Re: Bell Experiments and the Two-Slit Experiment
Richard Gill
On 5 Jun 2026, at 23:19, Bob Doyle <bobd...@informationphilosopher.com> wrote:
Hi Mark,Yes, you are one of dozens of scientists whose work on free will I've studied and included on my website.Richard said many alternative derivations of QM have been made using conservation theorems.I am not attempting an alternative derivation. My work on quantum entanglement is based on standard quantum mechanics as presented by Schrödinger, Dirac, et al., as I learned it while getting a Ph.D. at Harvard in the 1960's.I do use the conservation of spin angular momentum as an explanation for the perfect correlation of Alice and Bob's measurements as long as they agree in advance on their measurement angles to preserve the symmetry of the two-particle state, otherwise if they measure at different angles their correlations fall off as the square of the cosine of their measurement angle difference, the well know "law of Malus" in crossed polarizer measurements.The total spin angular momentum of the two particles (atoms or electrons) is zero. If they are atoms as in Bohm's original suggestion, they are in the 1Σg singlet state of the two atoms in a hydrogen molecule. The two hydrogen atoms in the hydrogen molecule ground state 1Σg+ are rotationally symmetric about the molecule axis. David Bohm's hidden variable experiment in 1952 started with a hydrogen molecule that was dissociating into two hydrogen atoms with total spin zero.As the hydrogen atoms "separate," the quasi-molecular wave function remains rotationally symmetric around the molecular axis. The total spin angular momentum remains zero at all times, unless the atoms are disturbed by the environment or a measurement is made.
This conservation of total spin angular momentum is equal to zero at all times, up to and including the measurements made by Alice and Bob, but if, and only if, 1) nothing external has disturbed their state since entanglement, and 2) their two measurements are made at exactly the same measurement angles, preserving the overall symmetry. Alice and Bob must agree before they experiment to the free choice of one angle in which to measure.
They must also measure at the same time (assuming the initial entanglement is centered between their measurement devices), to ensure they are measuring the correct pair of particles.
Should Alice and Bob measure at different angles, say angles separated by angle θ, they will lose the perfect correlations. Correlations will decline proportional to the square of the cosine of that angle difference, cos2θ. If they measure at right angles to one another, there will be no correlations, since the cosine of 90 degrees is zero.
I hope you have a chance to look at my analysis of John Bell and his strange claim that local hidden variables would produce straight line dependence on angle (the so-called Popescu-Rohrlich box with its Tsirelson bound) .We can illustrate the straight-line predictions of Bell's inequalities for local hidden variables, the cosine curves predicted by quantum mechanics and conservation of angular momentum, and the odd "kinks" at angles 0°, 90°, 180°, and 270°.
This inscribed square is called the Bell polytope.It shows Bell’s local hidden variables prediction as four straight lines of the inner square. The circular region of quantum mechanics correlations are found outside Bell's straight lines, "violating" his inequalities. Quantum mechanics and Bell's inequalities meet at the corners, where Bell's predictions show a distinctly non-physical right-angle that Bell called a "kink."
All experimental results have been found to lie along the curved quantum predictions called the "Tsirelson bound."
In 1976, Bell gave us this diagram of the "kinks" in his local hidden variables inequality. He says,
Unlike the quantum correlation, which is stationary in θ at θ = 0, at the hidden variable correlation must have a kink thereBell provides us no physical insight into the "kinky" square shape of his "local hidden variables" inequality.("Einstein-Podolsky-Rosen Experiments," republished in Speakable and Unspeakable in Quantum Mechanics," 1987, p. 85)Anyway, I am a bit discouraged to see Richard and Brian involved in a "pissing contest," as Richard said.Have you all considered a Zoom meeting to try to get to some agreement. I'd be happy to set one up.Cheeers,BobOn Thu, May 28, 2026 at 9:17 AM Mark Hadley <sunshine...@googlemail.com> wrote:Dear Bob,Welcome to the forum.And thanks for the awesome philosophy web site
I think I'm on there with my challenge model of free will.CHeersMark HadleyOn Thu, 28 May 2026 at 17:09, Bob Doyle <bobd...@informationphilosopher.com> wrote:Richard,True. Quantum entanglement of electron spins are non-local. There are no hidden variables. There is nothing moving between the electrons.There is only a "hidden?" constant of the motion - which is the total spin zero conserved angular momentum at all times which guarantees the spins will be found in opposite directions when measured, otherwise a fundamental conservation principle will have been violated.Conservation principles (state symmetries, see Emmy Noether) are true in both quantum and classical mechanics, right?BobOn Thu, May 28, 2026 at 8:00 AM Richard Gill <gill...@gmail.com> wrote:Dear Bob,Unfortunately your model is non-local. If it is a hidden variable model it is non-local. It does require spooky action at a distance.RichardSent from my iPhoneOn 28 May 2026, at 16:08, Bob Doyle <bobd...@informationphilosopher.com> wrote:Dear Richard,As I see it, Erwin Schrödinger's wave equation and his two-particle solution ψ12 say nothing about "hidden variables," an idea that was proposed by David Bohm sixteen years after EPR with this explanation...We consider a molecule of total spin zero consisting of two atoms, each of spin one-half. The wave function of the system is thereforeψ12 = (1/√2) [ ψ+ (1) ψ- (2) - ψ- (1) ψ+ (2) ]where ψ+ (1) refers to the wave function of the atomic state in which one particle (A) has spin +ℏ/2, etc. The two atoms are then separated by a method that does not influence the total spin. After they have separated enough so that they cease to interact, any desired component of the spin of the first particle (A) is measured. Then, because the total spin is still zero, it can immediately be concluded that the same component of the spin of the other particle (B) is opposite to that of A.
"Discussion of Experimental Proof for the Paradox of Einstein, Rosen, and Podolsky,” Physical Review, vol.108, no.4. p.1070, 1957Bohm's suggestion of hidden variables was famously explored by John Bell twelve years after Bohm. Bell concluded no local hidden variables exist. And no plausible mechanism for hidden variables has ever been accepted.Bell suggested that hidden variables would produce a straight-line dependence on angle where quantum mechanics would produce a cosine-squared dependence.We can illustrate the straight-line predictions of Bell's inequalities for local hidden variables, the cosine curves predicted by quantum mechanics and conservation of angular momentum, and the odd "kinks" at angles 0°, 90°, 180°, and 270°, with what is called a "Popescu-Rorhlich box."This inscribed square is called the Bell polytope.<Polytope.png>It shows Bell’s local hidden variables prediction as four straight line edges of the inner square. The circular region of quantum mechanics correlations are found outside Bell's straight lines, "violating" his inequalities. Quantum mechanics and Bell's inequalities meet at the corners, where Bell's predictions show a distinctly non-physical right-angle that Bell called a "kink."
All experimental results have been found to lie along the curved quantum predictions called "Tsirelson's bound."
In 1976, Bell gave us this diagram of the "kinks" in his local hidden variables inequality. He says,
Unlike the quantum correlation, which is stationary in θ at θ = 0, at the hidden variable correlation must have a kink thereBell provides us no physical insight into the distinctly non-physical("Einstein-Podolsky-Rosen Experiments," republished in Speakable and Unspeakable in Quantum Mechanics," 1987, p. 85)"kinky" square shape of his "local hidden variables" inequality.
