Bell's Blunder

[Bryan Sanctuary]

Hi all

Here is a link to my view of the error Bell made in his Theorem,

http://blog.mchmultimedia.com/2022/04/24/bells-blunder/

Bryan 

[Richard Gill]

Bryan writes:

“The error in Bell’s Theorem [11] is his assumption that his random variables always carry the values of ±1. This is not supported by the existence of LHV. Bell assumed polarization, |±⟩ ⟨±|, always exists from the source to detection: the flags are always flying. However, the flags only appear upon the measurement of spin. In contrast, for coherence, |±⟩ ⟨∓|, the flags are furled, and describes a spin in isotropy. [11] Bell, J. S. (2004). p. 139 or 147, Speakable and unspeakable in quantum mechanics: Collected papers on quantum philosophy. Cambridge university press.”

Bryan is mistaken. Bell did not assume that the outcomes +/-1 always exist from source to destination. He only assumed that the outcomes appear upon measurement.

Bryan sees spin from a quantum-mechanical point of view. He argues that all these years, we have been missing something connected to complementarity. We have missed:

“that spin components do not commute, that quantum mechanics reveals ‘inverse’ spaces. What, then, is the inverse space for spin angular momentum? All we know of spin is its measured vector polarizations, |±⟩ ⟨±|. It turns out that the inverse spin space is the coherencies expressed by, |±⟩ ⟨∓|. These support other spin properties which account for the missing correlation”

So instead of adding classical hidden variables, Bryan seems to be adding unobservable quantum observables: |+><-| and |-><+| are operators acting on the Hilbert space  C^2, but they are not self-adjoint. Their eigenvalues are purely imaginary.

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On 24 Apr 2022, at 23:34, Bryan Sanctuary <bryancs...@gmail.com> wrote:



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[Jan-Åke Larsson]

I read the paper. It does not contain a counterexample.

The paper contains the claim that the "coherencies expressed by |+><-| and |-><+| ... support spin properties which account for the missing correlation," but no description of how they account for the missing correlation.

Bryan, you will need to provide that description.

Best

Jan-Åke

[David H Oaknin]

Dear Jan-Ake,

Here you can find a detailed explanation of how the GHZ argument can be bypassed: 

arXiv:1709.00167

"Solving the Greenberger-Horne-Zeilinger paradox: an explicitly local and realistic model of hidden variables for the GHZ quantum state"

Maybe this is what Bryan has in mind.

Best wishes,

David Oaknin

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[Bryan Sanctuary]

Hi Jan-Åke,

Agreed, I have deliberately left that out for now. The note is really a "what if" but  "if so" and a counter example exists, well there must be an error in his proof, and this is my view,

Thanks for the comment

Bryan

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[Bryan Sanctuary]

Thanks for your comment Richard:  

First you say:

“Bryan is mistaken. Bell did not assume that the outcomes +/-1 always exist from source to destination. He only assumed that the outcomes appear upon measurement.”

My response:

This is categorically and emphatically untrue.  Bell’s random variables only take values of +/-1, all the time, everywhere, no question. The immediate consequence of your statement is that qubits, superpositions of +/-1, only exist upon measurement! That will upset quantum computing programmers.  Second that means that the singlet state is not (|up>|dn> - |dn>|up>).  This expression is the only one I have seen for the singlet: flags always flying whether measured or not. Third spin is measured in a Stern-Gerlach experiment to have values of only |+/-1>, which is exactly what Bell uses. Sorry Richard, nice try.

I challenge you to point out anywhere in the literature that you have a spin, or a spin function, that is NOT composed of polarized up/dn states.  I doubt you can.

Bell’s assumption is a result of Bell not being able to think quantum mechanically.  I see that in his papers.  He is tied to classical thought, just like his useful inequalities. He forced his classical system (socks) to be non-classical and the result is non-locality. It is that simple. Non-locality is the only consequence in the absence of other elements of reality.

Second you say:

“So instead of adding classical hidden variables, Bryan seems to be adding unobservable quantum observables: |+><-| and |-><+| are operators acting on the Hilbert space  C^2, but they are not self-adjoint. Their eigenvalues are purely imaginary.”

My response:

This is exactly what I am saying.  The coherences are unobservable (LHiddenV) which is why they have been missed for 100 years. Indeed, the states are non-Hermitian, but Richard is wrong, all the eigenvalues are real +/-1.  They are not imaginary at all. Finally, the non-Hermiticity breaks up into two spaces, which are complementary and carry Hermitian operators (polarizations) and anti-Hermitian operators (coherences).

My space is not is Hilbert Space C^2 but a single space of 4x4 gamma matrices that describe a single spin which is embedded in spacetime.

I should point out that Bell’s Blunder is the first of very sobering results which you will find quite unsetting. It is interesting that you cannot come up with any other points of contention in that little Blunder paper.  You will find, as I finally get these out, that one by one your notions will fall until finally you will convert to local realism.

[GeraldoAlexandreBarbosa]

Bryan,

It seems that everyone agrees that Bell’s inequalities were set in a classical context.

In a classical context, particles are distinguishable (although such distinguishability may be practically impossible in many cases – e.g., particles in a gas). In a classical context, a magnet has two distinct positions, and they are distinguishable, and they do not live in a superposition state.

This implies that a classical state can be perfectly copied, as many times as our resources allow (flying “flags” can be copied).

 

Also, derivation of quantum aspects within a classical context can lead to weird conclusions.

A quantum state, representing a spin (a quantum entity), represents our knowledge of that spin, and it may as well represent a superposition state.

An expected value for a measurement on that state includes a space axis for that measurement (e.g. a magnetic field orientation). That measurement axis can be set even after the spins have left their original site. While the preparation of the initial state of two spins (in the same position) could be made along an axis z₀, a measurement could occur along any z axis.

(Calculated) Complementary measurements at position A and position B would always give – along an arbitrary z direction, the + and – results, regardless of the distances between A and B. That implies that the + and – are NOT rigidly attached to the initial axis z₀ (=”flying flags”). It is also true that the correlation of the +/- results are only seen after the measured signals are compared (light speed bound correlation).

Quantum models allow entangled states, not the classical models.

I could not understand how you apply your idea of classical “locality” to explain correlations at distant places along arbitrary measurement axis. Are you also discarding quantum mechanics? Are you challenging the idea of correlation at distant positions? … I am a bit confused … Your note did not help me.

Geraldo

Geraldo A. Barbosa, PhD

KeyBITS Encryption Technologies LLC

https://www.keybits.tech/

1540 Moorings Drive #2B, Reston VA 20190

E-Mail: Geraldo...@gmail.com

Skype: geraldo.a.barbosa

Cellphone: 1-443-891-7138 (US)

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[Bryan Sanctuary]

Geraldo

Thanks very much for that feedback and comments. I basically agree with everything you say.  One point about knowledge (of a spin) which I now say is incomplete. We observe polarizations but not coherences.  This actually goes against the No-hiding theorem which says all info is available.  You cannot see information contained in spin coherence, a real property of Nature.

You are absolutely right that I did not convince you because I left out the key point.  I am really at a loss as to what to do. Waiting for the 4th journal to decide to review not, has been going on for three months. 

If I am refused a peer review the fourth time I will have to make them public somehow, maybe my blog.

"A Peer Review, A Peer Review, a horse for a Peer Review!"

Thank you for your patience.  It is appreciated.

Bryan

[Richard Gill]

Dear Bryan

You can get peer review by publishing in a PPPR (post publication peer review) journal like F1000research.com

It’s perfectly suited for original non-mainstream work which gets held up by conventional, cautious, journals. I have several young friends who use it for the speed, and as a statement against the broken peer review and parasitical nature of the conventional commercially exploited journals.

