Quantum correlations are like classical correlations between gloves and socks, except for properties that are mutually exclusive.

Sincerely,
Ghenadie.

[Parker Emmerson]

Subject: Re: [Bell_quantum_foundations] Bell experiment with two independent computers — correction

Richard, Ghenadie,

You are right and I was wrong. I described the settings as freely tossed and the template as setting-independent, and concluded "so far nothing is amiss." That was a claim about code I had not read. I have now read it and run it. The correction is worth more than the retraction, so here is all of it, including a classification that I think settles what the model is.

First, the template does define a genuine local model. Reconstructing A(a,λ) and B(b,λ) with λ the cycle step gives a complete response table on all four observables, and every one of the eight λ values yields CHSH exactly +2:

    step   A1  A2  B1  B2    CHSH
      0    +1  +1  +1  +1     +2
      1    -1  +1  +1  +1     +2
      2    -1  +1  -1  +1     +2
      3    -1  -1  -1  +1     +2
      4    -1  -1  -1  -1     +2
      5    +1  -1  -1  -1     +2
      6    +1  -1  +1  -1     +2
      7    +1  +1  +1  -1     +2

A local deterministic model sitting exactly on the Bell bound at every hidden-variable value. The entire observed violation must therefore come from the post-processing, and it does. Running the published scripts and isolating the last step:

    no post-processing       E11 +0.508  E21 +0.501  E22 +0.504  E12 -0.503   S = 2.016
    randomize spread sign    E11 +0.757  E21 +0.751  E22 +0.752  E12 -0.754   S = 3.013
    discard spread pairs     E11 +1.000  E21 +1.000  E22 +1.000  E12 -1.000   S = 4.000

Richard, that is why you said to look at S = 4: it is pure post-selection, and the published S = 3 is the same selection softened by overwriting a sign rather than dropping the trial.

Where my error was, precisely. What random.choice selects is not a setting but a slot, and the slot is simultaneously the setting label, the outcome sign and the time stamp — ['A1+','','A2+',…] against ['','B1+','','B2+',…]. Because the slot is the time, the coincidence condition, that the two picks land three apart, is a deterministic function of the two setting choices. The coincidence window is not a timing fact the settings happen to interact with; it is the setting pair under another name.

Now the classification, since three different labels have been used in this thread and the code decides between them.

It is not superdeterminism. The test is whether λ is correlated with the settings. Conditioning on each of the four setting pairs, the distribution over the eight steps is uniform in every context:

    (A1,B1): 0.124 0.125 0.124 0.123 0.126 0.127 0.125 0.126
    (A1,B2): 0.126 0.127 0.125 0.124 0.126 0.123 0.124 0.126
    (A2,B1): 0.125 0.125 0.125 0.126 0.123 0.125 0.126 0.125
    (A2,B2): 0.126 0.124 0.126 0.127 0.125 0.125 0.124 0.122

P(λ | a,b) = P(λ) = 1/8. Measurement independence holds exactly. It is worth separating two things that both get called superdeterminism: a program being deterministic given its seeds, and λ being statistically correlated with the settings. Only the second is the Bell-relevant condition, and it fails here — Alice's chooser never consults the step counter, and both her settings are available at every step.

It is not nonseparable either, which is where I was wrong rather than where anyone else was. The response functions exist, completely and separably; that is the table above.

What it is: non-factorizable setting-dependent post-selection. At fixed λ the acceptance table is

           B1  B2
      A1    1   0
      A2    1   1        determinant = 1

Rank 2, so γ(a,b,λ) cannot be written as γ_A(a,λ)·γ_B(b,λ). It is therefore not interpretable as independent local detector inefficiencies; it is intrinsically a joint filter. That is the coincidence loophole, in its non-factorizable form.

And here is the part I think is worth the group's attention beyond this one model. Under the discard variant the acceptance rate is the same in every context:

    Z(A1,B1) = 0.7507   Z(A1,B2) = 0.7489   Z(A2,B1) = 0.7497   Z(A2,B2) = 0.7496

Flat at 3/4 across all four setting pairs, while S runs to its algebraic maximum of 4. An audit that checks only whether the acceptance rate varies with settings sees nothing at all. The reason is that context-independence of the scalar acceptance rate does not imply context-independence of the accepted subensemble: what matters is P(accept | λ, a, b), not its λ-average. Here the subensembles differ sharply between contexts while their masses agree exactly. The selection-inflation bound S ≤ 2 + 2Δ_Q then forces Δ_Q ≥ 1, the maximum. I think that is a genuinely useful cautionary example for anyone auditing a real coincidence pipeline, and it is in the data whatever one concludes about the rest.

One consequence for the argument to real experiments, Ghenadie. Your mechanism requires the acceptance criterion to be a function of the setting pair, and it gets that by identifying the setting choice with the time slot. In a Bell test the detection time is not chosen by the analyzer setting, so there is no analogue of that identification. Carrying the argument across would require showing that the coincidence condition in the loophole-free data is likewise a function of both settings, and I do not think it is.

My apologies for asserting the structure of your code before reading it, and Richard, thanks for the push — the flat-Z result exists only because you sent me back to look.

Parker

[Ghenadie Mardari]

Dear Friends,

My model has two unusual properties:

1. Alice and Bob make perfectly free measurement choices. In the simulation, they are based on the outcome of random number generators. Though, we can also supply instructions from outside, or toss coins, or just make choices on a whim – it makes no difference.

2. I achieve correlations where hidden variables are indeed correlated with measurement settings.

Usually, these two elements are perceived as mutually exclusive.
So, what is going on?

The answer, as I suggested in my previous message, is that all the known arguments about Local Realism have one thing in common: they are based on considerations about simultaneous properties (captured by jointly distributed variables). They simply fall apart when we consider mutually exclusive properties.

Allow me to explain.

Scenario 1.
We have a set of properties that are expressed at the same time.
They have a common cause. Therefore, the values are fixed at the source.
Ergo, the hidden variable profile is also fixed at the source.
The logical flow is clear: source => hidden variable =>measurement setting choice.
According to this description, a correlation between hidden variables and measurement choices implies a causal effect of hidden variables on measurement choices.
In other words, Bell violations with free choices should be impossible, unless we have some kind of cosmic conspiracy (aka “superdeterminism”).

Scenario 2.
We have a set of properties that are mutually exclusive.
They can only exist one at a time.
So, every time we make a choice, we need to force a physical transformation. (This is the famous quantum preparation).
You see, the logical flow is now in the opposite direction:
Free choice => preparation => transformation => hidden variable.

Now you might say: what about correlations? If hidden variables are changed after the fact, what explains the strong coefficients?

The answer is that we can have “inherited correlations”.
We start with two systems that are perfectly coordinated at the source.
They share the same hidden variable profile "lambda_zero".
Then each system is transformed, in order to make observations.
Different transformations add a new parameter to the input profile Lambda (and sometimes diminish the correlation), but the surviving connection remains strong enough for Bell violations.

Lambda_Alice = Lambda_zero + Lambda_a

Lambda_Bob = Lambda_zero + Lambda_b 

So, Alice and Bob have different hidden variables, but only with regard to the last contribution.

In conclusion, do not feel compelled to attribute “superdeterminism” or "retrocausality" to combine.py. 

Mathematical relationships are abstract and multiple interpretations are possible. 

When I am done explaining, you will see that I have the same exact mechanism as in a real Bell experiment with closed loopholes.

Best wishes,
Ghenadie.

[Justo Pastor Lambare]

The Bell theorem, as Richard pointed out, is a mathematical theorem, and a very elementary one by the way, so trying to disprove it seems very naive indeed.

The only way to violate it is through violating one of its hypotheses and this is what seems to be happening here.

According to Mardari we have:

 1. We can have classical systems with jointly distributed variables.

2. We can have classical systems without jointly distributed variables.

The condition 1. does not hold if estatistical independence is requied, so by imposing 2, the measurement independence condition is violated.  

Regards,

      Justo Pastor Lambaré

--
You received this message because you are subscribed to the Google Groups "Bell inequalities and quantum foundations" group.
To unsubscribe from this group and stop receiving emails from it, send an email to Bell_quantum_found...@googlegroups.com.

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CADqzJUofdVOxXKzVb-mGuGZmcbNZCiEVYn4mFWBnH_bYCJ1H_Q%40mail.gmail.com.

[Richard Gill]

Ghenadie, you are talking nonsense.

In your S = 4 model neither Alice nor Bob make any choices at all.

Your two spinning disks are copies of one another. One is always one step ahead of the other. The system is completely deterministic. It can be thought of as an 8 step deterministic Markov chain where the transitions are 

… 8 -> 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7 -> 8 -> 1 -> …

Each state contains the information on two successive segments of the disk (or if you like, the current segments of disk 1 and disk 2)

One reads off of them: Alice setting, Alice’s outcome, Bob’s setting, Bob’s outcome.

The complete history of the system is determined by the initial state. 

This is a model of an “experiment” in which a completely deterministic system starts from an initial state with two settings and two outcomes and then proceeds deterministically, cyclically, for as long as you like.

So you could start the system by letting Alice and Bob choose a pair of settings and outcomes from the list of 8 pairs available.

Your model is not a model for two independent computers. It is a model for one computer since the Alice and bob programs can be run inside the “combine” computer

Your S = 3 and S = 2 models bring in various modifications and these modifications could be independent random but they could also be achieved by other simple synchronous and cyclical processes.

You said  "1. Alice and Bob make perfectly free measurement choices.”. NOT TRUE

You said: “2. I achieve correlations where hidden variables are indeed correlated with measurement settings”. TRUE, your model is NON LOCAL. The hidden variable could be considered the position in the cycle of 8 

Your models incorporate non-locality and super-determinism. They do not tell us anything which we did not already know.

They are ingenious. And they remind us to choose settings by independent random mechanisms, again and again, and not to use simple periodic systems.

State of the art pseudo random number generators would be OK - they are of course in general periodic but the period is so huge that one does not arrive at a plausible physical model from this.