I have proposed that instead of "hidden variables," there is a hidden constant of the motion that completely explains the perfect correlations between entangled particles with no "spooky action at a distance." That hidden constant is simply the conserved total spin angular momentum zero of the two particles which means the two particles are at all times pointing in opposite directions.This conservation of total spin can be interpreted as a "cause," a "common cause," keeping the spins in opposite directions, as predicted by Schrödinger's two-particle solution.On Sat, May 23, 2026 at 11:30 PM Richard Gill <gill...@gmail.com> wrote:Dear BobUnfortunately Schrödinger’s solution would imply that a local hidden variables description is valid, and hence that the CHSH inequalities are satisfied.YoursRichardSent from my iPhoneOn 23 May 2026, at 21:22, Bob Doyle <bobd...@informationphilosopher.com> wrote:Dear Richard and Brian,I'm enjoying your discussions on Evo-Devo, but thought I would write to you off-list so as not to disturb the conversation.Frankly your math is beyond me and I'm not qualified to comment intelligently on your work, but I would very much appreciate your comments on my quantum physics explanations.I wrote a Ph.D. thesis at Harvard in 1968 on two hydrogen atoms in collision that I treated with molecular wave functions rather than atomic wave functions.I called them a hydrogen "quasi-molecule (two hydrogen atoms absorbing and emitting light while they are colliding and separating).I explained how the Lyman alpha spectroscopic line at 1216 Å becomes a broad continuous ultraviolet spectrum out to 2000 Å. It was observed around the star Spica by early rocket experiments which first saw stars from above the atmosphere.This work gave me an insight into the symmetric molecular ground state with total spin zero that perfectly describes David Bohm's original proposed test of John Bell's theorem and the idea of hidden variables.In 1952, Bohm reformulated the two material particles of the 1935 Einstein-Podolsky-Rosen paper as two atoms in a hydrogen molecule in the singlet 1Σg state separating as the hydrogen molecule dissociates into two hydrogen atoms in singlet s states (with spins at all time in opposite directions to conserve spin angular momentum equal to zero).As I see it, this perfect correlation of the two spins at all times is a consequence of the fundamental principle of conservation of angular momentum that is true in classical and quantum mechanics. As Emmy Noether explained, every conservation principle is the result of some physical symmetry.Instead of a hidden variable, I proposed a hidden constant (that always-conserved total spin zero) as completely explaining quantum entanglement without Einstein's "spooky action at a distance."Instead of Einstein's idea that the measurement of particle A "causes" particle B to become correlated (or that B causes A), this conservation of total spin zero can be viewed as a sort of common cause acting on both particles at all times!Further details are on my John Bell page and the several menu items under my Entanglement menu.My thoughts on the Two-Slit Experiment are under my Quantum menu.You might also see how Erwin Schrödinger told Einstein exactly how two particles become disentangled.Critical comments most appreciated.Cheers,Bob--metaphysicist.comObservatory HillSkype: bobdoyleYouTube: infophilosopherTwitter: @infophilosopherFacebook: infophilosopherMy Books: informationphilosopher.com/booksMy Online Lectures: informationphilosopher.com/lecturesMy Desktop Video Group: dtvgroup.comMy EContent Articles: cmsreview.com/EContentMy First Podcasts firstpodcasts.orgMy iTV-Studio: itv-studio.comMy Reading Research readingwithphonics.orgMy Amazon page: amazon.com/author/bobodoyleAcademia: bobdoyle.academia.eduORCID 0000-0001-0001-0035--metaphysicist.comObservatory HillSkype: bobdoyleYouTube: infophilosopherTwitter: @infophilosopherFacebook: infophilosopherMy Books: informationphilosopher.com/booksMy Online Lectures: informationphilosopher.com/lecturesMy Desktop Video Group: dtvgroup.comMy EContent Articles: cmsreview.com/EContentMy First Podcasts firstpodcasts.orgMy iTV-Studio: itv-studio.comMy Reading Research readingwithphonics.orgMy Amazon page: amazon.com/author/bobodoyleAcademia: bobdoyle.academia.eduORCID 0000-0001-0001-0035--metaphysicist.comObservatory HillSkype: bobdoyleYouTube: infophilosopherTwitter: @infophilosopherFacebook: infophilosopherMy Books: informationphilosopher.com/booksMy Online Lectures: informationphilosopher.com/lecturesMy Desktop Video Group: dtvgroup.comMy EContent Articles: cmsreview.com/EContentMy First Podcasts firstpodcasts.orgMy iTV-Studio: itv-studio.comMy Reading Research readingwithphonics.orgMy Amazon page: amazon.com/author/bobodoyleAcademia: bobdoyle.academia.eduORCID 0000-0001-0001-0035--metaphysicist.comObservatory HillSkype: bobdoyleYouTube: infophilosopherTwitter: @infophilosopherFacebook: infophilosopherMy Books: informationphilosopher.com/booksMy Online Lectures: informationphilosopher.com/lecturesMy Desktop Video Group: dtvgroup.comMy EContent Articles: cmsreview.com/EContentMy First Podcasts firstpodcasts.orgMy iTV-Studio: itv-studio.comMy Reading Research readingwithphonics.orgMy Reading App touchmeteachme.comMy Amazon page: amazon.com/author/bobodoyleAcademia: bobdoyle.academia.eduORCID 0000-0001-0001-0035
Richard Gill
On 6 Jun 2026, at 17:03, Bob Doyle <bobd...@informationphilosopher.com> wrote:
Dear Richard,Thanks very much for your kind words.And thanks for quoting those critical lines from my website that the giants of quantum mechanics, Schrödinger, Dirac, and yes Feynman, gave us, not as an explanation of an underlying mechanism, but simply showing the power of pure mathematical equations to predict experimental outcomes.John Bell's great contribution was to say that local hidden variables could not provide that explanation, that something non-local was happening.I have not understood enough of Brian Sanctuary's math so I'm reluctant to comment. If it did reproduce all the predictions of Schrödinger's two-particle equation, that would be very impressive, but still would not give us what so many critics of entanglement are looking for - the realistic causal explanation of these instantaneous correlations over vast distances that Einstein looked for all his life.David Mermin famously thinks the particles are carrying instruction sets, a reply to Schrödinger's insight that the particles somehow seem to know the answer to questions in advance.In 1936 Schrödinger replied to the EPR paper within a few weeks, giving us the math with those perfect statistical predictions. He said the entangled particles cannot be separated. Einstein's "separability principle" (Trennungsprinzip) is simply wrong.Over the past decades dozens of correspondents have written to me with their original ideas explaining the great problems and puzzles of physics and philosophy. I always reply and encourage them to read and study more carefully how their work differs from the existing literature, then include how their work differs. Some, like Mark Hadley, contained an original element that I thought I should include on my website.If anyone in your group would like a copy of my Einstein book (which includes my comments on Bell), send me your mailing address. Otherwise it is available as a free PDF download which is in color and with animations, where the print book is static and black and white. https://informationphilosopher.com/books/einstein/Cheers,Bob
On Sat, Jun 6, 2026 at 1:18 AM Richard Gill <gill...@gmail.com> wrote:
Dear BobA zoom meeting won’t get agreement. One might be able to agree to disagree, but still, Bryan made a bet, lost it, and refuses to pay up, so his scientific credibility / integrity has been damaged. There are many witnesses.I see the situation as follows. Bryan instinctively rejects spooky action at a distance. He has a computation starting from the standard QM expression for the EPR correlations, rewriting it in the language of Geometric Algebra, and evaluating what comes out. He evaluates the formula and gets the negative cosine. Maybe we can all agree on that? Ie agree on his math, shorn of physical interpretation.He looks at his derivation and interprets it physically, visualises it, and writes about his visualisation, illustrating them with yet more diagrams.Most people look at his math and can only see in them the fact that the joint probability distribution of the binary outcomes x and y depends on settings an and b, exactly as QM predicts. His simulation experiment does not even bother to produce the outcomes x and y, it only produces the Boolean “x = y” (true or false).I have asked him again and again for a computer program which generates data lines “time stamp, a, b, x, y” using his model.Still waiting,Richard
Hi Mark,Yes, you are one of dozens of scientists whose work on free will I've studied and included on my website.Richard said many alternative derivations of QM have been made using conservation theorems.I am not attempting an alternative derivation. My work on quantum entanglement is based on standard quantum mechanics as presented by Schrödinger, Dirac, et al., as I learned it while getting a Ph.D. at Harvard in the 1960's.I do use the conservation of spin angular momentum as an explanation for the perfect correlation of Alice and Bob's measurements as long as they agree in advance on their measurement angles to preserve the symmetry of the two-particle state, otherwise if they measure at different angles their correlations fall off as the square of the cosine of their measurement angle difference, the well know "law of Malus" in crossed polarizer measurements.The total spin angular momentum of the two particles (atoms or electrons) is zero. If they are atoms as in Bohm's original suggestion, they are in the 1Σg singlet state of the two atoms in a hydrogen molecule. The two hydrogen atoms in the hydrogen molecule ground state 1Σg+ are rotationally symmetric about the molecule axis. David Bohm's hidden variable experiment in 1952 started with a hydrogen molecule that was dissociating into two hydrogen atoms with total spin zero.As the hydrogen atoms "separate," the quasi-molecular wave function remains rotationally symmetric around the molecular axis. The total spin angular momentum remains zero at all times, unless the atoms are disturbed by the environment or a measurement is made.
This conservation of total spin angular momentum is equal to zero at all times, up to and including the measurements made by Alice and Bob, but if, and only if, 1) nothing external has disturbed their state since entanglement, and 2) their two measurements are made at exactly the same measurement angles, preserving the overall symmetry. Alice and Bob must agree before they experiment to the free choice of one angle in which to measure.