Richard

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On 25 Apr 2022, at 19:34, Bryan Sanctuary <bryancs...@gmail.com> wrote:



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[Richard Gill]

Dear Bryan

You are categorically and emphatically wrong. I will write to you personally with exact with quotes from Bell, proving this.

You refer to two page numbers of your edition of “Speakable and unspeakable”. Please send me a pdf/photo of each of those pages, or quote a salient sentence from each.

You apparently utterly mistake Bell’s intention. You say Bell could only think classically. His main work at CERN was top level orthodox QM work. The point of his foundational work was to prove that classical thinking could not explain certain QM predictions. He succeeded in showing exactly why this was so.

In other words: you agree with Bell. Feynman already said: we already knew this! It’s not interesting, not useful!

You could have more success with your mission if you would stop maligning Bell by putting claims into his mouth which he never made. It gives everyone a license to ignore the “meat” in your work.

Richard

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On 25 Apr 2022, at 16:03, Bryan Sanctuary <bryancs...@gmail.com> wrote:



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[Richard Gill]

You can publish your paper today on F1000. It doesn’t prevent any decent journal from re-publishing your paper after conventional peer review.

When it is published on F1000 you email us, and very soon you’ll get extensive and constructive peer review, also published, from people on this group.

It’s a refreshing new mode of science publishing. The young folk are adopting it. There’s no time to waste.

“Publish” means “make public”. In the 21st century there are better ways to do this than how we did it in the 18th, 19th, 20th

R.

Sent from my iPhone

On 26 Apr 2022, at 01:26, Bryan Sanctuary <bryancs...@gmail.com> wrote:



Hi

Thanks, I will wait for the journal response, and decide what to do. I do not want to delay much longer, not fair to delay.

Bryan

On Mon., Apr. 25, 2022, 19:18 Richard Gill, <gill...@gmail.com> wrote:

Dear Bryan

You can get peer review by publishing in a PPPR (post publication peer review) journal like F1000research.com

It’s perfectly suited for original non-mainstream work which gets held up by conventional, cautious, journals. I have several young friends who use it for the speed, and as a statement against the broken peer review and parasitical nature of the conventional commercially exploited journals.

Richard

Sent from my iPhone



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[Bryan Sanctuary]

Hi Richard

I can understand why you are upset.  You are a Bellist and have great regard for the work John Stewart Bell, especially his Theorem.  I am attacking that but I am not denigrating his career at CERN (of which I know little) or his other successes or him personally.  However he made an enormous Blunder in the proof of his theorem and that is his legacy now.  Still, 60 years on,  people are using his Theorem to justify so much work that is misleading and incorrect, like the Big Bell Test*, and for quantum teleportation**.  It must change.

*BIG Bell Test Collaboration. "Challenging local realism with human choices." Nature 557.7704 (2018): 212-216.

**Bennett, C. H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., & Wootters, W. K. (1993). Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Physical review letters, 70(13), 1895.

The reason for Bell's error is he believed that spin is always polarized, and it is not.  That means to me, he could not image beyond his classical states--hence my comment about his Positivist attitude.   

The end result is that his theorem, and then the CHSH successful experiment, has seared into physics the absurd notion on non-locality.  I find it boggling that the world of Physics succumbed and accepted such nonsense in the first place, because, think of it, non-locality, EPR channels make no sense, and constitutes, as Alexey says, religion.

MY GOAL: This is an academic war about knowledge.  I will win but first I must fight. I did not fight until I had the ammunition.  My intention is to completely change the world view of spin from a two level vector observable to a four level hyperspin.  From this, gobsmacking consequences arise, like the Dirac equation does NOT produce anti-matter. (First time I told you that).

I know what I am up against:  a chemist with little credibility is telling physics they have spin wrong, Quantum Information Theory must change, and that antimatter is not produced!!  No wonder there is skepticism and disbelieve. 

If in a meek and mild way I posted somewhere, my work would be ignored.  How long did Bell's 1964 paper sit unnoticed?  By delaying the repudiation of non-locality, billions of research funds are being wasted and myriad research projects will result in misleading ideas.  If I am to change the field of Quantum Information and stop teleportation nonsense, I have to attack Bell's Theorem. I also must be assertive.  I only bet you to get attention, and, of course, the certainty that I will win.  

There will be casualties in my attack, like your papers being retracted, and the gurus who have hyped the field for so long will convert to local realism, or retire. I have no qualms about personal consequences: hey it has had a number of negative effects on me by sticking to my values.  

In my short Bell's Blunder paper, please tell me where I am not truthful, obfuscating or wrong.  So far you have nothing credible so I surmise that if I give you that LHV part, and you accept this as a counter example, then Bell's Theorem is disproven,

Finally, in this, my intention is absolute honesty and integrity.  I would never think of "putting any words" in any one's mouth.  Any other approach than honesty will fail and I will lose.  Hence I am forceful, assertive, but guided by truth, justice and the (well I'll not finish that).

I guess there are various editions of speakable, with the pages not the same.  Sorry about that. I attach the page with Bell's quote"  The others are there somewhere in your edition, I hope you find them.  I made nothing up:  Bell said:

"If [a hidden-variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local."  Bell, John S., (1987). Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press. p. 65. 

Brest wishes,

Bryan

[sgl...@nist.gov]

Bryan,

When you say that you have found an error in the proof of "Bell's Theorem", I am not certain about the precise theorem that you think is in error.  I wasn't able to find a statement of the theorem in your "Bell's Blunder" paper.

I can think of a few different possibilities for theorems related to Bell:

1. The marginal distributions produced by joint probability distributions obey some inequalities ("Bell Inequalities").

2. Quantum theory predicts that the marginal distributions produced by some entangled systems can violate the Bell Inequalities.

3. Spacelike separated measurements on entangled particles cannot be described by a fixed joint probability distribution.

I haven't stated any of those formally, but it would be helpful if you could specify which statement you object to.  Then we might work on where exactly you think the mathematical error lies.

Scott

[Bryan Sanctuary]

Hi Scott

I state  Bell's THeorem:

 ``If [a hidden-variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local."

I really have never been interested in the veracity of BI  I went through the math years ago and am not interested in any challenge.  I accept and in fact really see them as Bell's achievement.  Its just that his theorem is wrong.  

I just posted my first paper.  I resolves the EPR paradox, it is here

http://blog.mchmultimedia.com/2022/04/26/hyperhelicity-the-completion-of-spin/

Thanks

Bryan

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[sgl...@nist.gov]

Bryan,

To understand what you mean when you say that you have disproved the statement "If [a hidden-variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local.", we need to have a mapping between all of the words in that statement and mathematical concepts.  If you think that the statement is false and Bell thinks that the statement is true, the disagreement could be caused by you and Bell having different interpretations of those words as mathematical concepts. To me, that quote seems like an informal summary of the statements 1, 2, and 3 that I mentioned earlier.  I think that Bell was trying to translate some formal statements about probability distributions into natural, English language.  When Bell says "If a [hidden variable theory] is local", I think that he simply means those theories that produce probability distributions that are constrained by Bell Inequalities.

Could the disagreement be that you think that "local hidden variable theory" is not a good description of those theories whose probability distributions obey Bell Inequalities?  Or do you think the disagreement lies elsewhere?

Scott

[Richard Gill]

I think that Bell describes mathematically exactly what he takes to be a hidden variable theory. Bryan has not paid attention to what Bell wrote in “Bertlmann’s socks”, which is Bell’s final comprehensive exposition of his contribution. Note that Bell’s thinking evolved considerably from his famous first paper, through the contribution of CHSH, and up till his last works.

