Bell's biggest mistake
Fred Diether
Eugen Muchowski
What was Bell's biggest mistake?
Bell proved that the predictions of quantum mechanics for polarization measurements on entangled particles cannot be determined by a model based on the assumption that quantum particles have fixed properties and are connected by a common parameter. From this, he concludes in his 1964 paper:
“In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements , without changing the statistical predictions , there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously , so that such a theory could not be Lorentz invariant.”
This is his biggest mistake, because his proof does not apply to models in which the particle properties depend on the position of the measuring instruments. There are local contextual models with hidden variables that reproduce the quantum correlations. However, many physicists concluded from Bell's theorem that nature is non-local. Theories were developed that claimed that the position of measuring instruments was somehow influenced (superdeterminism). This is reminiscent of ancient times when supernatural beings were believed to be responsible for the phenomena of nature. But this has nothing to do with physics.
There is another objection to Bell's proof: It relies on common parameters of the entangled particles. But this is impossible for entanglement swapping, in which particles are entangled that have never been in contact with each other before. A common parameter is therefore not a valid explanation for nature.
A model that describes the measurement results without hidden variables can be found at:
https://doi.org/10.5281/zenodo.15083468
Muchowski, E. (2025). On Superposition and Entanglement of Polarized Photons without Hidden Variables. International Journal of Quantum Foundations, 11(2), 185–190.
Mark Hadley
Can any of you Bell fans take a guess at what Bell's biggest mistake is?
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Jan-Åke Larsson
To this I agree.
He would have got a Nobel prize had he lived long enough, probably sooner than 2022.
Not that I know anything about these matters...
Best
Jan-Åke
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Jan-Åke Larsson
Professor, Head of Department
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GeraldoAlexandreBarbosa
The use of formalisms in Physics, like using Pauli operators, demands a strict understanding of the associations of operators with the entities or models one is trying to represent. Otherwise, one may find answers decoupled from any reality (I understand “reality” as model confirmed by repeated measurements).
Regarding your statement “In isotropy, the electron has mass only. It has no charge, no helicity”: It is “standard” knowledge that charge is invariant, which does not appear to be your point of view.
It is common knowledge that there are many experiments on the invariance of the electron charge. You are familiar with the Millikan oil-drop experiment, demonstrating that charges on the oil droplets are always in integer multiples of the electron charge. You may argue that oil droplets or the geometry involved in the experiment violates your assumption of “isotropy”.
Isotropy may be seen as a relative concept as well: if two electrons in free space are separated by kilometers, can it be assumed that each electron is in an isotropic condition?
In your view, in respect to what isotropy should be defined? Space, charge free region, electromagnetic field free, mass free? From what kind of interaction should your electron be free to be considered in an isotropic condition?
Furthermore, how could your idea be experimentally tested?
Consider this as well: An experiment that could falsify a model positing non-invariant electron charge (e.g., charge varying under Lorentz transformations or in different reference frames) is the precision measurement of atomic neutrality. In heavy atoms, electrons orbit at relativistic speeds while protons in the nucleus do not. Yet atoms remain electrically neutral to an extremely high degree of precision (better than 1 part in 10^21). If an electron charge is not Lorentz invariant, the effective charge of these fast-moving electrons would differ from that of the slower protons, leading to a net charge on the atom that would be detectable. However, this state is not observed. The above supports the standard invariant charge model and contradicts any non-invariant alternative.
More direct tests include hydrogen spectroscopy experiments comparing the 2S-1S transition frequencies in boosted frames (e.g., using high-precision optical clocks on moving platforms or in Earth's orbital motion), which probe electron boost invariance and have confirmed no violations to parts in 10^17. Any deviation would indicate charge non-invariance. Yet, none has been found.
Bryan, there is no issue with proposing models - but models must be experimentally confirmed and have repeatability in measurements to acquire the status of a “reality”.