Metaphysically, we can spend all night discussing whether or not real randomness exists. That’s a debate which will go on for ever.

[Richard Gill]

Ghenardi’s abstract:

We present a simulation with two isolated computers (“Alice” and “Bob”) generating coincident events with independently randomized measurement settings. 

     NOT TRUE. Settings are not independently randomised.

The underlying model is fully deterministic and yields CHSH violations up to S ≈ 3, despite satisfying the operational requirements of loophole-free Bell experiments. 

     NOT TRUE. The model does not satisfy the operational requirements of loophole-free Bell experiments,

The effect arises from a system of mutually exclusive observables combined with a protocol for handling missing detections.

     NOT TRUE. Everything is observed.

Surprisingly, injecting random values can strengthen rather than suppress observed violations, especially in the case of measurement-induced counter-correlations.

     NOT TRUE. Injecting random values decreases the size of observed violations

Furthermore, we argue that pairwise measurements with alternative settings impose a monogamy-like constraint on quantum event structures.

     The paper has nothing to do with quantum theory.

Predicted Bell violations, though natural in such systems, cannot be observed without correcting displaced events.

     The paper has nothing to do with real experiments.

[Alexandre de Castro]

Dear Justo, 

that is not entirely true. It is not difficult to show that the predictions of quantum mechanics for the singlet state can be obtained from a uniform distribution of local hidden variables. 

Bell's theorem is not quite a theorem, but rather an undecidable hypothesis...moreover, Fine's theorem isn't very good either.

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CAKAF9vV%3D6U4e8BRos9R6LENtGPTjWQb8vN3dGDGrD78P6hV4dA%40mail.gmail.com.

[Bryan Sanctuary]

Richard,

Please show that the predictions of quantum mechanics for the singlet state can be obtained from a uniform distribution of local hidden variables. 

I bet you cannot without changing the singlet state to a non-singlet state.  So please put your money where your mouth is.

Bryan

[Ghenadie Mardari]

Dear Richard,

Thank you very much for your comments.
Now I understand the source of confusion.

Let us consider the TV Game “Wheel of Fortune”.
The mechanism is deterministic, but contestants do not get to win all the prizes on the table.

1. They spin the table.
2. The table stops (not purely random, but unpredictable).
3. Only one sector (the one under the arrow) is in play.

Similarly, in my model:

1. The table spins.
2. The table stops at 1 of 8 possible points.
3. Alice tosses a coin.
4. Depending on the outcome, she “wins” the next a1 or a2 sector past the stopping point.

Ergo, the choice is 100% free, and it determines the setting that gets to be used for each measurement.

I repeat: it is not predetermined which value will be recorded in each repetition.

Regarding random replacement. 

I can increase the window of coincidence until all the pairs have two recorded values.

Yet, just like in a real Bell experiment, this destroys the violation.

So, I keep the small windows and replace missing events with random values.

As you can see, random replacement exposes the objective input violation that is suppressed by the protocol. 

The only other way is to discard the incomplete pairs (and then I would get S=4, but this is not allowed in a loophole-free experiment).

To sum up, the loophole free protocol entails no violation, unless we use random replacement (just like in a real Bell experiment). 

So, my statement is true: random event replacement increases the violation from "undetectable" to "strong".

Please note: this is a mechanism that only works with mutually exclusive properties.
You can try to do this with Bertlmann’s socks, but you will see that it is impossible.
(Not without tricks, or magic).

In short, my solution has three necessary conditions:

1. We have an objective propensity for a Bell violation at the input.
2. This propensity is foiled by the measurement protocol.
3. Random replacement neutralizes the effect of the measurement scheme.

All 3 conditions need to be satisfied, in order to enable a Bell experiment with two computers (and zero communication between Alice and Bob, or their measurement devices).

Best wishes,
Ghenadie.

[Richard Gill]

Dear Ghenardi

I don’t know the (US) TV Game Wheel of Fortune.

The description you give in this email is incomplete and it does not correspond to the description in your paper, nor to the computer programs.

This time, in your email,  you have written “they spin the table”. But in the paper there are two tables?

You say Alice tosses a coin, but I thought you want Alice and Bob both toss a coin.

What do you mean by “next” sector past the stopping point? And what happens next?

You talk about a complete cycle. So do you mean that one cycle produces the data of 8 trials?

Richard

[Richard Gill]

Bryan, you are replying to an email by Alexandre de Castro. I can’t do what you ask.

[Bryan Sanctuary]

Richard,

You claim that the predictions of quantum mechanics for the singlet state can be obtained from a uniform distribution of local hidden variables. 

I bet you can't show that without changing the singlet state to a non-singlet state. 

(NOTE: Richard wrote to me privately and said he cannot do it.!!!!!!)

If anyone else can, please let me know.  A singlet is isotropic, but a vector is measured (which is not isotropic).  

Since Richard cannot do it, I guess no one can, so his claim is bogus.

Bryan

On Fri, Aug 7, 2026 at 8:28 AM Alexandre de Castro <alx...@gmail.com> wrote:

[Richard Gill]

Bryan, I have never claimed that the predictions of quantum mechanics for the singlet state can be obtained from a uniform distribution of local hidden variables.

What makes you think that?

[Ghenadie Mardari]

  Dear Richard,

The "Wheel of Fortune" set-up is like a rotary lottery.

The table has many sectors.

You spin the table.

When it stops, you have the chance to win whatever happens to be written (or placed) on the selected sector (under the fixed arrow). 

In my version, this works like a role-playing video-game (RPG).

As you know, a video game is not a movie.

It starts with a preprogrammed scenario (like a movie), but suddenly the game stops and asks the player to make a choice.

So, the free will of the player decides how the game continues.

Similarly, in my "game", the table stops, but Alice (or Bob) do not get the first sector automatically. They choose one of two settings: a1/a2 or b1/b2 respectively. If Alice chooses a2, she "measures" the value on the nearest sector a2 after the stopping point. If Bob chooses b1, then Bob "measures" the value of the nearest sector b1 after the stopping point.

Of course, we need two tables for an Alice-Bob experiment with isolated stations. 

So, we engineer two identical tables. 

Alice and Bob each get one table. 

Though, to maintain correlations, both tables are rigged to stop at the same point. 

Suppose that both tables stop at T0. 

Alice tosses a coin and the outcome is "heads". She records the value A1+ from her table.

Bob tosses a coin and his outcome is "tails". He records the value B2+ from his table. 

This completes the iteration.

The same protocol is repeated 10,000 times, until we accumulate 10,000 coincidences (or any other large number N).

In short, Alice and Bob make independent random measurement choices.

This is their input.

The hidden variables (the game table) determine the corresponding output ("+" or "'-" for the corresponding setting).

The end result is just as you would expect: no Bell violation.

Why? 

Because the requirement of random choice destroys the input profile with Bell violations.

Knowing that input violations are suppressed by the mismatches of the measurement scheme, we can isolate the displaced pairings with coincidence windows.

In other words, coincidence windows identify truncated pairs, resulting in missing events.

We replace these missing events with random values and restore 50% of the input violation.

You see, we have an ideal experiment with perfect detection. Therefore, detector efficiency is not a problem.

Instead, we only get missing events from counter-correlations, induced by the measurement scheme. 

This is why random replacement cannot attenuate input correlations.

Instead, it attenuates the induced counter-correlations.

To sum up, we start with a profile that naturally produces Bell violations.

This propensity for Bell violations is suppressed by the measurement protocol.

We then neutralize the effect of the protocol with passive random replacement.

Combine.py does not know what kind of pairs are incomplete. 

It replaces missing events blindly, just like in a real Bell experiment.

This mechanism was not known when loophole-free Bell experiments were designed.

This is why the interpretation was different.

Best wishes,

Ghenadie.

[Bryan Sanctuary]

Richard,

I thought you did, but if you did not, no worries.  But  or anyone do this:

 that the predictions of quantum mechanics for the singlet state can be obtained from a uniform distribution of local hidden variables.

I want to see how HV are expressed in a singlet state. Can anyone show this, an example?

That is all

Bryan

[Alexandre de Castro]

Hi Bryan,

I was the one who replied to Justo, not Richard. 

Alexandre

[Parker Emmerson]

The concept - I think, Bryan, is similar to deriving the standard model from PV-REC, a work in progress...

[Mark Hadley]

Do you mean a one particle system or two particles. Im fairly sure it can be done for the former but not the latter.

Mark

--
You received this message because you are subscribed to the Google Groups "Bell inequalities and quantum foundations" group.
To unsubscribe from this group and stop receiving emails from it, send an email to Bell_quantum_found...@googlegroups.com.

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CALLw9YxyzEGFjfNzVx6URqX8W5tK6BFqu2O%3DhVr_0fr1HYQRcg%40mail.gmail.com.

[Parker Emmerson]

I understand there is this thing called, "the standard model," but this follows STANDARD mathematics, and it demonstrates something interesting --- it's quantum mechanics related, offers and alternate vantage point on quantum chemistry, and predicts orbitals for superheavy elements. It got rejected from MATCH, but I think it's interesting all the same. 

[Bryan Sanctuary]

Ok thanks Alexandre, So can you show me how HV exist in a singlet?   I see a way I think, but the singlet must remain  isotropic

Bryan

[Alexandre de Castro]

Bryan (cc Justo)
here are the notes (pdf)
Alexandre

[Richard Gill]

Alexandre is referring to proofs in Sakurai’s book.

Wigner proved Bell’s theorem under the assumption that outcomes are equal and opposite when measurements are done in the same direction. Ie the original Bell theorem, not the later Bell-CHSH theorem

On page 227 (following Wigner) Sakurai shows that the predictions of the singlet state when measuring in the x and z directions only (four pairs of possible joint measurements) can be reproduced by a local hidden variable model with four equally likely values of the hidden variable

On the next page (again following Wigner) Sakurai shows that the analogous result cannot be obtained when three different directions are involved. The hidden variable would need to take on eight different values because each single particle would have to carry an instruction for the outcome of each of three different measurements, and the pair of particles would have equal and opposite instructions. One can find a set of three directions such that the singlet state predictions can’t be matched, for any probability distribution of the 8 values of the hidden variable.