Bell defines “local hidden variables” as follows. He does this in the context of a Bell type experiment. Alice and Bob are at two distant labs. In one trial of the experiment Alice and Bob insert settings a and b into devices in their labs. Shortly later, they observe binary outputs x and y. The distance between the two locations is such that Alice’s output is observed before a signal travelling at the speed of light could carry Bob’s output to Alice’s lab and vice-versa.

Let lambda denote the microscopic state of all the stuff in the two labs and in between them at some time instant before the settings are introduced (in a convenient frame of reference)

*A hidden variable theory*

is essentially a deterministic theory which states that there are some functions A and B such that x = A(lambda, a, b) and y = B(lambda, a, b) and a probability distribution rho of lambda. The joint probability distribution of x and y conditional on a and b follows from the specification of A, B and rho in the usual way. Example of a successful hidden variables theory: Bohmian mechanics.

*A local hidden variable theory* is a hidden variable theory in which A does not depend on B and B does not depend on a. So x = A(lambda, a) and y = B(lambda, b). Bohmian mechanics is not a *local* hidden variables theory.

Note that there is nothing here at all about spin or about particles. Bell does not assume that the particles have something called a spin at all times, or indeed at any time. His model describes the probabilities of the four possible outcomes given any possible inputs of just one trial.

I showed nearly 25 years ago that there is no need to suppose that the same functions A and B and the same probability distribution rho are in force for each and every one of a sequence of trials, provided one assumes that settings are chosen by external randomisation, in each trial anew. One can still prove Bell’s theorem.

Bell’s theorem states that a local hidden variables theory cannot reproduce the singlet correlations. Not even approximately.

Note that the adjective “local” applies to the concept “hidden variables theory”. Bell explains again and again that it does not apply to “hidden variables”. The hidden variables are not local, not localised anyway.

Sent from my iPad

> On 27 Apr 2022, at 05:15, 'sgl...@nist.gov' via Bell inequalities and quantum foundations <Bell_quantum...@googlegroups.com> wrote:
>
> If

[Bryan Sanctuary]

Richard,

Why are you still talking about Bell's proof? I disproved it.

Bryan

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[Алексей Никулов]

Dear Bryan,

You wrote 25 April in your response to Richard: “The immediate

consequence of your statement is that qubits, superpositions of +/-1,

only exist upon measurement!” It is a correct remark. The majority's
confidence that a real device, a quantum computer, can be made on the
basis of the refutation of realism testifies not just to the
regression of physical thinking, but to stupidity. Especially
surprising Alain Aspect who states in his Viewpoint: ”Closing the Door
on Einstein and Bohrs Quantum Debate”: ”By closing two loopholes at
once, three experimental tests of Bell's inequalities remove the last
doubts that we should renounce local realism. They also open the door
to new quantum information technologies'' [1]. Alain Aspect is a
wonderful experimenter, but his statement is logical nonsense. I
should note that Bell had the opposite opinion about experiments of
Alain Aspect. He said in 1984 that these experiments indicate problems
with quantum mechanics rather than about refutation of local realism.

Your attacks on Bell are often unfounded. Richard is right that Bell
never claimed that spin is always polarized. Moreover, Bell understood
that the creators of quantum mechanics rejected determinism in Nature
and he guessed it was a mistake. Bell understood much better than most
modern physicists, but worse than Greta Herman, German mathematics and
philosophy, who tried in the early thirties to convince Heisenberg and
Weizsacker that quantum mechanics cannot be a scientific theory
because of the rejection of determinism, see CONCLUSION in my
manuscript “Physical thinking and the GHZ theorem”.

Bell misled everyone because he considered Bohm's quantum mechanics as
orthodox quantum mechanics, although these quantum mechanics are
fundamentally different. According to the orthodox quantum mechanics
operators acting on different particles commute. Quantum mechanics
cannot predict the EPR correlation, violation of Bell’s inequalities
and contradicts locality according to this principle, which was not
explicitly rejected by anyone. But Bohm rejected this principle in his
book [1] and in the paper [2] when he postulated the EPR correlation.
Bell proposed his inequalities on the basis of Bohm's publications
according to which quantum mechanics predicts the EPR correlation. But
Bell did not understand that Bohm had to reject the principle of the
orthodox quantum mechanics in order to postulate the EPR correlation.

This inattention of Bell led to the mass delusion and, in particular,
to mathematical mistakes in the derivation of the GHZ theorem [4,5].
The authors [5] use the principle of the orthodox quantum mechanics
that operators acting on different particles commute in the derivation
of the GHZ theorem in the Appendix F. According to this principle the
measurement results of two particles cannot be fundamentally
different. But the authors [5], following Bell, have written in the
Appendix B the expression (B4) according to which the probability 1/2
to observe spin up of the first particle fundamentally differs from
the probability to observe spin up of the second particle, which
depends on the angle between the directions of measurement of spin
projection of the first and second particles. I hope Richard, as a
mathematician, understands that this fundamental difference cannot be
possible if operators acting on different particles commute.

[1] D. Bohm, Quantum Theory. (New York: Prentice-Hall, 1951).
[2] D. Bohm and Y. Aharonov, Phys. Rev. 108, 1070 (1957).
[3] J.S. Bell, On the Einstein-Podolsky-Rosen paradox, Physics 1, 195 (1964).
[4] D.M. Greenberger, M.A. Home and A. Zeilinger, Bell’s Theorem,
Quantum Theory and Conceptions of the Universe, edited by M. Kafatos
(Dordrecht: Kluwer Academic), pp. 73-76 (1989).
[5] D.M. Greenberger, M.A. Home, A. Shimony and A. Zeilinger, Bell’s
theorem without inequalities, Amer. J. Phys. 58, 1131 (1990).

With best wishes,
Alexey

ср, 27 апр. 2022 г. в 08:01, Bryan Sanctuary <bryancs...@gmail.com>:

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[Inge Svein Helland]

Dear Alexey, dear Bryan, dear Richard, dear all.

There seems to be much confusion around Bell's theorem. I completely agree with Richard's description of it, which implies that I have to disagree with some of the other considerations.

In my opinion, it is all connected with the decisions that we make in some given context. Some of these are based on our habits, some of our cultural background and upbringing, and some part of our decisions rely on the variables that we have in our mind during the decision process.

In this respect we are all limited. In connection to the Bell experiment, I have demonstrated this mathematically in the attached article, just accepted for publication in Foundations of Physics. Any actor observing the situation, even the actor which receives all the data after the experiment, is limited because he is not able to keep enough variables in his mind during his decision process. He may communicate with words with other people. According to Zwirn's convivial solipsism, such communication can also be seen as a measurement of each actor upon the other one. And it is related to the same limitation of actors.

We all go through life making decisions after decisions. Some of the same analysis can be made in this connection. Some of the decisions that certain people make, are cruel, and have terrible consequences; look at President Putin and his collaborators. Such decisions should be opposed by all sensible people. For the rest of us, we just must accept that we may make mistakes in our decisions.

The attached paper is based upon my  views on the foundation of quantum mechanics; I mean that it should be based upon a general epistemic interpretation, which includes, but is not identical to QBism. I will of course wellcome any discussion of these views, but I will be grateful if this discussion could be based either upon my book 'Epistemic Processes' or upon some of my recent articles.