Best,
Geraldo
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Fred Diether
Mark Hadley
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Richard Gill
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Eugen Muchowski
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Richard Gill
Richard Gill
On 7 Oct 2025, at 11:14, Eugen Muchowski <eu...@muchowski.de> wrote:
Eugen Muchowski
Muchowski, E., What connects entangled photons? International Journal of Quantum Foundations Volume 9, Issue 4, October 2023
https://ijqf.org/archives/category/all-volumes/volume-9-issue-4-october-2023
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Richard Gill
On 7 Oct 2025, at 17:25, Eugen Muchowski <eu...@muchowski.de> wrote:
Here is one:
Fred Diether
fred.d...@einstein-physics.org
Sent: Tuesday, October 7, 2025 3:46 PM
To: Fred Diether <fredi...@gmail.com>
Subject: Re: [Bell_quantum_foundations] Bell's biggest mistake
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Mark Hadley
Fred Diether
Mark Hadley
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Fred Diether
Alexandre de Castro
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Richard Gill
Richard Gill
On 8 Oct 2025, at 03:26, Fred Diether <fredi...@gmail.com> wrote:
That is NOT what I said. I am talking about described by a local QM theory.
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Alexandre de Castro
But I don’t need to bet... I can easily show that...and you just need to show where the error is.
Richard Gill
Eugen Muchowski
Dear Richard,
You have to think the other way around. It's not about refuting Bell's theorem, but about understanding nature. Bell's theorem only contributes to this insofar as it establishes that quantum correlations cannot be reproduced by non-contextual models.
It's not about replacing quantum mechanics with realistic models, but rather supplementing it, as EPR has demanded. One such supplement is Born's rule. Quantum mechanics therefore remains valid with its statements.
However, the formalism of quantum mechanics does not provide certain statements. It does not provide any information about whether, for example, measured values of polarization are already fixed before the measurement. This is the reason for the whole discussion about nonlocality. Therefore, we must take known phenomena into account when building models. It may be that our understanding of reality also needs to be adjusted.
In my 2025 paper, I proposed a useful supplement to quantum mechanics. Physically, it is based on the fact that indistinguishable particles can adopt a common polarization, which has been confirmed experimentally, for example, in the Mach-Zehnder interferometer. This applies to entangled photons and non-entangled photons in superposition as well. It is permissible to use physical insights from quantum mechanics to describe the phenomena. For example, from the conservation of spin angular momentum, it can be concluded that a Bell state is rotationally symmetric.
https://ijqf.org/wp-content/uploads/2025/03/IJQF2025v11n2p6.pdf
Muchowski, E. (2025). On Superposition and Entanglement of Polarized Photons without Hidden Variables. International Journal of Quantum Foundations, 11(2), 185–190.
Best regards,
Eugen
Jan-Åke Larsson
No Eugen.
You are claiming that, I quote: There are local contextual models with hidden variables that reproduce the quantum correlations. This statement is false.
You must either drop realism: that there is a more complete theory (in EPRs sense): one that provides (in your words) "information about whether, for example, measured values of polarization are already fixed before the measurement."
Or drop locality: that the local measurement outcome is independent of remote measurement inputs.
Local contextuality only allows the local measurement outcome to depend on the local setting, not the remote setting. Then you cannot reproduce known phenomena that by your own words "we must take ... into account when building models."
If you claim to reproduce the phenomena we see in experiment, your model must either be non-realist, or realist but nonlocal.
/Jan-Åke
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Austin Fearnley
So you are somewhat suspicious in some respect of the information theoretical principle paper workings?
Mark Hadley
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Austin Fearnley
(Note: you replied to me but not to the group.)
I already knew that you would be sure of winning the bet, but the paper you gave a link to could worry me w.r.t physics, maybe.
QM is IMO non-local as it uses singlet terms such as |1.up 2.down> - |1.down 2.up> for the joint state of polarisation of two entangled particles. Weighting factor ignored. I do not see how that term can work legitimately without using non-locality and/or contravening special relativity.
The linked paper appears (I have skimmed through it) to avoid using non-locality, implying perhaps that there may be a non-local way to achieve the QM correlations. It would take me too many ages to understand the paper. I followed Susskind's online 'theoretical minimum' courses and in one lecture he said his courses were good for (old) people who do not have much time (left!).