They must also measure at the same time (assuming the initial entanglement is centered between their measurement devices), to ensure they are measuring the correct pair of particles.
Should Alice and Bob measure at different angles, say angles separated by angle θ, they will lose the perfect correlations. Correlations will decline proportional to the square of the cosine of that angle difference, cos2θ. If they measure at right angles to one another, there will be no correlations, since the cosine of 90 degrees is zero.
I hope you have a chance to look at my analysis of John Bell and his strange claim that local hidden variables would produce straight line dependence on angle (the so-called Popescu-Rohrlich box with its Tsirelson bound) .
Richard Gill
David Mermin famously thinks the particles are carrying instruction sets, a reply to Schrödinger's insight that the particles somehow seem to know the answer to questions in advance.
Mark Hadley
Bryan Sanctuary
Austin Fearnley
In my preon model, SM particles carry the properties of electric charge, spin, weak isospin and colour charge in smaller components or preons. Not 'instructions' or 'instruction sets' but fixed properties. I agree that this in itself does not solve Bell/EPR. IMO what is needed is backwards-in-time influences such as those noted by Costa de Beauregard. These influences in my model are carried by the antipreons, some of which are contained in every SM particle. Say Bob measures an electron. The polarisation of that electron was formed at the instant of creation of the entanglement. That creation involved a positron (with backward in time antipreons carrying spin information) which had (already!) been measured by Alice at Measurement A. That spin information at the instant of creation of entanglement was transmitted to the electron during the interaction which created that electron. The preons in the electron with the correct spin information were not directly taken from the positron. The antipreons in Bob's the positron contained the correct polarisation angle of Bob's device setting as, after measurement B, the positron is polarised along Bob's device angle b. Angle b is then transmitted to Alice's electron. Carried not by the antipreon in the electron but by a preon in the electron. In my preon model interactions are not between two SM particles but between four, e.g. two photons and an e-/e+ pair. So Alice's electron carries in its preons the polarisation Angle of Bob's device setting. I see a connection between these ideas and TSVF. My backwards-in-time antipreon properties could restrict TSVF propagator influences to be contained in preons entirely within the particles rather than being external influences. I have always been dubious about weak measurement but am trying to see it as an extension of off-shell effects. Very distant off-shell effects! I have no qualms about off-shell effects. For example, can a QM entangled particle pair be viewed as a long distance off-shell effect?
Following Mark's praise I read some of Bob's internet pages. I enjoyed reading the passages about Einstein at Solvay.
Austin Fearnley
In my preon model, SM particles carry the properties of electric charge, spin, weak isospin and colour charge in smaller components or preons. Not 'instructions' or 'instruction sets' but fixed properties. I agree that this in itself does not solve Bell/EPR. IMO what is needed is backwards-in-time influences such as those noted by Costa de Beauregard. These influences in my model are carried by the antipreons, some of which are contained in every SM particle. Say Bob measures an electron. The polarisation of that electron was formed at the instant of creation of the entanglement. That creation involved a positron (with backward in time antipreons carrying spin information) which had (already!) been measured by Alice at Measurement A. That spin information at the instant of creation of entanglement was transmitted to the electron during the interaction which created that electron. The preons in the electron with the correct spin information were not directly taken from the positron. The antipreons in Alice's positron contained the correct polarisation angle of Alice's device setting as, after measurement A, the positron is polarised along Alice's device angle a. Angle a is then transmitted to Bob's electron. Carried not by the antipreon in the electron but by a preon in the electron. In my preon model interactions are not between two SM particles but between four, e.g. two photons and an e-/e+ pair. So Bob's electron carries in its preons the polarisation Angle of Alice's device setting. I see a connection between these ideas and TSVF. My backwards-in-time antipreon properties could restrict TSVF propagator influences to be contained in preons entirely within the particles rather than being external influences. I have always been dubious about weak measurement but am trying to see it as an extension of off-shell effects. Very distant off-shell effects! I have no qualms about off-shell effects. For example, can a QM entangled particle pair be viewed as a long distance off-shell effect?
Richard Gill
Richard Gill
Begin forwarded message:
From: Mark Hadley <sunshine...@googlemail.com>
Date: 6 June 2026 at 18:18:59 CEST
To: Bob Doyle <bobd...@informationphilosopher.com>
Cc: Richard Gill <gill...@gmail.com>, Briane Sanctuary <BryanCS...@gmail.com>, Ghenadie Mardari <gmar...@gmail.com>
Subject: Re: Bell Experiments and the Two-Slit Experiment
Zoom won't work.Bryan has mistakes in his maths, everyone who studied his work has seen the same errors. He does not address the detailed problems, just presents another paper to study.For studies of non locality, I find the CSHS derivation cleaner and simpler.I didn't think Bell gave actual correlation coefficients. QM does.There is a fundamental philosophical distinction that explains the correlation coefficients. In classical nets the uncertainty is due to some unknown parameters. The probability is then an integral over weighted volume spaces. over the parameter space. The areas of a Venn diagram if you like.in QM it is context dependent. So the hidden variables, if they exist, depend on the measurement that will be made. The only way to represent these is with subspaces of a Hilbert space and then the only way to get a scalar for a probability is with the quadratic function ( trace or scalar product) as in the Born rule.There are no other options. Just two different probability expressions, one for context dependent physics and one for classical physics, the latter being a special case of the former.Mark
On Fri, 5 Jun 2026, 23:19 Bob Doyle, <bobd...@informationphilosopher.com> wrote:
Hi Mark,Yes, you are one of dozens of scientists whose work on free will I've studied and included on my website.Richard said many alternative derivations of QM have been made using conservation theorems.I am not attempting an alternative derivation. My work on quantum entanglement is based on standard quantum mechanics as presented by Schrödinger, Dirac, et al., as I learned it while getting a Ph.D. at Harvard in the 1960's.I do use the conservation of spin angular momentum as an explanation for the perfect correlation of Alice and Bob's measurements as long as they agree in advance on their measurement angles to preserve the symmetry of the two-particle state, otherwise if they measure at different angles their correlations fall off as the square of the cosine of their measurement angle difference, the well know "law of Malus" in crossed polarizer measurements.The total spin angular momentum of the two particles (atoms or electrons) is zero. If they are atoms as in Bohm's original suggestion, they are in the 1Σg singlet state of the two atoms in a hydrogen molecule. The two hydrogen atoms in the hydrogen molecule ground state 1Σg+ are rotationally symmetric about the molecule axis. David Bohm's hidden variable experiment in 1952 started with a hydrogen molecule that was dissociating into two hydrogen atoms with total spin zero.As the hydrogen atoms "separate," the quasi-molecular wave function remains rotationally symmetric around the molecular axis. The total spin angular momentum remains zero at all times, unless the atoms are disturbed by the environment or a measurement is made.
This conservation of total spin angular momentum is equal to zero at all times, up to and including the measurements made by Alice and Bob, but if, and only if, 1) nothing external has disturbed their state since entanglement, and 2) their two measurements are made at exactly the same measurement angles, preserving the overall symmetry. Alice and Bob must agree before they experiment to the free choice of one angle in which to measure.
They must also measure at the same time (assuming the initial entanglement is centered between their measurement devices), to ensure they are measuring the correct pair of particles.
Should Alice and Bob measure at different angles, say angles separated by angle θ, they will lose the perfect correlations. Correlations will decline proportional to the square of the cosine of that angle difference, cos2θ. If they measure at right angles to one another, there will be no correlations, since the cosine of 90 degrees is zero.
I hope you have a chance to look at my analysis of John Bell and his strange claim that local hidden variables would produce straight line dependence on angle (the so-called Popescu-Rohrlich box with its Tsirelson bound) .
Richard Gill
On 6 Jun 2026, at 21:11, Richard Gill <gill...@gmail.com> wrote:
This message from Bob Doyle didn’t go to the whole group. I hope Bob doesn’t mind I add it. Otherwise some of us are missing key parts of the conversation.