Best regards

Inge

---

From: bell_quantum...@googlegroups.com <bell_quantum...@googlegroups.com> on behalf of Алексей Никулов <nikulo...@gmail.com>
Sent: 27 April 2022 10:21:52
To: Bryan Sanctuary
Cc: Richard Gill; Bell inequalities and quantum foundations; sgl...@nist.gov
Subject: Re: [Bell_quantum_foundations] Bell's Blunder

 

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[Алексей Никулов]

Dear Inge,

Your point of view opens the door to meaningless fantasies, such as
QBism, Zwirn's ‘convivial solipsism’ and many others, but makes
science impossible. Science is primarily critical thinking, not
unrestrained fantasies. Modern scientists have forgotten or do not
know that our cognition of Nature is based not only on empirical
knowledge, but above all, on our a priori knowledge such as logic,
mathematics and the regulative principles of our reason.

The unrestrained fantasies about quantum mechanics became possible
since its creators rejected our a priori knowledge in order to
describe at any cost paradoxical quantum phenomena. This led to such
stupidity as the refutation of realism and such nonsense as Qbism and
‘convivial solipsism’. Numerous modern authors refuting realism do not
want to understand that the inability of our reason to describe
realistically some quantum phenomena reveals only the inability of our
reason, and not the absence of reality. Most modern scientists do not
want to admit that the possibilities of our reason may be limited even
in the realm of our experience.

They do not understand that realism and determinism are the regulative
principles of our reason which determine the very possibility of
empirical cognition. Qbism, ‘convivial solipsism’ and other
unrestrained fantasies are consequences of degradation of physical
thinking as the result of rejection of realism as the presupposition
of every kind of physical thinking. Do not even the obvious
mathematical mistakes made by the authors [1] convince you that the
rejection of realism leads to the degradation of physical thinking?

Editors of Foundations of Physics rejected without consideration my
manuscript “Only critics understood quantum mechanics” and published
Zwirn's paper about ‘convivial solipsism’, despite my two sharply
negative reviews. Your point of view that in science it is necessary
to fantasize rather than to think critically, is now shared by the
majority. But the history of science witnesses that the majority is
often mistaken.

[1] D.M. Greenberger, M.A. Home, A. Shimony and A. Zeilinger, Bell’s

theorem without inequalities, Amer. J. Phys. 58, 1131 (1990).

With best wishes,

Alexey

ср, 27 апр. 2022 г. в 11:57, Inge Svein Helland <in...@math.uio.no>:

[Inge Svein Helland]

Dear Alexey.

I simply disagree with your main thesis that 'realism and determinism are the regulative

principles of our reason which determine the very possibility of

empirical cognition'. What you call meaningless fantasies, are honest attempts to understand nature on the basis of empirical results, specifically that Bell's inequalities are violated in certain situations.

Inge

---

From: Алексей Никулов <nikulo...@gmail.com>
Sent: 27 April 2022 12:12:45
To: Inge Svein Helland
Cc: Bryan Sanctuary; Richard Gill; Bell inequalities and quantum foundations; sgl...@nist.gov

[Richard Gill]

Well said, Inge!

And to Alexey: in my opinion, QBism and convivial solipsism are intellectually respectable and minimal starting points for scientific integrity. They are really the same as Descartes’ “cogito ergo sum”. They are necessary and in some sense, sufficient. One can try to “complete” them with some kind of “realist” picture of the whole universe, but there is no guarantee that such a picture even exists. 

I think that the later Wittgenstein understood this very well.

We have nothing but our empirical knowledge and basic principles of logic (mathematics). Evolution has delivered us some core beliefs about the world. Most of them are reasonable and indisputable, but not all of them.

Sent from my iPad

On 27 Apr 2022, at 12:50, Inge Svein Helland <in...@math.uio.no> wrote:



[Jan-Åke Larsson]

Bryan,

Your paper does not mention what the outcomes are at Alice and Bob. 

You calculate the correlation directly from a tensor expression, not from statistical averages over measurement outcomes.

I can calculate the correlation directly from a vector expression (the singlet quantum state). This is not a local hidden variable theory calculation, and does not disprove the Bell theorem. The quantum calculation can be rewritten as a statistical average over measurement outcomes through Born's rule, but this does not give a description in terms of a local hidden variable theory.

To convince us, you will need to explain how your expressions can be rewritten as a statistical average over measurement outcomes, and also how that constitutes a local hidden variable theory.

Your paper does not provide a counterexample. What is your equivalent of the "Born rule"?

Best

Jan-Åke

[Richard Gill]

Dear Bryan

You repeatedly show that you are not able to read what Bell wrote. You have a prior QM vision of the world and are incapable of seeing anything else.

You referred to two pages of “Speakable and Unspeakable” where you said Bell said things about spin, which I do not recognise. Please email us pdf’s or jpg’s from those two pages. Or quote the sentences which you claim to be false.

I am not a Bellist. I have great regard for Bell’s clear thinking and sharp analyses, and I greatly enjoy his sense of humour. I don’t share his opinions. He indeed proved some nice things which can be expressed as true mathematical theorems along with the necessary rigorous proofs. Those theorems can even be strengthened in many ways. It is not my job to defend other people’s interpretations of them. But I do see it as my job to vigorously oppose obviously wrong statements, such as a number of yours. 

It is interesting to see your list of recent publications opposing Bell. A number of them make mathematical claims which are easily seen (ie, even by non mathematicians) to be false. A number of them argue for super-determinism or retro-causality, and I know you absolutely do not agree with those ideas. In short, despite the length of the list, not one of those scientists proposes anything like you do. The closest is maybe Khrennikov, who nowadays follows Bohr. Bell himself said that Bohr would have been simply uninterested in Bell’s theorem. He would have said “I told you so”. Feynman said the same, explicitly. “We already knew this”.

If Bohr and Feynman were happy with QM as it was, and did not see anything horribly wrong with it, I don’t understand why you think it needs being supplemented with “quantum hidden variables”. QM does not permit action at a distance. It can be completely harmonised with relativity theory. If you are happy with irreducible randomness, there is nothing weird or nonlocal about it. You have not come up with a local hidden variables model (a local pseudo-deterministic model) which explains the singlet correlations. You have no counter-example to Bell’s theorem.

Richard 

Sent from my iPad

On 26 Apr 2022, at 14:47, Bryan Sanctuary <bryancs...@gmail.com> wrote:

Hi Richard

[Bryan Sanctuary]

Hi Scott

I do not think you have read my paper,

http://blog.mchmultimedia.com/2022/04/26/hyperhelicity-the-completion-of-spin/

Here is the NUTSHELL:    Bell says " if it agrees with quantum mechanics it will not be local"

Hyperhelicity is a LHV, that accounts for the violation of BI, Therefore I have  disproven Bell's Theorem by counter example.END OF STORY.

WIth that we do not have to waste our time talking about the issues you raise.  His theorem is toast.

In short, from now on there is no reason to even mention the theorem, let alone worry about its  proof. It is wrong. The reason it is wrong is he  made a bad assumption just like von Neuman did.

I have no interest in discussing anything of Bell's Theorem.  It is now relegated to the "Annals of Lost causes and Bad Ideas"  Bell's theorem are now only of historical interest and must be removed from physics

Do you agree?

Bryan

To view this discussion on the web visit https://groups.google.com/d/msgid/Bell_quantum_foundations/71c26209-1e54-4c92-9b4a-9557eb709603n%40googlegroups.com.

[Bryan Sanctuary]

Dear Alexey

Your arguments are completely moot and now of no consequence.  I have dispoven Bell's theorem.  It is no longer worth discussing and I am not going to waste my time or yours on arguing  about nuances in his proof that you perpetrate and others nit-pick.  Total waste of time.

If you want to challenge me, your ONLY avenue is to question the existence of hyperhelicty--disprove my LHV, only way.