The implication of the linked paper is that there could be a local realist method giving the QM correlations which would mean that there is no need to aim for local non-realist methods. https://arxiv.org/abs/0905.2292
There can of course be more than one upper bound, and just because one proves (using locality) an upper bound of 0.707 does not mean that there cannot be simultaneously be a second upper bound of 0.5. So I will not feel the need to try to get to grips with the paper. At school I was keen on pure maths and physics. At university I included statistics, on taking advice, as statistics was useful for employment. And it was. When I retired in 2006, I thought that I was putting aside statistics to concentrate on particle physics. I did not realise then that QM was a branch of statistics and that the difficulty of distinguishing ontology from non-ontology (especially of superpositions) was caused by the statistical nature of QM and gives rise to apparent spookiness. For me there exists the real spookiness that is quantum retrocausality.
Austin
Austin Fearnley
Jan-Åke Larsson
QM according to Copenhagen is non-realist in which case the Bell
inequality does not apply.
Bohmian mechanics gives the same predictions and is realist and
nonlocal in which case the Bell inequality does not apply.
(QM is signal-local: you cannot communicate faster than light, but that is weaker than Bell-locality. Bell-locality implies signal-locality, not the other way around)
The paper you mention does not imply there could be a local realist method giving the QM correlations. You seem to need to read it more thoroughly.
/JÅ
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Austin Fearnley
QM is non-realist. I agree
Bohmian Mechanics is non-local. OK. Guiding waves looks to be a non-local influence.
I have not paid attention to Bohm as I avoid waves and work with particle models. I have two popular books by Bohm but did not want to finish either of them. OTOH I am interested in Aharonov's work on TSVF in connection to quantum retrocausality. Aharonov said in an online lecture that Bohm wrote up Aharonov's PhD thesis! I am not really very accepting of weak interactions.
Signal-local versus Bell-local. I had to google this:
"In quantum mechanics (QM), Bell locality refers to the non-local correlations between entangled particles that defy explanation by local hidden variables, as demonstrated by Bell's theorem. In contrast, signal locality refers to the principle that no information or signal can be transmitted faster than the speed of light, a concept QM upholds despite its inherent non-locality. Therefore, QM features Bell non-locality (entanglement, faster-than-light correlations) but adheres to signal locality (no faster-than-light information transfer)."
It seems that the term Bell locality is used above to be the same as Bell non-locality. Like flammable is the same as inflammable. Strange.
Yes, I ought to read the paper better but I don't think it is worth too much of my time. The wrong implications were only in my own thinking rather than claims made in the paper.
Austin
Алексей Никулов
You claim that it is impossible to disprove Bell’s theorem by doing
calculations within quantum mechanics because you didn't want to
understand the essence of my article [1]. The orthodox quantum
mechanics cannot predict the EPR correlation and violation of the Bell
inequalities because of its principle that the operators can fail to
commute only if they act on the same particle, since according to
quantum formalism "the commutability of the operators is a necessary
and sufficient condition for the physical quantities to be
simultaneously measurable" [2]. I show in section 4. “The Assumption
used at the Deduction of the GHZ Theorem makes Impossible the
Prediction of Violation of Bell’s Inequalities” of the article [1],
following to the Bell article on Bertlmann’s socks, that the orthodox
quantum mechanics can predict violation of the Bell inequalities only
for the case of measurement of single particles.
It is obvious that the orthodox quantum mechanics predicts violation
of the Bell inequalities in this case due to the Dirac jump. The
orthodox quantum mechanics cannot predict violation of the Bell
inequalities in the case of measurement of two particles of the EPR
pair since the mind of the observer creates or changes the eigenstate
only the particle which he observes, according to the Dirac jump. Bell
misled several generations of physicists, and not only physicists,
because he himself was misled by Bohm. Bohm postulated the EPR
correlation in 1951 with help of the absurd claim that the mind of the
observer can create the eigenstate of not only the particle he
observes, but also of another particle he does not observe. I show in
section 6 “The Rejection of Realism Results to the Absurd” of the
article [1] that the Bohm claim about the omnipotence of the mind of
the observer, which can only be compared to the omnipotence of God,
logically leads to the absurd conclusion that two observers can create
different eigenstates of the same particles. The orthodox quantum
mechanics avoided this absurdity thanks to its principle that
operators acting on different particles commute.