I think Alexandre has not understood Sakurai’s argument.

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CAPcOYani1DZ6kW5fU%3Dv%3DsaQNMCJoNW%3Di%3DDpkK68wQHxGdk2Hqg%40mail.gmail.com.
<LHV (1).pdf>

[Alexandre de Castro]

There is no arguing with the facts.

[Richard Gill]

Bryan asked to see a hidden variable middle for the singlet state.

Bohmian mechanics derives the usual EPR-B predictions with a non-local hidden variable. The singlet wave-function is the hidden variable.

See for instance

https://arxiv.org/abs/0806.4577

A New Causal Interpretation of EPR-B Experiment

Michel Gondran, Alexandre Gondran (SET)

In this paper we study a two-step version of EPR-B experiment, the Bohm version of the Einstein-Podolsky-Rosen experiment. Its theoretical resolution in space and time enables us to refute the classic "impossibility" to decompose a pair of entangled atoms into two distinct states, one for each atom. We propose a new causal interpretation of the EPR-B experiment where each atom has a position and a spin while the singlet wave function verifies the two-body Pauli equation. In conclusion we suggest a physical explanation of non-local influences, compatible with Einstein's point of view on relativity.

Sent from my iPad

On 7 Aug 2026, at 14:42, Bryan Sanctuary <bryancs...@gmail.com> wrote:



[Mark Hadley]

In Bohm the wave function may well be hidden, but it's usually the initial position that is called the hidden variable.

The wave function depends on the context. But then the +/- result depends on the initial position..

In many respects a qm measurement reduces to a position measurement in a measuring device.

Mark

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/5CC88C31-87EE-4C0D-9232-B90A0F2A2528%40gmail.com.

[Richard Gill]

Yes Mark, you’re right, and Gondran and Gondran would also agree with you. The word “hidden” and the phrase “hidden variable” can mean different things in different contexts.

The wave function is hidden in the sense that we don’t see it directly.

Bryan might like Gondran and Gondran’s maths. Lots of Dirac spinors. I would like to know if their computations are correct. One might disagree with assumptions and/or interpretations.

Sent from my iPad

On 8 Aug 2026, at 08:48, Mark Hadley <sunshine...@googlemail.com> wrote:



[Richard Gill]

Mark, surely “the singlet state” is by definition a state of a quantum system having two identifiable components. Could be two binary properties of one object. More often, binary properties of two particles.

Sent from my iPad

On 7 Aug 2026, at 19:17, Mark Hadley <sunshine...@googlemail.com> wrote:



[Bart Jongejan]

Dear Ghenadie,

I think that I agree with much of what you are saying about QM, but I don't think that the wheel of fortune is a useful illustration. 

I have my doubts about how you define and use coincidence windows. It seems that your algorithm establishes a temporal order between Alice's and Bob's measurements (T1,T2,T3, ....), and that Ts that are too far apart (i.e. not adjacent) are outside the coincidence window of size 2. But how can a temporal order be established in real Bell type trials? Isn't it the whole point of the setups in Bell's and EPR's  thought experiments that the spatio-temporal separation between Alice's and Bob's measurements is space-like and that it is not physically meaningful to say that one came before the other? How is Carol going to decide which pairs of measurement results to replace with randomly chosen values? Concretely, in your Table 2 page 10 of manuscript_BE2IC_gm.pdf on GitHub, in the first iteration, why is B2+ at T3 too far from A1+ at T0 to be in the same coincidence window? That can only be the case if the B2+ event is strictly in the future light cone of the A1+ event, or do I misunderstand something? Furthermore, if Bob had chosen B1 instead of B2, that event would have obtained the timestamp T1, and thus fall within the coincidence window together with A1+. Why would Bob's choice of setting influence the obtained time stamp?

Bart

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/92A0D2D6-9204-42EA-883A-6E50EE9F01BD%40gmail.com.

[Bryan Sanctuary]

Richard,

Bohmian mechanics is beside the point. It is an alternative formulation of quantum mechanics and is explicitly nonlocal. That is not the kind of local hidden-variable model Bell discusses. I am sure you know this.

I am asking for something much more specific: give me an explicit example of the local hidden variables (\lambda) that Bell assumes are hidden in the singlet state, or complete it objectively, with local outcomes A(a,\lambda),\qquad B(b,\lambda), and a setting-independent distribution (\rho(\lambda)).

Alexandre’s construction he sent me, does not provide an example; it searches for assignments satisfying the Wigner–Bell inequality.

So the question is: what is one explicit physical example of Bell’s local hidden variables for the singlet? So far, no one has given me one.  I suggest HV just do not exist as a ubiquitous catchall for stuff that magically does the trick. HV are supposed to be essential to a system and improve it.  Therefore, if they exist, any good theory will expose them. 

I agree with von Neumann, and disagree with Bell's '66 proof that I can discuss if raised. If  HV are needed, they most certainly emerge  from the theory.  Hidden variables suggest incomplete knowledge of the system. 

Bryan

[Austin Fearnley]

I know from Susskind's lecture years ago that the singlet state is not something that is just tacked on to QM as it arises from group theory as a separate state in its own right.  It fits my quantum retrocausal model very nicely just as it fits Costa de Beauregard's V-shaped retrocausal path in time.  Don't really need to explain how HVs work in this scenario as it is obvious.  However it requires a new view of reality.

I have a lot of respect for QM and QFT and recently have been trying to understand GHZ using QM pathways so as to apply three-way entanglement to my retrocausal approach.  Other retrocausal methods seem to me to use hand-waving philosophy. But maybe I just don't understand philosophy.  I have been using Excel VB to model GHZ in 3-qubit quantumm computer circuits. As there are only 3 qubits one does not need a fully functioning quantum computer to do this.  But I have paused that (as I have an aversion to using VB nit-picking due to my old age) to work on human brain and memory using retrocausality.  Also painting intervenes as does old age (had another birthday this week).

And yes, I agree that hidden variables indicate lack of knowledge of the system.  It is turtles all the way down and one will never escape from lack of knowledge, whatever level one sinks to.  The question of random versus deterministic (mentioned I think by Anton) should be associated with a level of reference.  At QM level or at the level of the universe's hidden processing?  I wrote an unpublished paper on Rasch and CCC which dealt with determinism and I thought that the universe was completely determininstic at the nodes, ie origin and end collapse, but much less deterministic at mid-nodes, ie now.

[Richard Gill]

Of course I know that. And I wrote that. A Bohmian solution is a non-local hidden variable model. But you might be interested in the math those French guys used.

Bell’s theorem says there is no LHV model reproducing the singlet correlations in their entirety. You know that, right? So what are you asking for?

As you know, Bell-CHSV shows there exist two settings for Alice and two for Bob such that the resulting four combinations can’t be simultaneously reproduced by a LHV.

Sent from my iPad

[Richard Gill]

Dear Bart

Do take a look at Ghenadie’s Python programs. I found out that they do not match the descriptions in his paper.

I hope to report some further discoveries in a few days. Right now, I suspect that his computer programmer has deceived him. He got the desired results by some of his own tricks.

Fortunately AI translation from Python to R worked like a dream and I can now more easily experiment with the programs now.

Richard.

PS The programs first simply combine datasets generated by Alice and Bob separately into one. Then a process of adding in noise *increases* correlations in absolute value taking S = 2 to S = 3. The scheme used in the program for getting S = 2 is not described in the paper.

I’d like Ghenadie to give us a program with which one can generate data sets for S = 2, S = 3 and S = 4 by choice of the user, and I’d like the paper and the program to match one another properly.

Sent from my iPad

On 8 Aug 2026, at 13:55, Bart Jongejan <bart.j...@gmail.com> wrote:



[Richard Gill]

Bart,

Ghenadie’s wheel of fortune has 8 fields (segments of a disc). You spin it once and the wheel stops with the pointer pointing at a boundary between two fields. (There are 8 such points). The fields are marked with a letter (A or B), a number (1 or 2), and a sign (+ or -). 2 x 2 x 2 =8. A and B alternate. Left and right half, and top and bottom half determine the distribution of signs and numbers. 

So the pointer selects *two* fields, eg B2+ and A1-, and that would mean Alice uses setting 1 and observes outcome -, Bob uses setting w and observes outcome +.

He writes about an arrangement which would generate S = 4. But his programs create S = 2 and S = 3.

Seems to me all the materials need a lot if revision

The whole thing has nothing whatever to do with Bell experiments.

But it is a fun gadget to play with.

Richard.

Sent from my iPad

On 8 Aug 2026, at 13:55, Bart Jongejan <bart.j...@gmail.com> wrote:



[Mark Hadley]

Richard,

You are correct.

I was thinking of a mixed state. 

[Richard Gill]

Dear Bryan

Bell is doing a proof by contradiction (aka: Reductio ad absurdum)

1. Suppose local hidden variables exist  (number of different values, probability distribution therefore, can be anything) and suppose measurement functions A and B exist

2. Show they will always satisfy CHSH

3. Conclusion: there do not exist any reproducing the singlet state.

You ask for an explicit example: well, Bell’s explicit example (the one generating the triangle wave correlation function) is a fine example to start with.

It doesn’t deliver the goods. But Bell has proven that no example can be found which delivers the goods.

That’s the Bell-CHSH proof of Bell’s theorem.

I hope this answers your question adequately. It’s a good question.

Richard

On 8 Aug 2026, at 14:50, Bryan Sanctuary <bryancs...@gmail.com> wrote:

[Ghenadie Mardari]

  Dear Bart,

There is no communication between Alice and Bob in this illustration. Therefore, the relative flow of time does not matter.

You can imagine that the clocks are locally reset every time the tables stop. So, all the T-values are fixed in reference to the stopping time. 