If you can, I will listen.  Otherwise please accept that  Bell's theorem is now of only historical interest and is relegated to the "Annals of Lost Causes and Bad Ideas"

Please turn the page

Bryan

[Bryan Sanctuary]

Hi Inge

Do you agree that I have disproved Bell's Theorem?  Likely not. Just tell me why hyperhelicity is not a LHV that resolves EPR and disproves the theorem.  If you cannot, then the only recourse is to accept Local Reality.

End of story.

Bryan

[Richard Gill]

Thanks Bryan. You sent us a page from Bell’s paper “Nonlocality in quantum mechanics: reply to my critics”. It’s a very nice paper. He says what I said. 

He says that one can reproduce the predictions of QM with a hidden_variables_theory 

x = A(lambda, a, b), y = B(lambda, a, b), lambda ~ rho (independent of a and b);

 but not with a *local* hidden_variables_theory 

x = A(lambda, a), y = B(lambda, b), lambda ~ rho (independent of a and b)

Your theory is not a hidden variables theory in Bell’s sense. Bell spoke only of classical variables. Your theory is a modification or extension of conventional quantum mechanics. You introduce hidden local quantum variables, not hidden classical variables. Bell did not think in a classical way. He stood above that. He studied the difference between classical thinking and quantum thinking.

His personal preference seemed to veer towards a classical non-local model. My personal preference veers towards qBism, which is really just agnosticism. And since the different interpretations so far make no experimentally discernibly differing predictions, one can leave that discussion to the philosophers. They are “optional extras”. One can have different religions, or none, but still have the same morals. One will behave the same, as far as science is concerned. You might dress differently on some special day of the week and gather with others like you on those days.

BTW, Hossenfelder and Palmer, whom you cited approvingly, agree fully with Bell. They propose that the probability distribution of lambda should depend on a and b. I think you weaken your own arguments by citing numerous authorities who completely disagree with you as if they are supporting your criticism (as well as citing “authorities” who make glaring errors). This means that you have not studied the literature. This is why your papers keep getting rejected. Basic failures of logic, which you should easily have spotted yourself. Remarkable claims require remarkably strong evidence.

I believe that none of the anti-Bellists whom you cite, with the possible exception of Khrennikov, would support your “solution” to the EPR problem. Hence I’m confident of winning my bet!

Richard

PS if there are more Bell statements which you believe you have shown to be false, please show them to us. Preferably with the quotation of a complete sentence. Otherwise with a screenshot or photo of a page.

On Tuesday, April 26, 2022 at 2:47:26 PM UTC+2 bryancs...@gmail.com wrote:

Hi Richard

******

[Bryan Sanctuary]

Hey Richard.

Do you capitulate after my first paper?  If not, please tell me why?  Also your team of experts to judge:  how about Bennett, Gisin, Zeilinger, Fuchs, Larrson,etc

I look forward to your responses.

Bryan

[Bryan Sanctuary]

Dear Richard,

We have a bet. Please respond to my paper.  I have disproven Bell and you are grasping at straws now.  This is not about the nitty gritty of any of Bell's work except his bizarre statement:

 ``If [a hidden-variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local."

You still refer to Bell and your perennial claim I do not understand stuff. It is of no interest unless you find errors in my paper.  That is all I am listening to.  Bell's work is, thankfully, toast, there is no non-locality.  You have to change your thinking to local realism, of prove my helicity is wrong. 

Bell's error is in the assumption. I disproved it by counter example.  That is the only place you can attack my results.

Please do not obfuscate.

Bryan

[Bryan Sanctuary]

Richard,

You are avoiding the issue.  You have lost, or, if you do not agree,  disprove the existence of hyperhelicty.

 It is a waste of time to discuss Bell's theorem any more, it's gone unless hyperhelicty is rejected--your only recourse, so please face the facts and respond.

Bryan

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[Bryan Sanctuary]

Dear Tricky Dicky

Please stop deflecting from the issue. I have no interest any more in Bell's Theorem and non-local connectivity, Nature is now locally real.  Your thinking must change, your papers retracted and you must accept local realism. Alternatively you can tell me what is wrong with hyperhelcity.

I think others might start to pop up with comments.  I sent the links to the Foundations group and the Perimeter institute.  Let's see if they respond.

Its over Richard, face to music or respond objectively

Thanks

Bryan

On Wed, Apr 27, 2022 at 8:46 AM Richard Gill <gill...@gmail.com> wrote:

Bryan (just for you)

Your “hyperhelicity” is a quantum hidden variable. Bells theorem is about classical hidden variables.

You have extended or modified conventional quantum theory. You have not disproved Bell’s theorem.

The question of the locality of conventional quantum theory is much debated. Many people consider it to satisfy locality. For instance, it forbids “action at a distance”. If you consider the quantum state merely to encapsulate knowledge of a hypothetical agent, not to be something “real” and located in space-time, there is no non-locality in QM. Also the Schrödinger cat paradox is resolved by taking this point of view.

Richard

Sent from my iPad

On 27 Apr 2022, at 14:19, Bryan Sanctuary <bryancs...@gmail.com> wrote:



To view this discussion on the web visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CALLw9YwmM3o01eeeqrgss7FvqJcRA%2Bv06b5e5TLvwvUAhngBLA%40mail.gmail.com.

[Richard Gill]

Bryan

The bet we made was on the question whether or not the majority of our peers would agree that you have disproved Bell’s theorem (within another year and a half from now).

Right now the signs are not very favourable for you. I am not grasping at straws. I point out that you have not read Bell very closely. It turns out that you don’t even understand what Bell’s theorem says. You have merely picked up a common folk-lore misunderstanding. You disagree with a popular, imprecise, careless interpretation.

Notice: so far your paper failed moderation at the arXiv section for off-beat physics, and was turned down by three journal editors. You did not post it at F1000, where you could have invited your own reviewers, as well as get unsolicited reviews from someone like me or others in our group. In support of your ideas, you cite about 12 authorities who either agree that Bell’s theorem is correct, or whose papers contain obvious errors. None of them has given you any support on this mailing list, yet.

You specified the terms of the bet. I agreed to them, though reluctantly. Still, I think I am going to win. We must decide by Christmas/New Year 2023/2024. I hope we will both still be around then. I’m not optimistic about that, but I do believe it is already clear I’m going to win.

I’m not saying your work is not interesting! Maybe it is even important. It just doesn’t do what you claim it does.

Richard

Sent from my iPad

On 27 Apr 2022, at 14:45, Bryan Sanctuary <bryancs...@gmail.com> wrote:



[Richard Gill]

Bryan

Your “hyperhelicity” is a quantum hidden variable. Bells theorem is about classical hidden variables.

You have extended or modified conventional quantum theory. You have not disproved Bell’s theorem.

The question of the locality of conventional quantum theory is much debated. Many people consider it to satisfy locality. For instance, it forbids “action at a distance”. If you consider the quantum state merely to encapsulate knowledge of a hypothetical agent, not to be something “real” and located in space-time, there is no non-locality in QM. Also the Schrödinger cat paradox is resolved by taking this point of view.

As to who will win our bet, I recommend you check its precise wording. I didn’t see Anton Zeilinger or Gregor Weihs retracting any of their papers yet. I certainly see no reason to retract any of mine at this point.