I was shocked when I noticed that Daniel Greenberger, Michael Horne,
and Anton Zeilinger used this principle to prove that quantum
mechanics contradicts local realism. This is not the only mistake made
in the derivation of the GHZ theorem, which testifies to the
degradation of physical thinking. I have drawn attention to these
mistakes in [1] in order to demonstrate the degradation of physical
thinking, the main reason for which is the rejection of realism by the
creators of quantum mechanics. The 2022 Nobel Prize is a consequence
of this degradation of physical thinking. This year's Nobel Prize
testifies to the further degradation of physical thinking. The Nobel
Prize was awarded for the experimental ‘confirmation’ of the pet idea
of Anthony Leggett about the contradiction of quantum mechanics with
macroscopic realism [3]. I think I managed to convince Anthony Leggett
in 2009 that his pet idea contradicts the law of conservation of
angular momentum. He began to argue that the difficulties with the
conservation law “is just one of several paradoxes associated with the
concept of "measurement" in quantum mechanics”.
This is a correct remark. One of the logical contradictions of the
creators of quantum mechanics was that, having abandoned the
description of reality, they retained faith in the laws of
conservation. Only that which exists can be conserved, not that which
is observed or even measured. Believers in the EPR correlation and the
violation of Bell's inequalities should know that the conservation
laws are violated not only in microscopic but also in macroscopic
quantum phenomena [4], because of the prevailing illusion among most
physicists that Bohm postulated the EPR correlation on the base of the
law of conservation of angular momentum of the EPR pair. Even Gerard
't Hooft has this illusion.
Richard, I am sending my article [1]. Read at least section 4. “The
Assumption used at the Deduction of the GHZ Theorem makes Impossible
the Prediction of Violation of Bell’s Inequalities” and try to
understand that the violation of Bell's inequalities can be predicted
only by Bohm's absurd claim about the omnipotence of the mind of the
observer. Only Bohm's quantum mechanics but not the orthodox quantum
mechanics can predict the EPR correlation and the violation of Bell's
inequalities.
[1] A.V. Nikulov, Physical Thinking and the GHZ Theorem. Found. Phys.
53, 51 (2023) https://doi.org/10.1007/s10701-023-00693-y .
[2] L.D. Landau and E.M. Lifshitz, Quantum Mechanics: Non-Relativistic
Theory, vol. 3. Elsevier Science, Oxford (1977)
[3] A.J. Leggett and A. Garg, Quantum mechanics versus macroscopic
realism: Is the flux there when nobody looks? Phys. Rev. Lett. 54,
857–860 (1985).
[4] A.V. Nikulov, A problem with the conservation law observed in
macroscopic quantum phenomena is a consequence of violation of the
correspondence principle, Chinese Journal of Physics 92, 270-283
(2024).
With best wishes,
Alexey
вт, 7 окт. 2025 г. в 18:56, Richard Gill <gill...@gmail.com>:
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Mark Hadley
Fred Diether
Fred Diether
Mark Hadley
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Jan-Åke Larsson
Alexandre, you are not making sense, if the probabilities all equal p then the inequality is p <= p+p which is true.
QM violates the inequality in (3.9.15), how do you achieve that?
/JÅ
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Alexandre de Castro
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Jan-Åke Larsson
By all means, tell us.
Alexandre de Castro
Jan-Åke Larsson
Well, Sakurai tells us that using θab=2θac=2θbc=2θ\theta_{ab}=2 \theta_{ac}=2\theta_{bc}=2\theta in the probabilities in (3.9.11), the three probabilities are not equal. Two of them are much smaller than the third.
Attempting to insert those into the Bell inequality you obtain (3.9.12) and with θ\theta inserted this reads
sin2θ≤sin2(θ2)+sin2(θ2)\sin^2\theta\le\sin^2\Big(\frac\theta2 \Big)+\sin^2\Big(\frac\theta2 \Big)
Sakurai then writes
"For example θ=π/4\theta=\pi/4;
we then obtain 0.500 <0.292 ??