<image.png>
Richard Gill
On 6 Jun 2026, at 19:28, Bryan Sanctuary <bryancs...@gmail.com> wrote:
Mark Hadley
Parker Emmerson
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Parker Emmerson
Parker Emmerson
Bell’s theorem does not begin with locality and derive the impossibility of local physics. It begins, in effect, with a global counterfactual spreadsheet: A₀(λ), A₁(λ), B₀(λ), B₁(λ). The CHSH inequality is then just the arithmetic of that spreadsheet. PV-REC’s point is that a real boundary event need not be such a spreadsheet. Its event sections are K_ab(λ₀), indexed by the actual absorber context, with λ₀ preparation-independent and the observed marginals no-signalling. So when Richard’s replay test demands a single reusable λ and separated functions A(a,λ), B(b,λ), it is not neutrally testing locality; it is testing whether PV-REC can be squeezed into the very scalar-gluing architecture it rejects. Of course it fails. That is not a refutation. That is a category error dressed up as a theorem.
Parker Emmerson
Richard Gill
Mark Hadley
Richard Gill
Austin Fearnley
I am a naive amateur physicist. Someone else asked what PV was and could not find much help for a simple explanation. I have asked google search AI two questions: "how does phenomenological velocity apply to Bell's theorem?" and then "how does it explain chsh s>2.0?"
Here are some of the replies.
Some phenomenological velocity frameworks attempt to reconcile hidden variables with quantum correlations by introducing superluminal (faster-than-light) speeds for the "hidden" influences.
Phenomenological velocity explains a CHSH score of S > 2 by allowing a non-local "quantum potential" to instantly communicate the measurement setting of one detector to the other particle.
.... (this) keeps realism but ... abandons locality ...
Phenomenological Propagation: The information about angle a propagates across the spatial gap to Particle 2 at a phenomenological velocity that is effectively infinite ...
Because the outcome at B is a function of both settings, B(a,b), the independent probability distributions factorisation breaks down. This dependency unlocks the tight phase-matching needed to yield the quantum correlation value ...
These explanations tell me that my retrocausal explanation seems like a special case of PV, although I see my retrocausality as being local within a different reality. However, I see the value of Bell's Theorem in distinguishing classically local from non-local models.
Richard Gill
To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/11627783-3a0b-4970-aec7-5b6db6a0df37n%40googlegroups.com.
Parker Emmerson
PV has 4D aspects because the ordinary real height relation is treated as the reduced projection of a Lorentz-embedded algebraic kernel. The reciprocal insertion of κ(v) = √(1 − v²/c²) cancels in the observable product, but when the inverse problem is posed, the solution is controlled by the defect Δ. On Δ ≠ 0, the PV quotient gives a punctured branch direction; on Δ = 0, it becomes 0/0; and over ℂ, the argument of Δ produces real or imaginary velocity phases. Quaternionically, this is naturally read as a complexified rotor/biquaternion structure: real quaternion rotations are the spatial shadow, while the imaginary branches are Lorentz/boost or analytic-continuation sectors of the same event algebra.
Bryan’s program appears to compute a joint quaternion-context relation before digitizing outcomes. That means it may be a contextual event model, not a Bell-local factorized model. But that does not make the ontology trivial or incoherent; it only means Richard’s factorization test classifies it as non-Bell-local.
Richard's test says, "I will call your model local only if it can be written as , with one reusable ."
Then when Bryan says:
“My model does not work like that; the measurement context instantiates the geometry,”
Richard says: “Then it is not local.”
I do not accept the move from “BiSM is not Bell-factorized” to “BiSM is therefore nonlocal” as though that were a neutral physical conclusion.
The issue is that Bell’s theorem has been repeatedly defended by narrowing “locality” into a very particular formal surrogate: one setting-independent hidden variable, one probability space, and separated response functions (A(a,\lambda)), (B(b,\lambda)). Once that surrogate is granted, the inequality follows. But that does not prove that every physically local ontology must have that surrogate structure.
Bryan’s model should therefore be judged on the right questions:
- Are the local marginals no-signalling?
- Are the local detector interactions genuinely local?
- Is the quaternion/bivector event structure mathematically coherent?
- Does the program generate the claimed correlations without smuggling in the answer?
Those are real questions. But merely saying “it does not provide (A_0,A_1,B_0,B_1) on one reusable (\lambda)” does not refute the ontology. It only says that Bryan has rejected the scalar replay architecture Bell assumes.
In short: Bell-factorization is the judge of Bell-factorization. It is not automatically the judge of locality itself.
To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/6B3696FB-7412-40A2-902C-B7C387B69D8E%40gmail.com.
Mark Hadley
Parker Emmerson
Mark Hadley
Richard Gill
Bryan Sanctuary
- A bivector spin has a classical origin as a spinning bivector
- This gives a BFF where it spins and a LFF where we watch: from the LFF, spin is a blur of intrinsic angular momentum because we cannot see inside the BFF.
- The bivector spins so fast there is NO polarization present. The solution is simply a quaternionic rotor
- The singlet state in the BiSM is the identity in R^3. Alice and Bob states are the product of two quaternions and when they separate, they carry a common phase: I= exp(i\lambda Y)exp(-i\lambda Y).
- However, in the single, there is no lambda but when they separate, one goes L and the other R, then they each carry a compensating phase, \lambda.
- That phase is always present between A and B and gives long range correlation. Neither A nor B know
- The phase is a Lorentz scalar, and the same in all frames.
- When the bivector approaches a field, the correlation is calculated and give the following product of two quaternions:
- You see the fields with angles _a and _b are instantiated at A and B. There is no nonlocality. The two planes are (theta_a - \lambda) and (theta_b - \lambda).
- Here, finally, is the reason Bell cannot describe the above: the particles arrive as quaternions at the detectors and are converted to Boolean clicks: Bell is applicable and we get the inverted triangle and CHSH = 2
- However, there is more. Why do we get the cosine? It is because of \lambda and you guys do not have it in Bell's work. Consider this:
- A and B choose their field settings randomly using _a and _b. However, in general that means that two instantiated planes (theta_a - \lambda) and (theta_b - \lambda) are in DIFFERENT geometric environments depending on how close the settings are to \lambda. Now it turns out that when they are close, the correlation contains different numbers of particles to when the difference is large (N_even and N_odd differ with (a-b).
- I have shown that depending on the orientation of those planes, the geometric environment is pol or coh. Then, everytime you change settings, you get a different number of clicks than other settings.
- ONLY after the experiment, post analysis, and A and B bins are compared, is the violation observed.
- The phase correlation extends over the dimensions of the apparatus.
1. Sanctuary, B. Quaternion Spin. Mathematics 2024, 12, 1962. https://doi.org/10.3390/math12131962
2. Sanctuary, B. Spin Helicity and the Disproof of Bell’s Theorem. Quantum Rep. 2024, 6, 436–441. https://doi.org/10.3390/quantum6030028
3. Sanctuary, B. EPR Correlations Using Quaternion Spin. Quantum Rep. 2024, 6(3), 409-425; https://doi.org/10.3390/quantum6030026
4. Sanctuary, B. The Classical Origin of Spin: Vectors Versus Bivectors. Axioms 2025, 14, 668. https://doi.org/10.3390/axioms14090668
5. Sanctuary, B. The Fine-Structure Constant in the Bivector Standard Model. Axioms 2025, 14, 841. https://doi.org/10.3390/axioms14110841
6. Sanctuary, B. The Zitterbewegung in the Bivector Standard Model. Axioms 2026, 15, 116. https://doi.org/10.3390/axioms15020116
7. Sanctuary, B. The Double-Slit Experiment in the Bivector Standard Model. Axioms 2026, 15(6), 417; https://doi.org/10.3390/axioms15060417
Bryan Sanctuary
Mark Hadley
Bryan Sanctuary
Richard Gill
Mark Hadley
Bryan Sanctuary
Mark Hadley
Bryan Sanctuary
Richard Gill
Richard Gill
Richard Gill
A bivector spin has a classical origin as a spinning bivector
This gives a BFF where it spins and a LFF where we watch: from the LFF, spin is a blur of intrinsic angular momentum because we cannot see inside the BFF.
The bivector spins so fast there is NO polarization present. The solution is simply a quaternionic rotorThe singlet state in the BiSM is the identity in R^3. Alice and Bob states are the product of two quaternions and when they separate, they carry a common phase: I= exp(i\lambda Y)exp(-i\lambda Y).
However, in the single, there is no lambda but when they separate, one goes L and the other R, then they each carry a compensating phase, \lambda.
That phase is always present between A and B and gives long range correlation. Neither A nor B know.
The phase is a Lorentz scalar, and the same in all frames.
When the bivector approaches a field, the correlation is calculated and give the following product of two quaternions:
You see the fields with angles _a and _b are instantiated at A and B. There is no nonlocality. The two planes are (theta_a - \lambda) and (theta_b - \lambda).