Another way to think of this is that we have a correlation between two copies of the same video game, each in its own computer.

You see, the goal here is to demonstrate a Bell violation without communication.

The ontology of quantum correlations is a different topic that I addressed in this recent paper. As you will see in that text, there are many classical analogues for quantum spin. In particular, I derived cosine correlations (and Tsirelson's bound) for macroscopic measurements in classical fluid splitters. 

Best wishes,

Ghenadie.

[Parker Emmerson]

Dear Richard,

lolz.... "Bell is doing a proof by contradiction (aka: Reductio ad absurdum)" - care to retract the claim of its being a no-go?

Formalizing the Error

Definitions

Let:
• P = conjunction of the assumptions of the theorem
• Q = the “go” scenario (the statement being ruled out)
• ⊥ = logical contradiction (absurdity)

Reductio ad Absurdum (RAA)
A proof technique that, to prove ¬Q, assumes P ∧ Q and derives ⊥:

RAA(P,Q) ≡ (P ∧ Q ⊢ ⊥) ⇒ (P ⊢ ¬Q)

No-Go Theorem
A theorem whose conclusion is of the form ¬Q (that something is impossible), given P:

NoGo(P,Q) ≡ P ⊢ ¬Q

The Claim

Natural language:
“A no-go theorem can be proved by reductio ad absurdum.”

Formalized:
RAA(P,Q) proves NoGo(P,Q)

Unfolding the Circularity

Substituting the definitions:

The rule (P ∧ Q ⊢ ⊥) / (P ⊢ ¬Q) proves (P ⊢ ¬Q)

In inference-rule form:

P ∧ Q ⊢ ⊥
──────────── (RAA)
P ⊢ ¬Q

The conclusion of the rule is exactly the no-go theorem. So the statement reduces to:

RAA produces NoGo

which is:

f : (P ∧ Q ⊢ ⊥) → (P ⊢ ¬Q) yields an element of (P ⊢ ¬Q)

Type-Theoretic Framing of the Error

Treating propositions as types:

• NoGo : Prop, where NoGo ≡ P → ¬Q
• RAA : (P ∧ Q → ⊥) → (P → ¬Q)

The question “can RAA prove no-go theorems?” asks:

RAA ∈ Proofs(NoGo) ?

But RAA is the canonical proof constructor for NoGo:

RAA : Proofs(P ∧ Q → ⊥) → Proofs(NoGo)

The Nature of the Error

The statement is either:

1. A trivial identity — RAA is the inference rule that yields the no-go form.
   The claim is logically true but informationally vacuous:

   RAA(P,Q) ⊢ NoGo(P,Q) is a tautology

2. A use–mention confusion — presenting a rule–conclusion relationship
   as if it were a contingent methodological discovery.

In formal terms:

The error ≡ treating

( Γ, P ∧ Q ⊢ ⊥ )
( ────────────── ) ⊢ ( Γ, P ⊢ ¬Q )
( Γ, P ⊢ ¬Q )

as informative, when in fact the meta-statement is a logical identity.

Conclusion: The phrase is not strictly false, but it is logically degenerate —
a tautology disguised as an explanation.

[Ghenadie Mardari]

Dear Friends, 

I fully agree with Richard's explanation, but there is one caveat.

It is not enough for a theorem to be correct. 

It has to be applied in the correct context.

For example, it is true that "2+2=4", but it is wrong to say "therefore the sky is green".

Accordingly, I am not questioning Bell's theorem.

I am simply clarifying its domain of physical relevance.

What is the context for Bell's argument?

The two papers with the same title by EPR and Bohr. ("Can quantum mechanics...")

EPR suggested that quantum momentum and quantum position are like Bertlmann's socks.

Bohr suggested that classical realism is dead at the quantum level.

You see, this is a debate between two alternatives:
1. All the properties of a system can manifest at the same time.

2. Nothing is real.

In conclusion: Of course, we cannot reproduce quantum behavior with Bertlmann's socks.

We would need non-locality, or superdeterminism, if quantum theory produced violations with Bertlmann's socks. 

But this is not the case. Bell violations are only predicted for mutually exclusive properties. 

Accordingly, "Bell locality" does not mean "causal locality in the ontological sense". 

It means "Bertlmann's socks" (i.e., "all the properties exist at the same time, as part of a single system").

In other words, this is about imaginary universes in which all the variables are jointly distributed, and mutually exclusive properties do not exist. 

Yet, classical mechanics is full of mutually exclusive properties in our Universe. 

Some of them obey Tsirelson's bound. Some do not.

This is why Bell violations with isolated computers are possible.

 

Best wishes,

Ghenadie.

[Bart Jongejan]

Dear all, esp. Richard and Ghenadie

Does Ghenadie agree with Richard's interpretation of the pointer's role? Richard says that the pointer, when the wheel has come to rest, selects two fields, e.g. B2+ and A1-. That interpretation seems to contradict the first line in Table 2, which shows a possible output combination of A1+ and B2+. Those outputs are not in adjacent sectors of the wheel and can therefore not be pointed at with a single spin of the wheel. Can anybody explain?

Ghenadie does not answer my question: why can the choice of a setting by one participant potentially invalidate the whole trial? I don't understand the whole idea with the T labels and coincidence windows, I think.

I am not yet convinced that missing or out-of-coincidence-window observations have anything fundamentally to do with the EPR-Bell problem. They are just a nuisance that experimenters want to minimize. Richard has done a great job with a statistical method that makes the best out of lossy, noisy data, leading to excellent, convincing publications showing that the CHSH violation is real.

Bart

[Richard Gill]

Bart

You are right

The 8 possible positions generate 8 different sequences of four sectors

Now take the first row. The are 4 different combinations of an A field and a B field

4 times 8 = 32

Ghenardi’s basic model, creating S = 2, is essentially a uniform distribution over the 32 pairs

So those are all pairs of an A and a B with four consecutive fields of the disk

Ghenadie is quite incapable of explaining what he is doing, and moreover the text, the pictures, and the code, do not match.

Richard

[Parker Emmerson]

Dear All, - Richard, Ghenadie,

No dispute with the derivation. Your answer to Bryan is the right one — Bell's own model, 1964 §3, triangle wave, doesn't deliver, and the theorem is why nothing else will either.

The framing does no work though. RAA is the canonical constructor for P ⊢ ¬Q. "Proved by reductio" names the rule and nothing else. All the content is in P ∧ Q ⊢ ⊥ — pointwise algebra plus the singlet computation. I accept both.

Your step 3 is the interesting line: "there do not exist any reproducing the singlet state." That's a statement about the hypothesis class. It's also exactly what the proof gives you. Getting from there to a no-go about locality takes another step, and it isn't in your three lines. It isn't free either — no-signalling won't carry it, PR boxes reach 4; microcausality won't, field theory reaches 2√2. What's left is local causality and its screening premise. You've said the screen is what local causality has always meant and you're done arguing it. Fine. I'm pointing out that your own statement of the conclusion stops short of it.

That gap is my entire disagreement. It's why I've never contested the arithmetic.

My model isn't in your class. Not by evasion — by audit. Intervention independence holds, P(λ₀ | do(a), do(b)) = P(λ₀): not superdeterminism. γ ≡ 1, nothing discarded: not selection. Same audit I ran on Ghenadie's construction last week, and it came out the other way there. What fails is the preparation-side screen, and it fails by theorem: fixed λ₀, fixed b, flip a, Bob's outcome changes. Obstruction to completeness, not influence. Different exit from Bohm — he keeps complete Cauchy data and pays with a preferred foliation.

On fine-tuning, since that's the successor objection: in the balanced sector it doesn't bite. Take any table with m₊₊ = m₋₋, m₊₋ = m₋₊. Apply any f entrywise. Both row sums are f(u) + f(w). Marginals 1/2. No property of f is used — I checked exp, 1/(1+m), m⁷ + √m. Nothing moves. And the pairing symmetry is forced: rotational invariance plus perfect anticorrelation, Werner form by Schur, p = 1. So the independence holds across an infinite-dimensional family of deformations, not at a point.

Outside that sector there's no protection and the marginals get restored by hand. Saying it before someone else does.

Parker

[Richard Gill]

PS the reason that Ghenadie’s model produces any correlations at all, despite the fact that there is a separate Alice computer and a Bob computer, is because the two computers both have a clock which starts at the same *fixed* time and which both follow a cycle of length 8. You could say that the basic model is a LHV model with a source hidden variable taking 8 different values, it is simply “iteration number” modulo 8

Apart from that there are some independent random things going on at each iteration in each computer separately (each computer has some further local randomness

At that point, if he would compute the correlations and compute S, he would find S = 2.

In order to increase S from 2 to 3 Ghenadie has to not only bring the Alice and Bob data sets together but also randomly modify the combined data.  So that is a non local random modification to the data, ie depending on a non local hidden variable.

He only delivers the correlations after he has randomly massaged the combined data, and gets S = 3.

I haven’t figured out how to do S = 4 yet, with the computer programs as they are. But I think that with a window of length 2 instead of length 4 we would find S = 4. So there would still be a cycle of length 8 but with a window of length 2.

[Alexandre de Castro]

Bryan,

Perhaps your evaluation was a bit premature. This situation involving the singlet with the Wigner-Bell inequality at the same time it violates the CHSH inequality is not a very good thing to happen. 

That causes some problems...

[Parker Emmerson]

Thanks, Richard. We all know gatekeeping in physics has real costs.

[Richard Gill]

I now figured out Ghenardie’s spinning disk entirely.

His disk has 8 segments. There are eight ways to choose two neighbouring segments.

First game: Use these to generate the data of 8 trials. You will notice that each setting pair 11, 12, 21, 22 occurs twice. The two outcomes for pairs 11, 21 and 22 are always the same (+ + or - -), so their product is always +1. The two outcomes for the pair 12 is once + -, once - +, so the product is both times -1. Three correlations +1, one -1, means one particular one-sided S = 4

Second game: Similarly there are eight ways to choose two segments with a gap of two segments between them. For instance, we use a window of length 4, and look at the two segments at each end of the window. With a gap of two between. This gives us data of 8 trials in which it turns out that we now we have three correlations -1 and one +1. It’s the 12 correlation which is the exception so this means that the *same* S as before now takes the value -4.