(3.9.15)"
Fred Diether
Alexandre de Castro
Jan-Åke Larsson
Well, that is no wonder. You need to use specific settings to obtain the contradiction.
For these settings you will not be able to reproduce the quantum predictions from a local realist model.
Did you not claim you could reproduce all predictions from QM using a local realist model?
Jan-Åke Larsson
Who said anything about action?
The statement is that you cannot reproduce quantum predictions using a local realist model.
The claim is not that you need nonlocal action.
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Alexandre de Castro
Jan-Åke Larsson
Then by all means, tell us how.
Alexandre de Castro
Jan-Åke Larsson
For one specific case. Meaning, not the interesting case.
Mark Hadley
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Jan-Åke Larsson
The Bell inequality combines data from several experiments. The one in Sakurai uses three different experiments.
If you make the probabilities from all three experiments equal, there is a local hidden variable model that can describe all three.
For the combination in Sakurai, there is no such model.
Alexandre de Castro
Jan-Åke Larsson
Oh, but there is.
If there is nothing preventing this, across several setups, then show us how.
Explicitly.
Alexandre de Castro
Fred Diether
Jan-Åke Larsson
That is one special case. This is not general.
You need to do better.
Jan-Åke Larsson
If you do not want to understand, why are you here?
To ridicule actual scientists?
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Fred Diether
Jan-Åke Larsson
A real scientist would attempt to understand.
A real scientist has a role in society to educate others.
An internet troll has the role to use up other peoples time for no good.
I am attempting to educate others here.
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Alexandre de Castro
Fred Diether
Jan-Åke Larsson
Yes, exactly. One that can't reproduce all QM predictions.
Mark Hadley
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Alexandre de Castro
Fred Diether
Fred Diether
eq.(14)Mark Hadley
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Fred Diether
Richard Gill
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<bell14.jpg>
Richard Gill
Mark Hadley
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Mark Hadley
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Richard Gill
Mark Hadley
anton vrba
Hmm... I guess that is a NO. You are not going to ignore my posts. Ugh!Educate? That is BS! You are trying to indoctrinate people to Bell's nonsense. A real scientist wouldn't be that stupid.Ok, time to get back to physics and not nonsense.On Wednesday, October 8, 2025 at 10:18:28 PM UTC-7 Jan-Åke Larsson wrote:A real scientist would attempt to understand.
A real scientist has a role in society to educate others.
An internet troll has the role to use up other peoples time for no good.
I am attempting to educate others here.
Let me say at the outset, that in this discourse, I am opposing not a few special statements of quantum mechanics held today, I am opposing as it were the whole of it, I am opposing its basic views that have been shaped 25 years ago, when Max Born put forward his probability interpretation, which was accepted by almost everybody. It has been worked out in great detail to form a scheme of admirable logical consistency that has been inculcated ever since to every young student of theoretical physics.
The view I am opposing is so widely accepted, without ever being questioned, that I would have some difficulties in making you believe that I really, really consider it inadequate and wish to abandon it. It is, as I said, the probability view of quantum mechanics. You know how it pervades the whole system. It is always implied in everything a quantum theorist tells you. Nearly every result he pronounces is about the probability of this or that or that … happening ─ with usually a great many alternatives. The idea that they be not alternatives but all really happen simultaneously seems lunatic to him, just impossible. He thinks that if the laws of nature took this form for, let me say, a quarter of an hour, we should find our surroundings rapidly turning into a quagmire, or sort of a featureless jelly or plasma, all contours becoming blurred, we ourselves probably becoming jelly fish. It is strange that he should believe this. For I understand he grants that unobserved nature does behave this way ─ namely according to the wave equation. The aforesaid alternatives come into play only when we make an observation-which need, of course, not be a scientific observation. Still it would seem that, according to the quantum theorist, nature is prevented from rapid jellification only by our perceiving or observing it. And I wonder that he is not afraid, when he puts a ten-pound note {or his wrist-watch} into his drawer in the evening, he might find it dissolved in the morning, because he has not kept watching it.