Perhaps you should read some of them. One just got accepted.

https://arxiv.org/abs/2012.00719

Richard

Gull's theorem revisited

Richard D. Gill

Steve Gull, in unpublished work available on his Cambridge University homepage, has outlined a proof of Bell's theorem using Fourier theory. Gull's philosophy is that Bell's theorem (or perhaps a key lemma in its proof) can be seen as a no-go theorem for a project in distributed computing with classical, not quantum, computers. We present his argument, correcting misprints and filling gaps. In his argument, there were two completely separated computers in the network. We need three in order to fill all the gaps in his proof: a third computer supplies a stream of random numbers to the two computers representing the two measurement stations in Bell's work. One could also imagine that computer replaced by a cloned, virtual computer, generating the same pseudo-random numbers within each of Alice and Bob's computers. Either way, we need an assumption of the presence of shared i.i.d. randomness in the form of a synchronised sequence of realisations of i.i.d. hidden variables underlying the otherwise deterministic physics of the sequence of trials. Gull's proof then just needs a third step: rewriting an expectation as the expectation of a conditional expectation given the hidden variables.

Sent from my iPad

[Bryan Sanctuary]

Hi  Jan-Åke

Thank you.  "Outcomes at Alice and Bob":  I calculate the EPR correlation, that is enough.   I am not counting clicks but simply agreeing with the coincidence experiments and the violation.  That is all that is necessary at this stage. 

I mention that I use von Neumann's projective measure, equation (4).  My state operators are Eq. 2 and 3 are pure states.  So that should answer your question about statistical averages.

"I can calculate the correlation directly from a vector expression (the singlet quantum state)"  

I am not sure I understand, the singlet is not viable after the local pair separate if that is what you  mean.  Can you explain more about this please?

The Born rule is ok for polarizations, but it has a hard time with coherences  I use, as I said, von Neumann and the quantum trace accounts for pure and mixed states. 

So you disagree that hyperhelicty does not provide a counter example.  Why not? 

Look forward to your reply

Bryan

[Jan-Åke Larsson]

On ons, 2022-04-27 at 06:19 -0700, Bryan Sanctuary wrote:

Hi  Jan-Åke

Thank you.  "Outcomes at Alice and Bob":  I calculate the EPR correlation, that is enough.   I am not counting clicks but simply agreeing with the coincidence experiments and the violation.  That is all that is necessary at this stage. 

No it is not, it is necessary to describe measurement outcomes using a local hidden variable model, and statistics thereof. 

Bell's theorem is specifically about the possibility of providing such descriptions.

If you do not provide such a description, then your claim fails.

I mention that I use von Neumann's projective measure, equation (4).  My state operators are Eq. 2 and 3 are pure states.  So that should answer your question about statistical averages.

"I can calculate the correlation directly from a vector expression (the singlet quantum state)"  

I am not sure I understand, the singlet is not viable after the local pair separate if that is what you  mean.  Can you explain more about this please?

The singlet is the quantum-mechanical description of the entangled spin state of the combined pair system even when the pair has separated.

Born's rule gives the probabilities of the measurement outcomes, for such a system.

We know this is a good description because it describes the outcome statistics well.

The Born rule is ok for polarizations, but it has a hard time with coherences  I use, as I said, von Neumann and the quantum trace accounts for pure and mixed states. 

Born's rule, as used in modern textbooks, works well with mixed states.

So you disagree that hyperhelicty does not provide a counter example.  Why not? 

Because it does not provide a local hidden variable model.

The paper you posted will not convince me, nor Richard, nor any of the other people you mention.

Like Richard wrote, your description may be correct (or may not), but either way it does not contradict Bell's result.

Best
Jan-Åke

[Bryan Sanctuary]

Hi Richard

Ok, you want to stay with classical ideas only and not consider quantum ideas.  Indeed I have, and will, extend qm but that is what EPR suggested. No bell theorem, EPR is correct.

Are you seriously saying that you want to reject hyperhelicty because it is not classical?????

I am working on the QFT of hyperhecity, just the wording, and I will post that soon.

Of course I do understand that Bell uses only classical ideas in his work, and that is one problem.  That is why in Bell's Blunder you see my use of his classical socks.  He forces them to account for the violation and it can only happen with non-locality. 

It's nonsense. 

 I suggest to you that Gisin, Zeilinger et al do not reply because they are flummoxed and likely at a loss for words.  I think that Gregor may be open to new ideas because I know he does not like quantum weirdness and wants a rational explanation. However their non-local house of cards has collapsed, and all they can say is  "We don't like it!"

Bryan

[Bryan Sanctuary]

Hi Jan-Åke

Helicity is local, hidden and a variable.  It accounts for the correlation as a LHV.  Bell is disproven, it is math.

I disagree that I must use Bell's classical description to describe a quantum system.  I do not have to pay any attention to Bell's work.  All I have to do is agree with the experimental results and I do:  I account for the violation using helicity.  Then others can scratch their heads and wonder why it disagrees with Bell.  You want to stay classical.  I want to be quantum. 

Bell's approach does not include coherence.  It is classical and you want me to hammer a square peg into a round hole like Bell did.  It will not work, so you must give up Bell and turn to quantum LHV

The Born rules works, of course, for coherences.  I did not say it did not.  I like von Neumann  better which is much easier for me than states.  The two are equivalent so I do not need to use the Born rule.

Hope you accept these arguments.

Bryan

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[Jan-Åke Larsson]

Dear Bryan

Bell poses the question: "Can there exist a local hidden variable model?" (you call it "classical")  His theorem proves that the answer is "No".

(He proves that one can not hammer your "square peg" into your "round hole".)

There is no dispute that a quantum description can give the outcomes. All of us understand that it can.

But that is not the kind of model Bell asks his question about. 

Your paper is not a counterexample.

Best
Jan-Åke

[Bryan Sanctuary]

Hi again Jan-Åke

Bell's proof assumes spins are always polarized up or down.  I question that with helicity, flags are furled. 

I can not say more really and I suggest you sleep on this and I think you will come around.  There is more to spin than the 2x2 polarized states.  Spin is a 4x4 Dirac field.  It opens up a lot and will improve quantum computing. 

"Can there exist a local hidden variable model?"  Bell says no and I prove him wrong with a counter example. That is the end really unless you deny quantum correlation can exist.  You must also show that my equation 18 is wrong, and that expression is firmly established in GA and SO(3). 

Your only wiggle room is believing polarized states of +/-1 always exist.  

Bryan

Best wishes

Bryan

I also have quite a bit more on this that will be up soon.  

You really will have to give up the exclusive use of qubits and teleportation.  

To view this discussion on the web visit https://groups.google.com/d/msgid/Bell_quantum_foundations/03f93bfdb615e1f697812330391043f4ef0b4e26.camel%40liu.se.

[Jan-Åke Larsson]

Dear Bryan,

You will not convince anyone. You do not have a counterexample.

Best
Jan-Åke

[Richard Gill]

Bryan

I do not want to stay with classical ideas only. I do not question the usual quantum description of reality.  (Though I accept that it probably won’t be the last word.) For the time being it is the best thing we have.

Whether you want to call it “weird” or “wondrous” is up to you. You have to get familiar with the math, and then become creative with it. Be inquisitive. Creative. Push it to its boundaries.

I expect that Nicolas Gisin and Anton Zeilinger and Gregor Weihs have similar opinions. But I obviously can’t speak for them. I’m certain that they are not taking any notice of your work at all.

Bell hoped deeply that ultimately a classical description could work but he was wise enough to understand that that might not be the case. He was not dogmatic about this.

I have no opinion about helicity. Maybe you are onto something interesting there. But it has nothing whatsoever to do with Bell’s theorem.

Richard

Sent from my iPhone

On 27 Apr 2022, at 15:41, Bryan Sanctuary <bryancs...@gmail.com> wrote:



[Bryan Sanctuary]

coun·ter·ex·am·ple

/ˈkoun(t)əriɡˌzampəl/

Learn to pronounce

noun

noun: counter example

1. an example that opposes or contradicts an idea or theory.