Now we can start to play more games with this. 

Third game: Suppose we take one window of length 4 and use it to create data of 4 trials. After all, there are three AB segment pairs which are adjacent and one AB segment pair with a gap of two segments in between. Use all 8 windows giving us 32 trials. 3 groups of 8 belong to my first example giving S = +4, one group of 8 is the same as the second example (gap of two segments) for which the *same* S is -4.  3/4 x 4 + 1/4 x (-4), gives us S = 2

Fourth game: By completely randomly repeatedly switching between a window of size 4 and a window of size 2 ( mixing games 1 and 3) we get S = 3

It is all very simple and has nothing whatsoever to do with Bell’s theorem.

It has nothing whatsoever to do with loophole free Bell tests since loophole free tests are so-called because there are spatio temporal restrictions on inputs and outputs (and correlations are computed according to the usual recipes, and without any intermediate data processing).

He has not won my computer challenge, since he does not satisfy the basic requirements of my challenge. He has not won Sasha Vongehr's quantum Randi challenge, which is based on Bell’s original inequality.

https://arxiv.org/abs/1308.6752, https://arxiv.org/abs/1207.5294

I don’t think his ideas have anything to do with quantum monogamy, either.

Well, it was intriguing and it was fun, and I give Ghenadie top marks for ingenuity.

Ghenadie: do you agree? Shall we write a short paper about this together? Does anyone else want to collaborate?

[Parker Emmerson]

Richard, Ghenadie, Group of Theorists,

Your decomposition is right — I checked all four games against the code.

Adjacent pairs: each setting pair twice, E11 = E21 = E22 = +1, E12 = −1, S = +4. Ends of a 4-window: signs flip, 12 the exception, S = −4. All four pairings inside each window over 32 trials: exactly 2, and 3/4·(+4) + 1/4·(−4) is why. I had 2.016 from running the scripts. You have the reason.

One detail if this becomes a paper: your game 4 mixes window sizes 50/50, half at 4 and half at 2. combine.py does something else — it neutralises the spread quarter by overwriting a sign with a fair coin, 3/4·(+4) + 1/4·(0). Same 3, different mechanism, and only the second is what's published.

Yes to collaborating. Attached is a paper I've been writing on a different subject — fine-tuning and faithfulness — where §5 turned out to be about Ghenadie's construction. I'd rather show you the whole thing than describe it.

What's in there that came out of the analysis:

An exact eight-state reduction of the post-processing structure. Four base assignments, pointwise CHSH = +2 at each, one context rejected per hidden state, a global sign flip for unbiased marginals. It gives S_full = 2, S_obs = 4, and Z = 3/4 exactly in every one of the four contexts. The finite runs — 0.7507, 0.7489, 0.7497, 0.7496 — are just sampling noise around it.

The accepted laws then have Δ_Q = 1 and D_Q = 1/3, and both are extremal: 4(1−Z) = 1 and (1−Z)/Z = 1/3. It also hits the inflation lower bound (S−2)/2 = 1. Three bounds saturated at once.

Two things fell out that I wouldn't have found otherwise. A pairwise bound for contexts at equal rates, TV ≤ (1−Z)/Z for Z > 1/2 — written to check whether the 1/3 was extremal or accidental, and it's extremal. And a general flat-rate ceiling: Δ_Q ≤ Σ(1−Z_q) gives S ≤ 2 + 2Σ(1−Z_q), so at 2√2 a flat calibrated rate above (5−√2)/4 ≈ 0.8964 excludes every Bell-local MI selection model covered by the bound — not just the two-bin sign–cosine class, which stops at Z* ≈ 0.8786.

That last one is the piece with reach past this model, and it exists because of Ghenadie's.

So the offer: §5 and the equal-rate lemma belong in your paper more than mine. Take them. I'll cut them from mine — the rest is a symmetry theorem and a methodological proposal, a different subject entirely, and it reads better without someone else's construction as its foil.

Ghenadie — I want to be clear about how I read your model. It isn't wrong; it's a clean instance of something the literature knows about, made sharper than the standard examples. The flat-rate result is genuinely useful to experimentalists and it only exists because your construction is extremal. That's a better outcome than being right about Bell.

Attached. §5 is an exact eight-state reduction of Ghenadie's post-processing structure: four base assignments each at pointwise CHSH = +2, one context rejected per hidden state, a global sign flip for unbiased marginals. It gives S_full = 2, S_obs = 4, and Z = 3/4 exactly in all four contexts, with Δ_Q = 1 and D_Q = 1/3 — saturating 4(1−Z), (1−Z)/Z, and the inflation lower bound (S−2)/2 simultaneously. Two general results came out of getting there: a pairwise bound TV ≤ (1−Z)/Z for equal-rate contexts above Z = 1/2, written to test whether the 1/3 was extremal; and Δ_Q ≤ Σ(1−Z_q), hence S ≤ 2 + 2Σ(1−Z_q), so at 2√2 a flat calibrated rate above (5−√2)/4 ≈ 0.8964 excludes every Bell-local MI selection model the bound covers — not just the two-bin sign–cosine class, which stops at Z* ≈ 0.8786. That last one has reach past this model. §5, Lemma 3.5 and Corollary 3.4 are yours if you want them for the joint paper; Richard's combinatorial decomposition is cited and acknowledged either way.

Parker

[Richard Gill]

Very impressive, Parker! Fast work.

What is the difference between the two manuscripts?

Sent from my iPad

On 10 Aug 2026, at 13:12, Parker Emmerson <powerin...@gmail.com> wrote:



<Conservation_or_Conspiracy___Reduced_.pdf>

<Conservation_or_Conspiracy_.pdf>

[Parker Emmerson]

I had actually been working on it for more than a week - since this conversation started.

[Ghenadie Mardari]

  Dear Friends,

Thank you very much for your comments and questions.

I want to point out a very important nuance.

Bell’s argument does not say:
“Some statistical patterns are locally impossible, unless you are clever”.

It says:
“Some statistical patterns are locally impossible, period”.

Nonetheless, I achieved a Bell violation with two independent computers.

How is that possible?

Let us take a closer look.

My “wheel of fortune” is a deterministic classical system.

It produces maximal Bell violations:

a) with complete measurements, 

b) without missing events, and 

c) without reshuffling anything in-between measurements.

From a physical point of view,  this is a local system, without loopholes.

Nonetheless, it is described by Richard as “non-local”, in terms of the mathematical definition. 

In short, mathematical "nonlocality" is not the same as physical nonlocality.

But wait...

There is more!

Understanding these patterns is helpful, but not enough.

There is another aspect here that needs to be discussed, or else everything is confusing.

I discovered that mutually exclusive properties have very strange statistical patterns.

Even though they are classical, they look downright magical.

We cannot make sense of them with physics alone.

We also need an adequate theory of joint measurement.


What happens when two properties are mutually exclusive?
They cannot coincide! They can only take place one at a time.
That is why they are called “mutually exclusive”.

Yet, what happens when we make a joint measurement?
We force the manifestation of a joint distribution.

This means that joint measurements distort reality when we measure disjoint observables.

For example, quantum momentum and quantum position cannot be observed simultaneously. 

This is a fundamental property of Nature. 

Yet, we can engineer two entangled quanta and force a joint measurement across contexts, by measuring both quanta at the same time. 

As a result, we observe a joint distribution (after many pairwise detections) that cannot be attributed to any real physical system.

In a typical CHSH experiment, we always measure two properties at a time, and we only get pairwise joints. 

Yet the four properties, treated as a system, are not forced into a global joint. 

This is why CHSH violations are possible. 

Though, what happens if we measure four properties at the same time? 

In this case, the same rule applies: joint measurements produce joint distributions. 

Suddenly, we get a global joint distribution for all four observables, and Bell violations are no longer possible.

For example, we can prepare a quantum system with maximal entanglement. 

What happens if we use this system to measure four properties at the same time? 

The answer is that Bell violations are impossible. 

This is, by now, a very well-known feature of quantum mechanics, and is commonly described as “quantum monogamy”.

In short, there are two ways to enforce Bell’s inequality:
1. Using a system that is objectively unable of violations.
2. Using a measurement scheme that blocks objective violations.

The big surprise is that Bell experiments with fast-switching settings belong to this second category. 

Therefore, quantum theory also cannot predict Bell violations in ideal experiments of this kind (unless the counter-correlation is identified and neutralized).

 
As a result, we have a big mystery: how do we get violations in loophole-free quantum Bell experiments? 

This is the problem that I solved (and then clarified with my simulation).
Violations are enabled by random replacement.

Though, let me stop here to give you time to breathe.

Best wishes,
Ghenadie.

[Richard Gill]

No Ghenadie, you didn’t solve anything.

You did not achieve a Bell violation with two independent computers while respecting the spatio-temporal restrictions of a loophole-free Bell experiment. 

You did not win my challenge.

You did not win Sasha Vongehr’s challenge.

I have the impression that you can’t read and can’t think.

It’s a pity.

Richard

 

Sent from my iPhone

On 10 Aug 2026, at 13:45, Ghenadie Mardari <gmar...@gmail.com> wrote:



[Richard Gill]

Ghenadie,

Bell’s argument says, “under classical local causality, some patterns are impossible.

That’s a true mathematical theorem. It obviously depends on the mathematical definitions of the concepts involved.

If you achieved a Bell violation, you clearly did not satisfy Bell’s conditions. You moved the goalposts. 

If you are able to think, you should be able to figure out yourself how you created an apparent counter example to Bell’s theorem. Clearly, you don’t understand the theorem. And can’t think.

Sent from my iPad

On 10 Aug 2026, at 13:45, Ghenadie Mardari <gmar...@gmail.com> wrote:

[Bart Jongejan]

Ghenadie, you say "I achieved a Bell violation with two independent computers.