E. Schrödinger (Ed. Michel Bitbol), The Interpretation of Quantum Mechanics: Dublin Seminars (1949-1955 And Other Unpublished Essays). Ox-Bow Press, Connecticut, USA, 1995
Austin Fearnley
You wrote, to Fred: "I'm quite interested in how people respond to BI because I think one such result will lead to an explanation of QM." You might remember some of my views on QM as we spoke at length some time ago.
I first met Bell's Theorem through Fred and Joy Christian on the s.p.foundations website over a decade ago. I think Jay Yablon and 'Oh.No' were moderators, if I remember correctly. Fred has run two different websites of his own design since then with Fred and Jay as moderators, I believe. Fred was familiar with Bell's Theorem years before I was and his website welcomed Bell discussions. His website has been quiet in recent years though I notice that Jay Yablon has lately posted news of his new paper on quantum gravity. I try to avoid complicated maths papers but I always enjoyed working through Jay's many papers despite some having extensive length (100+ pp) and complexity. (Though I tire too easily now to enjoy that any more.)
On the other hand, I never had much time for theoretical study of Bell's Theorem, though I read a proof and agreed with it. My initial aim was to make a computer simulation, for Fred, based on Joy's one-page disproof paper. And after that encountered Richard who as we know was very interested in both theory and computing aspects.
My take, at some stage, on Bell's theorem became that it was obviously correct so that I did not need to concern myself much with the theory, although I have always paid attention to Richard's views online. I never managed to make a simulation which exceeded 0.5 while aiming for 0.707 correlation while using static vectors as models of polarisation vectors. That seemed obviously an effect of loss of precision when using integers (observed measures) after rounding from real-valued vector magnitudes (unknowable true scores). Correlation of true scores would give 0.707 while correlation of observed measures gives <0.707 and in my simulations give 0.5. Loss of precision reduces reliability of measurement from 1.0 down to not less than 0. "A reliability of .5 means that about half of the variance of the observed score is attributable to truth and half is attributable to error" taken from https://conjointly.com/kb/theory-of-reliability/
It seemed clear that to obtain 0.707 in a simulation, while using rounded integer magnitudes, implied use of non-locality and/or non-reality in the calculations. And to obtain 0.707 in a real experiment implied that the reality of the world was not simply our normal view of reality.
I continued with simulations as I had developed a gyroscopic particle model which allowed results in agreement with Malus's Law. This gets rid of the static vector model of particle polarisation. Bryan also ditched or bypassed the static vector polarisation model. This represented a half way stage whereby Malus's Law was obtained though not yet achieving the 0.707 correlation of QM. My simulation for Bell's Theorem using a gyroscopic model was disappointing as it only managed correl = 0.375. But it should have been expected as it was a local realist method, and the extra variability in the gyroscope model reduced the correl below even 0.5.
So I was driven to looking for non-local and/or non-realism answers. Which is how QM works as
|1.up 2.down> - |1.down 2.up> for a QM entangled joint singlet state of polarisation is non-realism.
I think the answer lies in quantum retrocausality, though I do not like current philosphical retrocausal papers. Anyway, Bell's Theorem has been very important but the future IMO does not lie in BT or BI but in finding a believable non-realist model.
thray1947
Can any of you Bell fans take a guess at what Bell's biggest mistake is?
Fred Diether
Richard Gill
On 10 Oct 2025, at 17:59, thray1947 <thra...@gmail.com> wrote:
https://www.researchgate.net/publication/383561991_The_Ferryman's_Dilemma Not a mistake. Simply a failure to recognize the value of topological orientation.
TomOn Sunday, October 5, 2025 at 10:49:11 PM UTC-4 fredi...@gmail.com wrote:Can any of you Bell fans take a guess at what Bell's biggest mistake is?
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Fred Diether
Richard Gill
On 11 Oct 2025, at 00:11, 'Mark Hadley' via Bell inequalities and quantum foundations <Bell_quantum...@googlegroups.com> wrote:
Richard Gill
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<bell15.jpg>
Richard Gill
On 10 Oct 2025, at 22:40, 'Mark Hadley' via Bell inequalities and quantum foundations <Bell_quantum...@googlegroups.com> wrote:
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To: Fred Diether <fredi...@gmail.com>
Subject: Re: [Bell_quantum_foundations] Bell's biggest mistake
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