Here, finally, is the reason Bell cannot describe the above: the particles arrive as quaternions at the detectors and are converted to Boolean clicks: Bell is applicable and we get the inverted triangle and CHSH = 2
However, there is more. Why do we get the cosine? It is because of \lambda and you guys do not have it in Bell's work. Consider this:A and B choose their field settings randomly using _a and _b. However, in general that means that two instantiated planes (theta_a - \lambda) and (theta_b - \lambda) are in DIFFERENT geometric environments depending on how close the settings are to \lambda. Now it turns out that when they are close, the correlation contains different numbers of particles to when the difference is large (N_even and N_odd differ with (a-b).
I have shown that depending on the orientation of those planes, the geometric environment is pol or coh. Then, everytime you change settings, you get a different number of clicks than other settings.ONLY after the experiment, post analysis, and A and B bins are compared, is the violation observed.The phase correlation extends over the dimensions of the apparatus.It is a long distance phase effect that is the origin of the violation.
On 7 Jun 2026, at 15:40, Bryan Sanctuary <bryancs...@gmail.com> wrote:
Bryan Sanctuary
What, in mathematical terms, is \lambda, what is Y?
I am afraid the rest of your points are just aimless rambling which I cannot correct, or even see relevance. Just a waste of time too, since you do not read my replies. There is nothing conjured or invented in what I do. You must just learn a bit of GA, think more geometrically and not in terms of abstract vectors of QM.
Richard Gill
On 7 Jun 2026, at 19:00, Bryan Sanctuary <bryancs...@gmail.com> wrote:
Richard,
Your questions just show me you have not even tried to understand. Your ideas are too entrenched in your mind to accept alternatives/My one reply
What, in mathematical terms, is \lambda, what is Y?lambda is a LHV, and is geometrically the phase carried by A and B, Y is the direction of linear momentum of the particles. Both are clearly defined in my papers etc.
I am afraid the rest of your points are just aimless rambling which I cannot correct, or even see relevance. Just a waste of time too, since you do not read my replies. There is nothing conjured or invented in what I do. You must just learn a bit of GA, think more geometrically and not in terms of abstract vectors of QM.You ask a lot about a phase: it is simply the phase of the Geometric Product (clearly in my paper again)I do not need you to lecture me on how the experiments are done. I understand them, BUT you are not willing to understand instantiation.Recall this:
<image.png>The Bivector Standard Model does just thatBryan
On Sun, Jun 7, 2026 at 11:39 AM Richard Gill <gill...@gmail.com> wrote:
Bryan, you asked for my comments on your bulleted points. I have three questions and four commentsA bivector spin has a classical origin as a spinning bivectorThis gives a BFF where it spins and a LFF where we watch: from the LFF, spin is a blur of intrinsic angular momentum because we cannot see inside the BFF.The bivector spins so fast there is NO polarization present. The solution is simply a quaternionic rotorThe singlet state in the BiSM is the identity in R^3. Alice and Bob states are the product of two quaternions and when they separate, they carry a common phase: I= exp(i\lambda Y)exp(-i\lambda Y).What, in mathematical terms, is \lambda, what is Y?However, in the single, there is no lambda but when they separate, one goes L and the other R, then they each carry a compensating phase, \lambda.“In the single”, what does that mean?That phase is always present between A and B and gives long range correlation. Neither A nor B know.The phase is a Lorentz scalar, and the same in all frames.The phase, is that is the “I” you just defined in terms of \lambda and Y?
But I don’t know what they are.
When the bivector approaches a field, the correlation is calculated and give the following product of two quaternions:
<cid:ii_mq3qtmxd5.png>
Richard Gill
Sent from my iPad
Bryan Sanctuary
PLEASE read
Richard Gill
Ugh RIchard, you say "I do not find them (lambda and Y) clearly, *mathematically*, defined in your papers. Please take the trouble to define them again, here."Gimma a break, you never looked at the papers. you really must look at the papers:I do not call lambda a HV in the paper, but it is in Bell's sense. It is the common phase between A and B at the source: (clearly defined)Here \lambda is \theta
<image.png><image.png>
The coordinate $Y$ is defined
<image.png><image.png>
Richard Gill
On 7 Jun 2026, at 19:00, Bryan Sanctuary <bryancs...@gmail.com> wrote:
Richard,
Your questions just show me you have not even tried to understand. Your ideas are too entrenched in your mind to accept alternatives/My one reply
What, in mathematical terms, is \lambda, what is Y?lambda is a LHV, and is geometrically the phase carried by A and B, Y is the direction of linear momentum of the particles. Both are clearly defined in my papers etc.
I am afraid the rest of your points are just aimless rambling which I cannot correct, or even see relevance. Just a waste of time too, since you do not read my replies. There is nothing conjured or invented in what I do. You must just learn a bit of GA, think more geometrically and not in terms of abstract vectors of QM.You ask a lot about a phase: it is simply the phase of the Geometric Product (clearly in my paper again)I do not need you to lecture me on how the experiments are done. I understand them, BUT you are not willing to understand instantiation.Recall this:
<image.png>The Bivector Standard Model does just thatBryan
On Sun, Jun 7, 2026 at 11:39 AM Richard Gill <gill...@gmail.com> wrote:
Bryan, you asked for my comments on your bulleted points. I have three questions and four commentsA bivector spin has a classical origin as a spinning bivectorThis gives a BFF where it spins and a LFF where we watch: from the LFF, spin is a blur of intrinsic angular momentum because we cannot see inside the BFF.The bivector spins so fast there is NO polarization present. The solution is simply a quaternionic rotorThe singlet state in the BiSM is the identity in R^3. Alice and Bob states are the product of two quaternions and when they separate, they carry a common phase: I= exp(i\lambda Y)exp(-i\lambda Y).What, in mathematical terms, is \lambda, what is Y?However, in the single, there is no lambda but when they separate, one goes L and the other R, then they each carry a compensating phase, \lambda.“In the single”, what does that mean?That phase is always present between A and B and gives long range correlation. Neither A nor B know.The phase is a Lorentz scalar, and the same in all frames.The phase, is that is the “I” you just defined in terms of \lambda and Y?
But I don’t know what they are.
When the bivector approaches a field, the correlation is calculated and give the following product of two quaternions:
<cid:ii_mq3qtmxd5.png>
Bryan Sanctuary
Richard Gill
Richard Gill
On 7 Jun 2026, at 20:50, Bryan Sanctuary <bryancs...@gmail.com> wrote:
Parker Emmerson
Parker Emmerson
Richard Gill
Parker Emmerson
Richard Gill
If Richard translates that as “nonlocal hidden variable theory,” he has not refuted the structure; he has relabeled every non-factorized local/contextual model as nonlocal by definition.
The burden then is on him to show actual marginal dependence, , not merely failure of Bell factorization.
Mark Hadley
Parker Emmerson
Mark Hadley
Richard Gill
>
> I think your answer is yes to both. that makes it non local because the setting at B may not have been decided when A takes a reading.
Parker Emmerson
- Dear Mark,
- The entire error is that you keep laundering an interpretive premise through the word “nonlocal.” Gill replay proves that PV-REC is not a Bell-scalar spreadsheet. It does not prove signalling, source-setting conspiracy, cross-wing dynamical influence, or failure of local marginals. It proves only that PV-REC refuses the global Boolean counterfactual ledger (A_0,A_1,B_0,B_1). But that refusal is the theory’s stated ontology, not a discovered defect. If you define locality as Bell-scalar replay, then of course everything outside Bell-scalar replay is “nonlocal”; but then the conclusion is won by definition. The real question is whether definite local records, preparation independence, no-signalling marginals, and cross-wing microcausality logically force Bell-scalar replay. You have not shown that. You simply keep assuming it. Bell’s theorem kills scalar replay. It does not kill every no-signalling boundary-event ontology. PV-REC rejects the ledger, not locality.
- You must admit Gill replay tests only Bell-scalar replay.
- You must admit no-signalling is not violated.
- You must admit preparation independence is preserved.
- You must admit cross-wing microcausality can hold.
- Then the only thing left is their interpretive move: [ \neg \BellScalarSep \Rightarrow \text{nonlocality}. ]
- And that is exactly the premise PV-REC contests.
- Why don't you go ahead and try to defend your hidden premise instead of letting hiding behind Bell’s algebra?