How is that possible?"

As I see it it is possible because you cherry pick results in the third computer, Carol's. You get CHSH violation if you count adjacent and non-adjacent observations in different ways. Which brings us to the T labels, which you don't explain very well.

Alice and Bob do see the identical copies of the wheel of fortune, and they both see where the pointer points, right?

Then, if Alice chooses a setting/outcome that is flanked by two Bob setting/outcomes, she can be sure that her outcome counts. The same goes for Bob. On the other hand, if Alice chooses the setting/outcome that is flanked by only one of Bob's within the 4-window, she cannot be sure that her outcome will be accepted by Carol. Perhaps Carol will rewrite history and change Alice's outcome. Same for Bob's outcome. In other words, Alice's outcome that appears in Carol's log book (factual or amended) is statistically dependent on Bob's setting, isn't it? Even if the wheel is hidden from Alice and Bob and they only can choose between two unlabeled buttons, Alice's outcome would still statistically depend on Bob's setting, and vice versa. 

Tell me where I make a mistake.

Bart 

--

You received this message because you are subscribed to the Google Groups "Bell inequalities and quantum foundations" group.
To unsubscribe from this group and stop receiving emails from it, send an email to Bell_quantum_found...@googlegroups.com.

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/776F38D8-0A83-475D-ADF3-4244E8520712%40gmail.com.

[Ghenadie Mardari]

Dear Bart,

The mistake is to ignore the difference between math and physics.

After all, everything that you can say about my simulation, you can also say about real Bell experiments.

Loophole-free tests also achieve Bell violations with random replacement.

You see, correlations by themselves cannot be local or non-local.
They are “abstract animals”.

 
Instead, we need to see: what kind of system expresses them?
Do they need to be arranged by hand, non-locally?
Do they emerge naturally?

Let us consider the S=4 pattern.
Am I the first to use it? Of course not.
Many people used it before me, but their solutions were non-local.
Why? Because they tried to achieve it with Bertlmann’s socks.

So, let us try to understand Bell’s inequality from a physical perspective.
What is the grain of truth behind all the math?

My favorite approach is to use a simple visual example.

Imagine a warehouse full of shirts.
We are interested in the relationship between the answers to three questions:
1. Are the shirts white? (Yes/No)
2. Are they made from cotton? (Yes/No)
3. Are the sleeves long? (Yes/No).

Suppose that we make two pairwise measurements and get the following results:
A. All the white shirts are made from cotton.
B. All the cotton shirts are long sleeved.

As you can see, the third relationship is now automatically fixed.
The only possible combination is that “All the white shirts have long sleeves”.

This is what happens when all the variables are jointly distributed.

A shirt must have color, fabric and style - all at the same time.
For this reason, some combinations of coefficients are logically impossible.

Therefore, we can check if we have compatible variables with a Bell test.

In a protocol with three observables, AB and BC automatically fix the value of AC.
In a protocol with four observables, AB, BC and CD automatically fix the value of AD.
Therefore, it is not possible to get S=4 with joint distributions.
We cannot have a mixture of three correlations and one anti-correlation.

As a result, any attempt to achieve this pattern will require magic or loopholes. 

Practically, the combinations for a Bell violation need to be arranged by hand, against local causality.

In contrast, this problem does not exist for mutually exclusive properties.

So, local solutions are also possible, without contradicting Bell's Theorem.

There is just one "catch". 
We need to acknowledge that such properties exist before we can use them.
So, in a manner of speaking, this is the Copernican revolution of our time.
We need to advance from “everything is socks” to “some things are not socks”.

Please take a minute to appreciate this aspect.

Best wishes,
Ghenadie.

[Parker Emmerson]

Dear Ghenadie,

I hope all is well with you. "The mistake is to ignore the difference between math and physics," - how do we know they are different? Perhaps we are just asking the wrong questions. For instance, the intersection of ordinal and cardinal numbers could be seen as yielding the periodic table itself, and we are simply within the actual manifestation of numerical values tangibly. There's math for that --- and it works. Alternatively, you could consider a priori to real or complex number --- the energy it requires and the symbolic representation of the configurations of that energy. What is the most efficient way to calculate a differential operator and how do you get information out of it? Is the symbolic representation of that act more or less efficient than the material embodiment of it?

Anyway, my thoughts.

All my best,

Parker Emmerson

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CADqzJUo6KuB8H1t6AtfafjFyyZPgW-_RC-atCu8n6axENAa__w%40mail.gmail.com.

[Richard Gill]

I would say: maths is the language of physics. It is both the handmaiden of the sciences and the queen of the sciences. Seeing them as different is not helpful.

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CANitqNkC8LEAEFrpLpJYpo7OKp%3DoaP85ZPw6S%2BiGmF2MDoszVA%40mail.gmail.com.

[Bart Jongejan]

Dear Ghenadie

In Bell experiments one attempts to make the random changes as small as possible to maximise the violation of the CHSH inequality. Ideally, there were no random changes at all. In your model it is the opposite: random changes are essential to violate the CHSH inequality. Without them there is no violation.

There is another side to the randomness that makes your model inconsequential in Bell matters. In Bell experiments, Alice can in no way influence the degree of violation if the experiment goes on for trillions of trials. She can of course obstruct the experiment by always choosing the same setting, but then it is impossible to compute S and the test remains undecided. In your model, on the other hand, if Alice always chooses the setting that is flanked by two Bob settings, the experiment will still make it possible to compute S, because the wheel stops at random angles. If Alice (and/or Bob) chooses that strategy, |S| will be 2. Only if she follows another tactic, |S| may be > 2, because then Bob's choices decide whether Carol has to have an extra look at Alice's outcomes. So if your model generates |S| > 2, it is because the outcomes of Alice and Bob are statistically dependent on the settings of Bob resp. Alice. Whether this is math or physics seems irrelevant to me.

If I understand you correctly, you don't believe in the simultaneous existence of values of incommensurable quantities. If that is so, then your model should not tell the opposite. The values of purportedly incommensurable quantities are right there, on the wheel of fortune, even if you make the wheels invisible. If, on the contrary, you do believe in their simultaneous existence, then you apparently accept the above mentioned statistical dependence as a fact. I find that unattractive. (Advertisement) In my model, I opt for the first alternative: no simultaneous existence of values of incommensurable quantities. So, not all assumptions underlying the accepted definition of what it takes to be a LHV theory are fulfilled in my model. I can live with that. My model nicely predicts violation up to the Tsirelson bound, provided that space has three dimensions. If space had more dimensions, |S| would be closer to 4. If fewer, it would be 2, no violation.

You still haven't explained the T labels. Aren't they a mathematical trick without a physical counterpart? 

Regards,

Bart

[Richard Gill]

Dear all

Ghenadie claims to have a LHV leading to S = 3

We know that this is impossible

So there is a “bug” in his model

It is his responsibility to find it.

His model is a hidden variables model with two independent hidden variables, both uniformly distributed, 

One hidden variable (HV1) takes 8 different values, the other (HV2) takes two different values

The flow of events is as follows

Alice picks a setting

Bob picks a setting

Hidden variable 1 determines a random  *window* of 4 consecutive sectors of Ghenadie’s disk

Within the window there are two sectors marked A and two sectors marked B

That gives us four A, B pairings.

Three of them correspond to adjacent sectors, but one A, B pairing has two sectors in between the A and B sectors.

Hidden variable 2 replaces the sign in the second sector of that third pairing with a new, random sign.

Clearly

Alice’s outcome is a function of Alice’s setting, Bob’s setting, HV1 and HV2.

Bob’s outcome is a function of Alice's setting, Bob’s setting, HV1 and HV2.

Because the resulting model has S = 3, Bell’s theorem tells us that those two functions cannot be rewritten as

Alice’s outcome is some other function of Alice’s setting alone, HV1 and HV2.

Bob’s outcome is some other function of Bob’s setting alone, HV1 and HV2.

This can be proven by finding a counter example, that is a pair of values of HV1 and of HV2 such that, in obvious notation,

the four pairs of outcomes

x11, y11

x12, y12

x21, y21

x22, y22

exhibit one of the four following “actions at a distance”

y11 != y21

y12 != y22

x11 != x12

x21 != x22

For instance, y11 != y21 means that Bob’s outcome has changed in response to Alice’s setting being switch while his own setting was not changed.

A short computer program can easily search through the eight possibilities.

it is really Ghenadie’s task to do this:

He claims to have a LHV leading to S = 3.

We know that this is impossible.

So there is a “bug” in his model.

It is his responsibility to find it.

Yours

Richard

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CAKEBkX50EAZN%2Bv_k1rX8w0KPZ024kc4tjuLW3o%2BsGT7NcrryOg%40mail.gmail.com.

[Mark Hadley]

As presented, it is a non local hidden variable theory.

It's up to the author to understand this and explain why it might be interesting.

Mark

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/E86FEE5B-36A6-4DAF-9237-E12844005101%40gmail.com.

[Richard Gill]

Exactly Mark. That’s almost exactly what I am saying. I am kindly explaining to him exactly how he can do that. 

I did say in my email that there were 8 possibilities to investigate. But I should have said 28 = N(N -1)/2 with N = 7

We need a *pair* of values of hidden variable 1, and a pair of values of hidden variable 2

There are 28 choices for the first pair, 1 choice for the second pair.

He just needs to check by running through the 28 possible pairs. and finding out exactly where his model implements action at a distance.

It’s a fact that at least one such example must exist. I’m guessing that there must be an awful lot - we have to get from S = 2 to S = 3.

Does anybody have an inspired guess?