   
   
2. Bell says no local hidden variable (whether classical or not) can reproduce all the correlations. 
3. 
   
4. So please tell me explicitly why helicity does not provide that counter example.  
5. 
   
6. Bryan 

To view this discussion on the web visit https://groups.google.com/d/msgid/Bell_quantum_foundations/f261c3048c9a5e2320c6c502bf525e823cd835e3.camel%40liu.se.

[Richard Gill]

Bryan, 

Bell’s proof does not assume that spins are always polarized up or down.

Show us where you think he makes such an assumption.

Bell’s proof (in, e.g., his Bertlmann’s socks paper) does not talk about spins or polarizations. It is about a macroscopic arrangement of laboratory devices which allow users to input settings and to observe outcomes. It is not about “measurement”. It is not about “observables”. It is not about “particles”.

Read it! With an open mind. Learn!

It assumes a classical physical world view.

We learn that classical physics cannot explain certain observable phenomena, which we nowadays describe with quantum mechanics.

It seems to me that you should be perfectly happy with this state of affairs. Forget local realism. Forget Bell’s theorem. Stick to quantum mechanics. You are fighting windmills, for no good reason whatsoever. Time you moved on, like most of the rest of us did, long ago.

Richard

Sent from my iPhone

On 27 Apr 2022, at 16:30, Bryan Sanctuary <bryancs...@gmail.com> wrote:



[Bryan Sanctuary]

Ok Richard, that is your position. 

You want me to go over again, ad nauseum, Bell's math!!!  waste of time, done that been there. He is wrong in assumption. 

 What is amazing is you admonish me and say "Be inquisitive. Creative. Push it to its boundaries." where it is the field of quantum info (and RIchard Gill) with the blinkers.

 You  won't even try to understand helity which I agree has nothing to do with any of Bell's work, except provide a counterexample and disproves his theorem. 

I know that it will not be the Bellists or the non-local missionaries that accept my work.  However at some point they will have to answer the demand for retractions.

You have lost, and teleportation and the Big Bell Test are in error,  but either you do not understand why or you won't admit it.  How do you see a counter example??

Thanks

Bryan

[Richard Gill]

Bell says no classical local hidden variable theory can reproduce quantum mechanical predictions for e.g. the singlet state.

His definition of a hidden_variable_theory includes classicality. Look at his precise mathematical formulation. Read his motivation for his precise assumptions in Bertlmann’s socks. He writes English but he also writes mathematical formulas. Study them carefully.

Sent from my iPhone

On 27 Apr 2022, at 17:00, Bryan Sanctuary <bryancs...@gmail.com> wrote:



To view this discussion on the web visit https://groups.google.com/d/msgid/Bell_quantum_foundations/CALLw9YyhmSFhHND%2B7g3N57f48SVEmTMmKOY50AVDHsrdh04qjw%40mail.gmail.com.

[Bryan Sanctuary]

Richard

Sigh--if you look at Bell's title and you read his work it is all about CLASSICAL spin which he expresses as CLASSICAL random variables with outcome of +/-1.  I have answered that before, won't repeat. 

You have all missed quantum coherence.  You think spin is always polarized:  S_z on states give only +/-1 in qm.  

Your other comments are not relevant and nothing new to me.  I do not think I have missed anything of importance in Bell's work, mainly because you and others are not telling me anything I have not already thought about.  

And YES his proof of BI and his theorem are all CLASSICAL.  He models spin as a classical up-down outcome system.  I have said that all along.  But there is more than classical

Bryan

[Bryan Sanctuary]

well Richard, actually, no,  I have done my due diligence and you have not.  Your ideas I am fully aware of.  It is incumbent on you to be aware of mine.

Bryan

[Jan-Åke Larsson]

Bryan,

Bell does not write about spins. He writes about MEASUREMENT OUTCOMES that are +/-1.

/JÅ

[Bryan Sanctuary]

ok, so it has nothing to do with quantum mechanics and therefore has no relevance.  Is that what you mean?

What do the coincidence experiments show?  Spins.  What does everyone do? look for violation of BI by spins.

Your suggestion that it is nothing about spin is not correct. besides, it does not affect my results.

Bryan

[Jan-Åke Larsson]

What are your measurement outcomes?

[GeraldoAlexandreBarbosa]

Hi Bryan,

TKS for your paper “Spin Helicity”. Your treatment of spin algebra and the treatment of possible spin products for a single state is text-book clear but your inferences may not be so clear, in my understanding. For example,

1)      At your conclusion, “We conclude with Bell’s theorem gone, nothing stands in the way of EPR: quantum mechanics is incomplete”. That QM is incomplete is a conclusion that did not need analysis of Bell’s theorem at all. Lack of a unified view for electrodynamics, gravitation … should more than enough for such conclusion.

Moreover, strictly, Bell’s inequalities only deal with classical entities. This weakens your conclusion and makes it disconnected from a larger perspective. Using Bell’s theorem to attack QM seems completely inappropriate.

2)      “In addition to polarization, we report a hitherto missed property of spin, its handedness, or hyperhelicity”. Missing property of spin? Helicity has been used for so long that I don’t know what you mean as a “discover” of a missed property.

3)      It seems that you have not touched the crucial fact that the correlation in the spin pair can be measured at separation distances that violates the possibility for signal propagation for that distance – with the caveat that the verification of such violation is bounded by the speed of light (difference of detection times in the experiment). This implies:

·         Your treatment is “local” by definition.

·         If we say that all your reasoning is valid for any distances between detection systems, that you are assuming an infinite speed for signal propagation. In this case, you have another serious problem at your hands.

4)      Your matrix rho12 (Eq. (2)), admits entanglement. Then you say that a local singlet presents a correlation between spin – and you keep your discussion locally and present “general” discussions with a “local” calculation. (Connected to 3) above)

5)      The comment “helicity is destroyed in anisotropy” is correct, but it was not used in your discussion. Is this relevant in your treatment?

Just as a curiosity, there is some literature along this subject (isotropy or anisotropy) applied to entangled states. Arnaut & Barbosa, in PRL 85, 286 (2000) shows that “States of light that are simultaneously eigenstates of orbital, intrinsic, and total angular momentum are found and eigenstates describing pairs of photons from spontaneous parametric down-conversion reveal classes of photon conversion with angular momentum conservation and cases where the initial angular momentum from the pump laser beam is shared between the converted photons and the generating medium. These angular momentum conservation laws open up a wide range of applications to be explored.”

That analysis shows that entangled photons from parametric down conversion will satisfy eigenvalues of the total angular momentum Jz of the electromagnetic field associated with the photons.

In case of interest in the subject, it was also shown (GAB, PRA 80, 063833 (2009)),

that there are cases of conservation and non-conservation of Jz depending on the crystal classes (symmetry classes) used to obtain the parametric down-conversion:

“Several wave-function approximations describing spontaneous parametric down-conversion can be found in the literature. Basically, all cases are derived from the standard Hamiltonian for parametric down-conversion. Most frequently, particular cases describing collinear or paraxial approximations are described. This work presents a wave function in compact form, valid for all cases of single photon-pair conversion (Type I or Type II), for all angles allowed by the phase-matching conditions and for all orbital angular momentum values l.

Examples are given of coincidence structures to be expected for signal and idler photons. Partial transfer of orbital angular momentum from the pump laser to the photon pair is discussed. Some hypotheses for the decay channels of the non-transferred part of the orbital angular momentum is made.”