Mark Hadley
Richard Gill
Parker Emmerson
Mark Hadley
Parker Emmerson
Dear Mark,
You can do one more thing: distinguish the mathematical condition from the physical conclusion you attach to it. I agree that A(a, λ), B(b, λ), no-signalling, CHSH, and related terms are standard. I am not objecting to the vocabulary itself. I am objecting to the slide from the standard mathematical condition X = X_A(a, λ), Y = Y_B(b, λ), to the physical verdict that anything not of that form is therefore nonlocal.
The condition A(a, λ), B(b, λ) is not a neutral synonym for locality. It is Bell scalar separability, and it is exactly the condition PV-REC denies. So to your simple question — can PV-REC give Bob’s hidden same-source replay value as Y = Y_B(b, λ₀), without Alice’s context? — the answer is no. If it could, PV-REC would be a Bell-scalar replay model, and CHSH would give S ≤ 2. I agree with that completely.
But the operational question is different: does Bob’s local observable distribution depend on Alice’s setting? No. PV-REC has P_B(y ∣ a, b) = P_B(y ∣ b), and similarly P_A(x ∣ a, b) = P_A(x ∣ a). In the singlet sector, the local marginals are exactly 1/2 on each side. Thus, failure of Y_B(b, λ₀) replay does not equal operational signalling.
PV-REC says the completed event is Λᶜᵒᵐᵖ_ab = (λ₀, ℬ_A(a), ℬ_B(b)), and the performed outcome is (X, Y) = K_ab(λ₀). That is not Bell scalar replay, and it was never claimed to be. So yes, in your standard language, PV-REC is not Bell-scalar-separable. But calling that “nonlocal” adds an interpretation: it defines physical locality as Bell scalar separability, then declares every failure of Bell scalar separability “nonlocal.” That is the definitional purchase I am objecting to.
Theoretical physicists also use “locality” in other standard senses: operational no-signalling, local commutation or microcausality in QFT, local detector records, local interaction terms, and so on. Bell scalar separability is one formal locality condition, not the word’s sole legitimate meaning. So I am not asking you to adopt private language. I am asking you not to let one standard formalism monopolize a physical word.
Bell proves BellScalarSep ⇒ S ≤ 2. PV-REC denies RealEvent + NoSignal + preparation independence + microcausality ⇒ BellScalarSep. That is the issue.
Best,
Parker
Richard Gill
Mark Hadley
From: Parker Emmerson <powerin...@gmail.com>
Date: Mon, 8 Jun 2026, 13:53
Subject: Re: [Bell_quantum_foundations] Bell Experiments and the Two-Slit Experiment
To: Mark Hadley <sunshine...@googlemail.com>
Cc: Richard Gill <gill...@gmail.com>, Bryan Sanctuary <bryancs...@gmail.com>, Austin Fearnley <ben...@hotmail.com>, Bell inequalities and quantum foundations <Bell_quantum...@googlegroups.com>
Dear Mark,
You can do one more thing: distinguish the mathematical condition from the physical conclusion you attach to it. I agree that A(a, λ), B(b, λ), no-signalling, CHSH, and related terms are standard. I am not objecting to the vocabulary itself.
*** GREAT
I am objecting to the slide from the standard mathematical condition X = X_A(a, λ), Y = Y_B(b, λ), to the physical verdict that anything not of that form is therefore nonlocal.
*** This puzzles me.
ObviouslyX = X_A(a,b, λ) is non local. I hope we agree on that.
Similarly X = X_A(a, λ(b)) is non local. Agreed?
The value of X must be + or - otherwise it cannot explain an individual event.
What is left? A is any function at all of any valiables \lambda from any parameter space at all.
The condition A(a, λ), B(b, λ) is not a neutral synonym for locality.
*** not sure what that means.
It is Bell scalar separability, and it is exactly the condition PV-REC denies. So to your simple question — can PV-REC give Bob’s hidden same-source replay value as Y = Y_B(b, λ₀), without Alice’s context? — the answer is no.
*** Great, you say the results at B depend in some way on the settings at A. That is clear. I thought that is what you are saying. Yes that is what scientists mean by non local. It also means you cannot explain the result at B even though it is measured and recorded before Alice's context is known. It makes the work rather inadequate in that it cant explain results at B. And rather unremarkable if it explains them knowing Alice's settings. This is what physicists call a non local hidden variable theory.
But the operational question is different: does Bob’s local observable distribution depend on Alice’s setting? No. PV-REC has P_B(y ∣ a, b) = P_B(y ∣ b), and similarly P_A(x ∣ a, b) = P_A(x ∣ a). In the singlet sector, the local marginals are exactly 1/2 on each side. Thus, failure of Y_B(b, λ₀) replay does not equal operational signalling.
*** Great, I disagree about that being the operatinal question. The question is about getting the correlation from individual results. The independnece of Bob's distribution is not generally an issue. It is inevitable independent for a local theory. It is also indpendent fro QM. It is essentially the smae as no-signalling I believe. No signalling is a separate property from non-local. Im not familiar with all the results. Bell does not say anything about no signaling as far as I know.
PV-REC says the completed event is Λᶜᵒᵐᵖ_ab = (λ₀, ℬ_A(a), ℬ_B(b)), and the performed outcome is (X, Y) = K_ab(λ₀). That is not Bell scalar replay, and it was never claimed to be.
*** I dont recognise that language.
So yes, in your standard language, PV-REC is not Bell-scalar-separable.
**** No that is not my language.
But calling that “nonlocal” adds an interpretation: it defines physical locality as Bell scalar separability, then declares every failure of Bell scalar separability “nonlocal.” That is the definitional purchase I am objecting to.
*** You use fancy words. We say it is nonlocal if the resutls at A cannot be determined without knowing the settings at B. Its hardly a remarkable or novel phrase/definition. It is by the way applicable to a theory that predicts results at A and B. I fully admit that apllying outside that context may warrant more care.
Theoretical physicists also use “locality” in other standard senses: operational no-signalling, local commutation or microcausality in QFT, local detector records, local interaction terms, and so on.
*** deiffernet terms are used in those cases.
Bell scalar separability
*** I dont recognise that term.
Parker Emmerson
Bryan’s BiSM proposal is useful precisely because it makes the same fault line visible in a different language. In Bryan’s contextual-instantiation paper, the pre-detection object is not a Boolean instruction value but a quaternionic rotor. Alice and Bob do not begin with pre-existing scalar answers (A(a,\lambda)), (B(b,\lambda)). They begin with a common phase structure and local instantiated planes. In his notation, the local phases are (ϕ_A = a − θ) and (ϕ_B = b − θ), and the relative rotor product is (Q_{AB} = Q_A Q_B^{-1}), with scalar part (cos(a−b)). That is not a Bell table. It is a pre-Boolean relational geometry whose observable statistical content appears only after the pair relation is formed.
This is also completely explicit in Bryan’s Fortran code. In the quaternion lane, the code does not locally generate Alice’s outcome from (a) and (θ), and Bob’s outcome from (b) and (θ), and then average the product. It forms the relative scalar first: (ϕ_A = a − θ), (ϕ_B = b − θ), so (ϕ_A − ϕ_B = a − b), and then (scalarAB = −cos(a−b)) in the singlet convention. It then sets (P_{same} = (1 + scalarAB)/2) and samples a same/opposite Boolean event. That reproduces the singlet product statistics, but it is not a separated Bell response mechanism. It is a pair-context probability sampler written in quaternion language.
So Richard is right about one narrow thing: Bryan’s current quaternion product code is not a Bell-local hidden-variable model in the separated scalar sense. It does not provide (X = X_A(a,λ)), (Y = Y_B(b,λ)). But Richard’s further rhetorical move — “therefore nonlocal” — again only follows if “nonlocal” has been defined to mean “not Bell scalar replay.” The code shows that Bryan is not filling Bell’s ledger. It does not by itself show a physical signal from Alice to Bob or Bob to Alice.
This is where Bryan’s work and PV-REC fit together naturally. Bryan supplies the pre-Boolean geometric compatibility layer. PV-REC supplies the event-completion and actualization layer. Bryan’s quaternionic phase geometry explains why the pair-context compatibility has a (cos(a−b)) dependence. PV-REC then treats that compatibility not as a Bell-local response function, but as a candidate event weight. In the singlet sector the compatibility kernel is (m_{xy}(a,b) = 1/4(1 − xy cos(a−b))). PV-REC assigns an event-action barrier (I_{xy} = −log(m_{xy})), rescales it by (κ(v) = √(1 − v²/c²)), and produces the event susceptibility (m_{xy}^{κ(v)}). After constant-flux normalization, the actual event law is (P_{PV}(x,y ∣ a,b,v) = m_{xy}(a,b)^{κ(v)} / Σ_{x′y′} m_{x′y′}(a,b)^{κ(v)}). At (v = 0), this reduces to the ordinary singlet law. For fixed (v ≠ 0), it predicts a non-Born angular deformation.