[Richard Gill]

I found a proof of non-locality

A(Alice setting 1, Bob setting 1, HV1 = "Table 2 iteration 2", HV2 = “+") = “+"

A(Alice settling 1, Bob setting 2, HV1 = "Table 2 iteration 3", HV2 = “+”) = “–"

Sorry Ghenardi, this destroys your argument and destroys your paper.

https://www.preprints.org/manuscript/202607.1722

Bell Experiment with Two Independent Computers

Ghenadie N. Mardari

We present a simulation with two isolated computers (“Alice” and “Bob”) generating coincident events with independently randomized measurement settings. The underlying model is fully deterministic and yields CHSH violations up to S ≈ 3, despite satisfying the operational requirements of loophole-free Bell experiments. The effect arises from a system of mutually exclusive observables combined with a protocol for handling missing detections. Surprisingly, injecting random values can strengthen rather than suppress observed violations, especially in the case of measurement-induced counter-correlations. Furthermore, we argue that pairwise measurements with alternative settings impose a monogamy-like constraint on quantum event structures. Predicted Bell violations, though natural in such systems, cannot be observed without correcting displaced events.

[Ghenadie Mardari]

Dear Friends,

The main discovery behind my simulation is that we have two different phenomena:
1. Bell experiments with fixed settings.
2. Bell experiments with random settings.

These two types of experiments enable two different types of outcomes.
1. Bell violations are possible for fixed settings (for example, with entangled quanta).
2. Bell violations are impossible for random settings.

Please allow me to explain.

Imagine that you have four printers in front of you, and they are programmed to print one character per minute, all at the same time.

If we combine the four streams of “data”, we get a full spreadsheet.
This configuration can only produce joint distributions of output values.
Therefore, Bell violations are absolutely impossible.

Indeed, when we measure 4 entangled quanta at the same time, we have four detectors that automatically generate joint distributions.
Accordingly, quantum theory does not predict violations in this case.
This is known as quantum monogamy.

You see, we have the following steps:
1. We start with a system that can produce Bell violations.
2. We impose a measurement structure that prevents Bell violations.

So, quantum or no quantum – Bell violations cannot be observed.

But wait a minute!
We started with a system that can produce violations.
How did we lose this propensity?

Well, some events got pushed out of their natural pairing (automatically).
If they are no longer in the input coincidence window, then we can identify exactly which pairs were perturbed.
So, we use a coincidence window.

Here is the amazing part.
We only know that some pairs are incomplete.
We know nothing else about them.
We cannot inspect their values to adjust the replacement by hand.
We just fill the missing events with random values.

You might say: 

“No way! Random replacement can only attenuate the input correlations!”

Yet missing events are produced by the measurement scheme in this case.
They “correlate” with the counter-correlation induced by the experiment.
So, random replacement acts blindly, without divine knowledge.
Nonetheless, it ends up neutralizing the counter-correlations, not the input correlations.

In conclusion, loophole-free experiments were designed without knowledge about quantum monogamy.

 At the time, it was known that:
1. Bell violations are prevented by the measurement scheme.
2. Random replacement can reveal suppressed violations.

Yet, we know that now. Therefore, we can reinterpret the results.
Quantum theory is correct, but the mechanism of correlation is local.

Best wishes,
Ghenadie.

PS: Enjoy the Eclipse today! 

[Richard Gill]

Sorry Ghenadie

Your clever little model proves nothing.

You modified a LHV model with S = 2 by converting the local HV into a nonlocal HV. It then achieved S = 3.

It allows action at a distance. 

I showed you how to change Bob’s setting without changing Alice’s, and make Alice’s output change!

It is amusing, not amazing.

It is all quite cute.

The LHV model with S = 2 was actually a 75%:25% mixture of a nonlocal model with S = 4 and a nonlocal model with S = 2.

It is all great fun, and it has pedagogical value.

Richard

[Richard Gill]

Dear Ghenadie

Please explain to us how it can be that when Bob’s setting is changed but Alice’s stays the same, Alice’s measurement outcome changes sign?

Richard

[Richard Gill]

Ghenadie

The sign changing operation needed when the two chosen sectors are not adjacent cannot be performed without knowing both settings.

Look for instance at Table 2, Iteration 2.

If Alice has chosen setting 1 her initial outcome according to column T4 is “–“.

But she may need to switch the outcome to “+”.

That depends on whether Bob has chosen setting 1 or 2. If Bob chosen 2 she must switch, if Bob chose 1 she mustn’t switch the sign.

The outcomes cannot be definitively fixed till after both settings are known. This was a case where Alice needs Bob’s setting.

The paper is called "Bell Experiment with Two Independent Computers”. But alas the model requires that the two computers are not independent.

Bob’s computer needs to know Alice’s setting, and vice versa.

Richard

PS I’ve now given you *three* mathematical proofs that your model is not local.

1. Bell’s theorem says so: S = 3 implies non-local

2. Your algorithm cannot be performed while keeping the computers separate

3. An explicit counter example based on consideration of Iteration 2, setting pair 11 versus 12. Alice’s output with setting 1 depends on Bob’s setting 1 or 2

It is so simple, so obvious! At last!

[Ghenadie Mardari]

  Dear Richard,

This is elementary:

Bertlmann's socks cannot violate Bell's inequality.

They cannot be used for anything that I described (unless we had some kind of magic, or picked individual properties by hand).

In contrast, entangled quanta are not like Bertlmann's socks.

They produce violations naturally.

So, all of this "magic" happens automatically.

We don't need to know anything, or pre-arrange anything.

This is physics.

Think of it this way:

If we assume that the Earth is in the center of the Universe, then other planets need magical forces to trace epi-cycles in the sky.

Similarly, if we assume that "everything is Bertlmann's socks", then we need magical forces to explain both quantum-like correlations and their disappearance in "monogamy" scenarios.

Best wishes,

Ghenadie.

[Richard Gill]

All that is true.

Quantum (or more extreme) correlations can only be explained classically by using non-locality.

You explain your S =3 correlations classically by using non-locality.

We are in agreement

Your paper is wrong.

Sent from my iPad

On 13 Aug 2026, at 14:20, Ghenadie Mardari <gmar...@gmail.com> wrote:



[Alexandre de Castro]

This is not true: "Quantum (or more extreme) correlations can only be explained classically by using non-locality."

We can have the singlet state violating CHSH, and that doesn't mean it's non-local behavior. There is a lot of confusion in that sentence by Richard.

--
You received this message because you are subscribed to the Google Groups "Bell inequalities and quantum foundations" group.
To unsubscribe from this group and stop receiving emails from it, send an email to Bell_quantum_found...@googlegroups.com.

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/D37C0D8E-DFA8-4B25-B23C-E8980207E5A5%40gmail.com.

[Richard Gill]

I didn’t say that the behaviour was non-local. I said it could only be explained in a classical way using non-locality

There was no confusion in my sentence.

You did not read it carefully enough, Alexandre

[anton vrba]

What is the definition of local?

Seen from the universe's perspective, even a 1,000 km separation is local.

What we describe as entanglement might be better explained as Noether’s theorem on steroids. (For those unfamiliar, Emmy Noether—who famously proved how conservation laws work—gave us one of the most fundamental theorems in physics, even if she was unjustly passed over for a Nobel Prize!)  

A singlet state carries information, and that information cannot be destroyed; it is always preserved. Take two entities (like photons or electrons), A and B, created in an event. They form a singlet state that preserves the original event's information. They remain entangled unless one entity, say B, transfers its information to a new entity, C. At that point, A and C form the new singlet state. Modern entanglement experiments prove this mechanism, yet it's often hand-waved as "Quantum Magic" instead of treating it as a real physical process.

A Bell state isn't a physical phenomenon—it’s just a record of our ignorance, representing what we don't know.

Frankly, I find many of these ongoing attempts to offer mathematical proofs or computer simulations a wasted effort. They won't bring us any closer to the underlying truth!

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

From "Richard Gill" <gill...@gmail.com>

To "Alexandre de Castro" <alx...@gmail.com>

Cc "Ghenadie Mardari" <gmar...@gmail.com>; "Mark Hadley" <sunshine...@googlemail.com>; "Bart Jongejan" <bart.j...@gmail.com>; "Parker Emmerson" <powerin...@gmail.com>; "Bell quantum foundations" <bell_quantum...@googlegroups.com>

Date 8/13/2026 4:13:46 PM

Subject Re: [Bell_quantum_foundations] Bell experiment with two independent computers

[Mark Hadley]

Anton,

Local is defined by the light cones of special relativity.

Thought experiments are easier than real ones.

Mark

[Richard Gill]

Anton, I agree with what you say here:

On 13 Aug 2026, at 17:40, anton vrba <anto...@gmail.com> wrote:

Frankly, I find many of these ongoing attempts to offer mathematical proofs or computer simulations a wasted effort. They won't bring us any closer to the underlying truth!

I’m more interested in psychology. Why can such intelligent people believe such impossible things? 

My hypothesis is it’s because they are very clever at finding ways to ignore logic, and because they are overconfident in their intuitive insights. Maybe: the confidence born of a successful academic career in STEM. 

Ghenadie’s case is for me a “case study”. He is ingenious. He thinks he’s made a brilliant discovery. He has dressed in up in such complexity that he himself does not recognise that his “model” simply conforms to Bell’s theorem. It predicts S = 3 and it does so by blatant non-locality, but explained so badly that he himself doesn’t see it, and nobody else does. At least not “at first sight”. Including myself.

I also think entanglement is a real physical process. It can be described mathematically and the predictions are born out by experiment. But I don’t think we can ever understand it. We can only get accustomed to it and become fluent in the maths, which means we can deal with it in a creative fashion. 

[Mark Hadley]

We can't understand QM.... Until we can.

Prediction: it will be explained. And then accepted like general relativity is. Puzzling at first and then we accept the theory and develop intuition.

A big step like this breaks a beloved assumption. I think it's blindingly obvious that causality will need to be dropped.