Thus the combined BiSM/PV-REC reading is not: “Bryan has produced a Bell-local hidden-variable model.” He has not. The better reading is: Bryan has produced a candidate quaternionic source-phase geometry for the pre-Boolean compatibility structure, and PV-REC turns such a compatibility structure into a no-signalling boundary-event actualization law. The combined model is not Bell replay. It is a contextual source-absorber event-completion theory.
This also answers whether Bryan “solves EPR.” If “solve EPR” means “produce separated scalar response functions (A(a,λ)), (B(b,λ)) reproducing (−cos(a−b)),” then no. Bell already rules that out. But if “solve EPR” means “supply a realist account in which performed outcomes are definite, no operational signal passes between wings, and the correlation arises from a real pre-Boolean phase/boundary structure rather than from a mysterious collapse signal,” then Bryan’s work points in the right direction — provided it is not misdescribed as Bell-local scalar hidden variables.
The precise correction is this: Bryan should not say Bell’s theorem is disproved. Bell’s scalar theorem is not disproved. What Bryan’s model challenges is the assumption that the only possible realist completion must be a Boolean ledger of source-side counterfactual outcomes. His rotor construction says the thing transported from the source is not a list of Boolean answers but a geometric phase structure. PV-REC then says that the final event is not an emission-time scalar instruction being read out, but a completed boundary event.
Richard’s replay audit will therefore classify Bryan’s code as not Gill-replay-admissible. That is expected. But the audit should not be overread. In a boundary-event or rotor-instantiation ontology, changing (a) or (b) changes the boundary context. It is not the same completed event being replayed under a different label. Demanding that the same source phase generate all four counterfactual scalar outputs is exactly the Bell ledger demand. Bryan’s construction refuses that demand by geometry; PV-REC refuses it by event ontology.
Mark’s objection that “the result at B depends on A” is therefore too crude. In the Bell scalar replay sense, yes: there is no (Y_B(b,λ)) that survives all Alice contexts. But in the operational sense, Bob’s local distribution does not depend on Alice’s setting. The combined BiSM/PV-REC model says: Bob’s local record is real, but the completed pair event is not decomposable into two pre-existing scalar answers. The pair event has a relational geometry. That is not a signal. It is a refusal to replace the geometry by a spreadsheet.
There is also a small but important sign issue in Bryan’s text. In one place the scalar component is written as (S(a,b) = cos(a−b)) with (P_{same} = (1+S)/2), which gives the positive cosine convention. The singlet requires (E(a,b) = −cos(a−b)). The code appears to use the singlet sign by taking (scalarAB = −cos(a−b)). That sign convention should be made explicit, but it is not the foundational issue. The foundational issue is whether the quaternion product is being treated as a Bell-local mechanism or as a pair-context compatibility.
So the clean synthesis is: BiSM supplies quaternionic phase compatibility; PV-REC supplies boundary-event completion. Together they do not “beat Bell” inside Bell’s own scalar replay class. They reject the scalar replay class as the wrong ontology for spin correlations. Bell kills the ledger. It does not kill every realist no-signalling boundary-event account.
Richard’s phrase “classical local causality” is useful only if it is treated as a label for Bell’s separated scalar response condition, not as a settled definition of locality itself. I will therefore state the point neutrally. PV-REC is not in the Bell/Gill separated scalar replay class. It does not assert that there exist functions X = X_A(a, λ) and Y = Y_B(b, λ), with one setting-independent source record λ carrying all counterfactual outcomes. If a model has that structure, then CHSH follows and S ≤ 2. I do not dispute that. What I dispute is the identification of that structure with locality itself.
Mark, you say that X = X_A(a,b,λ) is “obviously” nonlocal. But that is only obvious if “nonlocal” has already been defined to mean “not expressible as X_A(a,λ).” Then the conclusion is built into the definition. The physical questions are more specific: does Bob receive a controllable signal from Alice? Does Bob’s local marginal distribution depend on Alice’s setting? Does the source distribution depend conspiratorially on later settings? Does the model violate cross-wing microcausality? PV-REC says no to all of these. It assumes preparation independence, P(λ₀ ∣ a,b) = P(λ₀). It assumes definite performed outcomes, (X,Y) ∈ {±1}². It preserves operational no-signalling, P_A(x ∣ a,b) = P_A(x ∣ a) and P_B(y ∣ a,b) = P_B(y ∣ b). In the singlet sector, the local marginals are exactly 1/2 on both sides.
What PV-REC rejects is the claim that the preparation-side source record λ₀ is already the complete Bell screening variable. The completed event is not λ₀ alone. The completed event is Λᶜᵒᵐᵖ_ab = (λ₀, ℬ_A(a), ℬ_B(b)), and the actual event is (X,Y) = K_ab(λ₀). So yes: if you demand a hidden same-source replay value Y = Y_B(b,λ₀) for Bob independently of Alice’s realized boundary context, PV-REC says no. That object is not part of the ontology. But if you ask whether Bob has an actual local record distribution independent of Alice’s setting, the answer is yes: P_B(y ∣ a,b) = P_B(y ∣ b). Those are different claims.
You also say that this means PV-REC cannot explain Bob’s result when Bob’s result is measured and recorded before Alice’s context is known. That objection assumes precisely what PV-REC denies: that explanation must be a forward-only computation from an emission-side scalar λ₀ to Bob’s local outcome. PV-REC is not a source-to-detector instruction model. It is a boundary-event completion model. The completed event is a four-dimensional source-absorber object, not an emission-time answer sheet. In a spacelike Bell experiment, frame-dependent “before” and “after” ordering cannot be the foundation of the explanation. In one Lorentz frame Bob is first; in another Alice is first. PV-REC does not pick one of those frame-dependent orderings and turn it into a hidden mechanism. The explanatory object is the completed boundary context.
So the correct statement is not: “Bob’s result is unexplained unless Alice’s setting is locally known at Bob.” The correct statement is: “Bob’s result is not explained by a Bell-style source-only scalar replay function Y_B(b,λ₀). It is explained as one component of the completed boundary event K_ab(λ₀).” That is exactly the distinction. You can reject that ontology, but replay failure alone does not refute it. It only says the ontology is not a Bell scalar replay ontology.
The separated scalar response condition requires much more than locality per se. It requires that the same source record λ carry all unperformed counterfactual outcomes A₀(λ), A₁(λ), B₀(λ), B₁(λ). It requires one Kolmogorov probability space for mutually exclusive measurement contexts. It requires emission-time completeness. It requires same-source replay. It requires scalar screening-off. It requires that the actual joint event be decomposable into two separated scalar functions. None of that follows merely from local records, no-signalling, preparation independence, or microcausality.
Once that table is granted, CHSH is arithmetic: A₀B₀ + A₀B₁ + A₁B₀ − A₁B₁ = A₀(B₀ + B₁) + A₁(B₀ − B₁), and because B₀ and B₁ are each ±1, the value is always ±2. Averaging gives S ≤ 2. That proof is fine. The mistake is promoting the table from a classical model assumption into the definition of physical locality. The table is not discovered by locality; it is installed as the formal meaning of locality. PV-REC challenges that installation, not the arithmetic.
Bell proves: separated scalar response condition ⇒ S ≤ 2. He does not prove: definite performed outcomes + no-signalling + preparation independence + microcausality ⇒ separated scalar response condition. That second implication is the bridge PV-REC denies. If you want to call every failure of separated scalar replay “nonlocal,” then fine, but then “nonlocal” means only “outside the Bell scalar replay class.” It does not by itself establish a physical superluminal signal, a source-setting conspiracy, or an operational dependence of Bob’s statistics on Alice’s setting.
This is also why no-signalling is not a distraction. Of course no-signalling is distinct from Bell replay. That is the point. PV-REC lives exactly in that distinction. It says that Bell replay can fail while operational no-signalling remains exact. So saying “no-signalling is separate from nonlocality” does not answer the argument; it confirms that the word “nonlocality” is carrying an extra convention beyond the operational facts.
The answer to the EPR issue is therefore straightforward. EPR infers that if Alice can predict Bob’s result with certainty without disturbing Bob, then Bob’s corresponding value must be an element of reality. PV-REC accepts definite performed outcomes and perfect same-setting anti-correlation. What it rejects is the additional step that Bob’s element of reality must be an emission-time scalar value belonging to Bob alone and jointly existing for all possible measurement settings. In PV-REC, the real event is the completed source-absorber boundary event. Actual performed outcomes are real. Unperformed counterfactual settings are not all jointly scalarized on the same source record.