Mark

[Austin Fearnley]

I think of the singlet entity as completely identified with quantum retrocausality.  I am writing a paper comparing superdeterminism with quantum retrocausality and if I remember correctly KS is already explained in the paper.  I hit a problem with GHZ as it is a three-way entanglement, and four-way if you include the trigger. I am not familiar with three way effects whereas two way effects  of the singlet are easier.  I am convinced that QM has the answer and  quantum retrocausality will work the same way.  The difference only lying in the interpretation. So I am using Excel VB to model the GHZ experiment, though it might be easier to learn Python.  Excel VB has moved on since I previously used it and of course it is now more formalised and more complicated.  AI has offered to help but it isnt very good at programming.  Many holes in the logic and in initialising variables and .. well .. everywhere.  I am convinced the easiest interpretation of QM is two-way in time causality for micro particles.  This does not work for the macro worlds as the two ways are too jumbled up in macro bodies and thermodynamics stops the two-way in time effect.  But within human and animal brains there are electrical pathways which can allow two-ways within individual particles as in a preon model.  

The two-ways effect shows that QM is really coping with two-ways simultaneously.  It is marvellous that it can do so, but it obscures the underlying explanation by making out that statistical phenomena are reality, such as superposition.

[Mark Hadley]

I'm fairly sure that each interacting particle introduces another non trivial loop. And each loop add another topological variable.

Mark

--

You received this message because you are subscribed to the Google Groups "Bell inequalities and quantum foundations" group.
To unsubscribe from this group and stop receiving emails from it, send an email to Bell_quantum_found...@googlegroups.com.

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/4c39901c-caad-4e75-8499-04a83e4dda1en%40googlegroups.com.

[Parker Emmerson]

By declaring that the universe has "no center," mainstream physics didn't actually eliminate bias—it just swapped an Earth-centric bias for a non-centric bias (known formally as the Copernican or Cosmological Principle). When physicists solve Einstein’s equations for the whole universe, they plug in the "Cosmological Principle"—the assumption that the universe looks exactly the same in every direction from every point (homogeneous and isotropic). The absolute bedrock of General Relativity is diffeomorphism invariance. In plain English, this means the laws of physics must hold true regardless of how you draw your coordinate grid. If true relativity says any frame of reference is mathematically valid, then fixing the Earth as a stationary center $u^\mu = (1, 0, 0, 0)$ must be a valid, workable model. If a physicist says the Earth-centric model is "wrong" (rather than just "computationally annoying"), they are technically denying General Relativity.

I’ve been tracking a thought experiment all the way down to its logical bedrock, and it has evolved into something far larger than a clever math trick. What started as a bizarre play on coordinates has turned into a complete structural critique of modern cosmology, quantum mechanics, and the hidden biases of physical theory.

Here is the full synthesis—from the upside-down cosmos to the tensor mechanics and the resolution of Bell's Theorem.

1. The Setup: The Upside-Down Cosmos

We all know the Earth isn’t the center of the universe, but what if we forced the math to pretend it is?

If you stick a stationary Earth at the absolute center of a coordinate system, the universe has to spin around it once every 24 hours. That means distant stars—like Proxima Centauri—must travel at roughly 9,500 times the speed of light relative to us. Under General Relativity, coordinate velocity limits aren't strictly enforced on a global scale, so the math is technically legal.

To bridge the gap between those hyper-speed stars and the normal speed of light we measure on Earth, you have to invent a cosmic pipeline:

• The Energy Cascade: Invisible, hyper-speed rotational energy from the universe cascades down into localized photons.

• Matter from Light: That light condenses into the heavy solid matter of the stars pinned to our night sky (E = mc² and pair production).

It paints a stunning, upside-down picture of reality. But the immediate pushback from mainstream physics is always: "That’s just a coordinate transformation; coordinate shifts generate zero physical work."

2. Making It Real: The Einstein-Aether & Mirror Calculus Backend

To stop this from being mere sci-fi, we have to look at what a coordinate shift actually implies. In strict presence-only logic (the Mirror Calculus / TPN framework), treating a passive grid re-labeling as an energy source is a grammatical failure—a "surrogate zero" that tries to make an empty label behave like a physical object.

To make the energy cascade physically and mathematically legal without violating local energy-momentum conservation (∇_μ T^μν = 0), we have to elevate the "spinning universe" from a fake grid into a dynamic, energy-bearing background medium using an Einstein-Aether framework:

• The Dynamic Vector Field (u^μ): Space is saturated by a physical unit timelike vector field. The total action couples this field to space: S_total = (1 / 16πG) ∫ d⁴x √(-g) [ R + ℒ_ae + λ (g_μν u^μ u^ν + 1) ] + S_descent

• Mapping the Cascade via Tensor Invariants:

  • Global Rotation (w → ω): The global spin maps to the background vorticity tensor (ω² = ½ ω_μν ω^μν). This vorticity is the macroscopic dark matter equivalent, acting as a real gravitomagnetic reservoir.

  • The Energy Pipeline (s → a_μ): Descent scale maps to the spatial acceleration of flow lines (s = a_μ a^μ), tracking how energy falls out of global rotation into local frames.

  • The Coupling (ℒ_int): Real work is done because matter explicitly couples to the Aether via an interference charge: ℒ_int = q · φ² (u^μ a_μ) + κ q ω^μν F_μν. Energy isn't created from math tricks; it is transferred out of the kinetic vorticity density of the background field.

• Saving Local Physics: By aligning parameters (c₃ = -c₁, c₄ = -c₁), local Lorentz-violating PPN anomalies vanish, keeping Solar System tests happy while cosmic-scale vorticity runs the show.

3. The Philosophical Pivot: The Bias of Non-Centrism

This mechanics exposes a massive blind spot in modern physics: by declaring that the universe has "no center," mainstream physics didn't eliminate bias; it just swapped an Earth-centric bias for a dogmatic non-centric bias.

The Copernican Principle was plugged into Einstein’s equations as a computational shortcut, but it morphed into ideological dogma. True relativity—diffeomorphism invariance—demands that any frame of reference must be mathematically workable. If an Earth-centric, Aether-driven model functions mechanically, then "non-centrism" is just an optional perspective, not an exclusive truth. True relativity means every point can simultaneously be mathematically justified as the center.

4. The Quantum Resolution: Saving Causality and Bell’s Theorem

The ultimate payoff of this framework hits when you look at quantum mechanics.

Under the standard non-centric / frameless view, quantum entanglement creates a catastrophic paradox. When two particles collapse instantaneously across light-years, it looks like "spooky action at a distance." Because there is no universal clock or absolute frame, physicists were forced to abandon realism—concluding that reality is a probabilistic hallucination until observed, just to protect Einstein's "local causality."

When you reintroduce the dynamic Aether field, the paradox evaporates entirely:

• The Medium of Entanglement: The vacuum is not an empty void; it is a physical, energy-bearing medium saturated by cosmic vorticity. Entangled particles aren't communicating via magic through empty space; they are mechanically anchored to the same underlying u^μ infrastructure.

• Absolute Simultaneity & Causality: The vector field u^μ establishes a physical, preferred rest-frame—a universal cosmic clock. Instantaneous quantum coordination happens natively through the Aether's hidden tension, but because the background has a defined directional flow, time travel and causality violations are geometrically blocked.

The Bottom Line

By taking a bizarre geocentric thought experiment seriously and forcing it through rigorous tensor dynamics and presence-only logic, you don't just resurrect an old cosmological view—you build the physical medium required to save quantum mechanics from the trap of Bell's Theorem.

The center isn't just a coordinate choice. It is the anchor that allows causality, realism, and energy conservation to coexist.

Best,

Parker

[anton vrba]

" Why can such intelligent people believe such impossible things?  "

Richard, 

Dunning and Kruger explained it as ilusory superiority:  because "such intelligent people" are specialised and competent in A and lack the relevant specialised knowledge B, C and D required to evaluate the whole picture.  Dunning Kruger states people with limited understanding regularly overestimate their own competence, leading to a strong, unearned belief in their own expertise.

Today universities produce specialists required by industry, and not generalists required by the few managers.  Musk is the prime example:  a generalist with high visionary capabilities, but he only requires specialists for implementation.

https://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect

https://www.psychologytoday.com/gb/basics/dunning-kruger-effect

Regards

Anton

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

From "Richard Gill" <gill...@gmail.com>

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

Cc "Alexandre de Castro" <alx...@gmail.com>; "Ghenadie Mardari" <gmar...@gmail.com>; "Mark Hadley" <sunshine...@googlemail.com>; "Bart Jongejan" <bart.j...@gmail.com>; "Parker Emmerson" <powerin...@gmail.com>; "Bell quantum foundations" <bell_quantum...@googlegroups.com>

Date 8/13/2026 5:22:35 PM

Subject Re: [Bell_quantum_foundations] Bell experiment with two independent computers

[Richard Gill]

Anton, I agree with what you say here:

On 13 Aug 2026, at 17:40, anton vrba <anto...@gmail.com> wrote:

Frankly, I find many of these ongoing attempts to offer mathematical proofs or computer simulations a wasted effort. They won't bring us any closer to the underlying truth!

[Ghenadie Mardari]

Dear Friends,

This is my last contribution to this thread.
If anyone has additional questions or comments, please write to me directly.

For those who are interested, here is my final summary.

Local Bell violations are impossible in a Bell experiment with random settings.
I fully agree with Richard about this.
The nuance is that quantum theory does not predict impossible things.

Bell violations are natural in experiments with fixed settings.
Yet, random settings impose a joint distribution on the output stream, destroying the input profile. 

Therefore, “loophole-free” violations emerge from random replacement.

There is a precedent for this.
People expected 4-quantum entanglement to produce Bell violations and to close all the loopholes. 

Instead, we now have “quantum monogamy”.

The real problem is that Bell’s theorem is a narrow argument.
It talks about “locality”, but the demonstration is about joint distributions.
So, any conclusion about causality is based on loaded words that are accidentally associated with mathematical facts. 

It does not follow from the facts themselves.

Claiming that ontological non-locality is real (because of Bell violations) is like saying that the sky is green because 2+2=4. 

One does not follow from the other.

You see, math is essential for physics, but math is not physics.
Please give yourself permission to see this.

Best wishes,
Ghenadie.