So the disagreement is not about whether CHSH follows from X_A(a,λ), Y_B(b,λ). It does. The disagreement is whether physical locality is exhausted by that representation. PV-REC says no. Bell’s scalar response framework is not wrong as mathematics. It is wrong only when treated as though it exhausts locality itself. It is a classical scalar implementation of locality, not locality without remainder.
PV-REC rejects Bell’s scalar ledger. It does not reject local records, preparation independence, microcausality, or no-signalling. It gives definite performed outcomes, not a global table of unperformed outcomes.
Best,
Parker
Richard Gill
I think you are missing the point.
There already exist numerous realist completions. Bohmian mechanics is a realist completion of quantum mechanics. But it is non-local. Superdeterminism and retrocausality are paths to find realist completions.
Bell’s concerns were that all completions seem to be non-local (or worse!), and in my opinion, his concept of local causality nailed that. The thing is, physicists were not only looking for locality, but also for causal mechanisms. They were looking for classicality.
Bryan needs to get into his head that his BiSM violates classicality. I doubt it will catch on.
I agree, it is useful because it neatly illustrates the dimemma which the world presents to us.
To me, PV-REC looks like a device for obscuring the wood by planting far too many trees all over the place. A comfort blanket. Lipstick on a pig, perhaps. I doubt it will catch on.
But what the hell, everyone has their own hammer, and is looking for ways to use it. Diversity is wonderful. Thank heavens we don’t all think alike. Let a thousand flowers bloom.
Richard
Sent from my iPad
Richard Gill
You have constructed your own elaborate bureaucratisation. It provides you convenient labels in order to denounce those whom you see as enemies of the people.
Counterfactual outcomes are not real! They are part of thought experiments. They are science fiction, or science fantasy even.
Parker Emmerson
Here is the whole refutation compressed:
BellScalarSep ⇒ |S| ≤ 2
But quantum/no-signalling correlations satisfy:
RealEvent + PrepInd + NoSignal + |S| = 2√2
Therefore:
RealEvent + PrepInd + NoSignal ⇏ BellScalarSep
So your bridge is false.
The theorem survives. The overreach fails.... sorry Richard.
Mark Hadley
Parker Emmerson
I agree that merely replacing Bell local causality with no-signalling would not be enough. That is not the claim.
The claim is narrower: no-signalling, definite performed outcomes, and preparation independence do not logically imply Bell scalar replay. Bell proves that Bell scalar replay implies CHSH. PV-REC accepts that. PV-REC denies that λ₀ alone is a complete screening variable carrying a same-source table A₀(λ₀), A₁(λ₀), B₀(λ₀), B₁(λ₀).
Alice’s local record does not need Bob’s setting. Alice gets X ∈ {±1}, with P_A(x ∣ a, b) = P_A(x ∣ a). What depends on the joint context is the completed correlation event, not Alice’s local marginal record.
So if “model for EPR” means “Bell-scalar-separable model,” then PV-REC is not one. That is admitted. But that is not a refutation; it is the point. The question is whether failure of Bell scalar replay is identical to physical nonlocal influence, or whether it is failure of a specific classical screening condition.
The answer is: failure of Bell scalar replay is certainly failure of Bell local causality, but it is not identical to operational signalling or to a controllable superluminal influence. If one defines physical locality as Bell local causality, then one will call the failure “nonlocal.” PV-REC rejects that definition. It treats the failure as the failure of a specific classical screening/replay condition, while preserving local performed records, preparation independence, and operational no-signalling.
So anyone who wants to be technically careful here should not treat the word “nonlocal” as the end of the inquiry. The right conclusion is that Bell scalar replay fails. Whether that failure corresponds to a physical superluminal influence, a failure of classical screening, or some deeper context-completion structure is not settled by the label itself.
That is why a full experimental and technological investigation matters. If PV-REC is wrong, then sharper tests should expose it. If it is right, then improved event-level recording, timing control, detector-context characterization, and correlation reconstruction may reveal structure that the standard scalar replay vocabulary simply discards. Either way, the technically correct position is not to end the discussion by definition, but to ask what new measurements would actually distinguish the possibilities.
Mark Hadley
I agree that merely replacing Bell local causality with no-signalling would not be enough. That is not the claim.
The claim is narrower: no-signalling, definite performed outcomes, and preparation independence do not logically imply Bell scalar replay. Bell proves that Bell scalar replay implies CHSH. PV-REC accepts that. PV-REC denies that λ₀ alone is a complete screening variable carrying a same-source table A₀(λ₀), A₁(λ₀), B₀(λ₀), B₁(λ₀).
Alice’s local record does not need Bob’s setting. Alice gets X ∈ {±1}, with P_A(x ∣ a, b) = P_A(x ∣ a). What depends on the joint context is the completed correlation event, not Alice’s local marginal record.
So if “model for EPR” means “Bell-scalar-separable model,”
then PV-REC is not one. That is admitted. But that is not a refutation; it is the point. The question is whether failure of Bell scalar replay is identical to physical nonlocal influence, or whether it is failure of a specific classical screening condition.
The answer is: failure of Bell scalar replay is certainly failure of Bell local causality, but it is not identical to operational signalling or to a controllable superluminal influence. If one defines physical locality as Bell local causality, then one will call the failure “nonlocal.” PV-REC rejects that definition.
It treats the failure as the failure of a specific classical screening/replay condition, while preserving local performed records, preparation independence, and operational no-signalling.
So anyone who wants to be technically careful here should not treat the word “nonlocal” as the end of the inquiry. The right conclusion is that Bell scalar replay fails. Whether that failure corresponds to a physical superluminal influence, a failure of classical screening, or some deeper context-completion structure is not settled by the label itself.
That is why a full experimental and technological investigation matters.
Richard Gill
Richard Gill
On 9 Jun 2026, at 19:23, Mark Hadley <sunshine...@googlemail.com> wrote:
Richard Gill
Richard Gill
Parker Emmerson
Bell’s theorem is not an unconditional theorem. It does not say that any possible account of EPR correlations must satisfy CHSH. It says that if Bell-local factorizability, or Bell scalar replay, holds, then CHSH follows. Therefore, when experiments violate CHSH, the direct conclusion is the failure of that conditional screening structure. It does not, by algebra alone, prove operational signalling, a controllable superluminal influence, or the uniqueness of the standard quantum explanation. Those further conclusions depend on identifying physical locality with Bell local causality.
The point does not depend on quantum mechanics as a special mystery. Quantum correlations are one physically realized example, but the general mathematical fact is that no-signalling does not imply Bell factorizability. No-signalling says P_A(x ∣ a, b) = P_A(x ∣ a) and P_B(y ∣ a, b) = P_B(y ∣ b). Bell requires the stronger screening condition P(x, y ∣ a, b, λ) = P_A(x ∣ a, λ)P_B(y ∣ b, λ), or equivalently a same-source replay structure. Those are different mathematical requirements. Bell’s theorem is conditional on the stronger structure; it does not derive that structure from operational locality, preparation independence, or definite performed outcomes.
PV-REC enters exactly at that disputed step. It does not try to satisfy Bell-local scalar replay and then violate CHSH; that would be impossible. Instead, it rejects the claim that an EPR event must be represented by one setting-independent source variable λ₀ carrying all same-source responses A₀(λ₀), A₁(λ₀), B₀(λ₀), B₁(λ₀). PV-REC represents performed events as physically completed events, with the completed event indexed by the realized measurement context, not by λ₀ alone: Λᶜᵒᵐᵖ_ab = (λ₀, ℬ_A(a), ℬ_B(b)). Thus PV-REC preserves local performed records and operational no-signalling, but denies λ₀-complete Bell screening.
So the theorem survives as a conditional result. What fails is the over-reading. Bell plus experiment rules out Bell-scalar-separable completions of the relevant correlations. It does not, by algebra alone, prove that every failure of that screening condition is a controllable superluminal influence, nor that quantum mechanics is the only possible explanatory framework, nor that the observed phenomenon has been made conceptually transparent. Therefore, Bell neither successfully answered Einstein’s deeper locality challenge, nor demonstrated quantum mechanics as the only explanation, nor established a final explanation for the mystery PV-REC theorizes may not be as mysterious as Bell-theorem proponents make the observed phenomena out to be.