 

Geraldo

Geraldo A. Barbosa, PhD

KeyBITS Encryption Technologies LLC

https://www.keybits.tech/

1540 Moorings Drive #2B, Reston VA 20190

E-Mail: Geraldo...@gmail.com

Skype: geraldo.a.barbosa

Cellphone: 1-443-891-7138 (US)

On Mon, Apr 25, 2022 at 1:34 PM Bryan Sanctuary <bryancs...@gmail.com> wrote:

Geraldo

Thanks very much for that feedback and comments. I basically agree with everything you say.  One point about knowledge (of a spin) which I now say is incomplete. We observe polarizations but not coherences.  This actually goes against the No-hiding theorem which says all info is available.  You cannot see information contained in spin coherence, a real property of Nature.

You are absolutely right that I did not convince you because I left out the key point.  I am really at a loss as to what to do. Waiting for the 4th journal to decide to review not, has been going on for three months. 

If I am refused a peer review the fourth time I will have to make them public somehow, maybe my blog.

"A Peer Review, A Peer Review, a horse for a Peer Review!"

Thank you for your patience.  It is appreciated.

Bryan

On Mon, Apr 25, 2022 at 12:40 PM GeraldoAlexandreBarbosa <geraldo...@gmail.com> wrote:

Bryan,

It seems that everyone agrees that Bell’s inequalities were set in a classical context.

In a classical context, particles are distinguishable (although such distinguishability may be practically impossible in many cases – e.g., particles in a gas). In a classical context, a magnet has two distinct positions, and they are distinguishable, and they do not live in a superposition state.

This implies that a classical state can be perfectly copied, as many times as our resources allow (flying “flags” can be copied).

 

Also, derivation of quantum aspects within a classical context can lead to weird conclusions.

A quantum state, representing a spin (a quantum entity), represents our knowledge of that spin, and it may as well represent a superposition state.

An expected value for a measurement on that state includes a space axis for that measurement (e.g. a magnetic field orientation). That measurement axis can be set even after the spins have left their original site. While the preparation of the initial state of two spins (in the same position) could be made along an axis z₀, a measurement could occur along any z axis.

(Calculated) Complementary measurements at position A and position B would always give – along an arbitrary z direction, the + and – results, regardless of the distances between A and B. That implies that the + and – are NOT rigidly attached to the initial axis z₀ (=”flying flags”). It is also true that the correlation of the +/- results are only seen after the measured signals are compared (light speed bound correlation).

Quantum models allow entangled states, not the classical models.

I could not understand how you apply your idea of classical “locality” to explain correlations at distant places along arbitrary measurement axis. Are you also discarding quantum mechanics? Are you challenging the idea of correlation at distant positions? … I am a bit confused … Your note did not help me.

Geraldo

Geraldo A. Barbosa, PhD

KeyBITS Encryption Technologies LLC

https://www.keybits.tech/

1540 Moorings Drive #2B, Reston VA 20190

E-Mail: Geraldo...@gmail.com

Skype: geraldo.a.barbosa

Cellphone: 1-443-891-7138 (US)

On Mon, Apr 25, 2022 at 10:03 AM Bryan Sanctuary <bryancs...@gmail.com> wrote:

Thanks for your comment Richard:  

First you say:

“Bryan is mistaken. Bell did not assume that the outcomes +/-1 always exist from source to destination. He only assumed that the outcomes appear upon measurement.”

My response:

This is categorically and emphatically untrue.  Bell’s random variables only take values of +/-1, all the time, everywhere, no question. The immediate consequence of your statement is that qubits, superpositions of +/-1, only exist upon measurement! That will upset quantum computing programmers.  Second that means that the singlet state is not (|up>|dn> - |dn>|up>).  This expression is the only one I have seen for the singlet: flags always flying whether measured or not. Third spin is measured in a Stern-Gerlach experiment to have values of only |+/-1>, which is exactly what Bell uses. Sorry Richard, nice try.

I challenge you to point out anywhere in the literature that you have a spin, or a spin function, that is NOT composed of polarized up/dn states.  I doubt you can.

Bell’s assumption is a result of Bell not being able to think quantum mechanically.  I see that in his papers.  He is tied to classical thought, just like his useful inequalities. He forced his classical system (socks) to be non-classical and the result is non-locality. It is that simple. Non-locality is the only consequence in the absence of other elements of reality.

Second you say:

“So instead of adding classical hidden variables, Bryan seems to be adding unobservable quantum observables: |+><-| and |-><+| are operators acting on the Hilbert space  C^2, but they are not self-adjoint. Their eigenvalues are purely imaginary.”

My response:

This is exactly what I am saying.  The coherences are unobservable (LHiddenV) which is why they have been missed for 100 years. Indeed, the states are non-Hermitian, but Richard is wrong, all the eigenvalues are real +/-1.  They are not imaginary at all. Finally, the non-Hermiticity breaks up into two spaces, which are complementary and carry Hermitian operators (polarizations) and anti-Hermitian operators (coherences).

My space is not is Hilbert Space C^2 but a single space of 4x4 gamma matrices that describe a single spin which is embedded in spacetime.

I should point out that Bell’s Blunder is the first of very sobering results which you will find quite unsetting. It is interesting that you cannot come up with any other points of contention in that little Blunder paper.  You will find, as I finally get these out, that one by one your notions will fall until finally you will convert to local realism.

On Monday, April 25, 2022 at 12:36:28 AM UTC-4 Richard Gill wrote:

Bryan writes:

“The error in Bell’s Theorem [11] is his assumption that his random variables always carry the values of ±1. This is not supported by the existence of LHV. Bell assumed polarization, |±⟩ ⟨±|, always exists from the source to detection: the flags are always flying. However, the flags only appear upon the measurement of spin. In contrast, for coherence, |±⟩ ⟨∓|, the flags are furled, and describes a spin in isotropy. [11] Bell, J. S. (2004). p. 139 or 147, Speakable and unspeakable in quantum mechanics: Collected papers on quantum philosophy. Cambridge university press.”

Bryan is mistaken. Bell did not assume that the outcomes +/-1 always exist from source to destination. He only assumed that the outcomes appear upon measurement.

Bryan sees spin from a quantum-mechanical point of view. He argues that all these years, we have been missing something connected to complementarity. We have missed:

“that spin components do not commute, that quantum mechanics reveals ‘inverse’ spaces. What, then, is the inverse space for spin angular momentum? All we know of spin is its measured vector polarizations, |±⟩ ⟨±|. It turns out that the inverse spin space is the coherencies expressed by, |±⟩ ⟨∓|. These support other spin properties which account for the missing correlation”

So instead of adding classical hidden variables, Bryan seems to be adding unobservable quantum observables: |+><-| and |-><+| are operators acting on the Hilbert space  C^2, but they are not self-adjoint. Their eigenvalues are purely imaginary.

Sent from my iPad

On 24 Apr 2022, at 23:34, Bryan Sanctuary <bryancs...@gmail.com> wrote:



Hi all

Here is a link to my view of the error Bell made in his Theorem,

http://blog.mchmultimedia.com/2022/04/24/bells-blunder/

Bryan 

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[Chantal Roth]

Bryan,

I hope so very much that you are right, and I'd love to help.

Jan-Åke is correct though: an experiment at the end measures +/-1.

It does not matter what the spin is at all (it could be pink unicorn, it could be anything at all, it does not matter).

Somehow, a +1 or -1 comes out - we don't even have to understand how or why.

Bell (and others) make statements about what those correlations could be and in which models these correlations have certain values. That's it.

Whatever theory you have, it has to be able to reproduce similar correlations of those +1/-1 values as predicted by QM.

Best wishes,

Chantal

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[Алексей Никулов]

Dear Richard,

It is correct that “Bell’s proof does not assume that spins are always
polarized up or down”. But it is not correct that “no classical local

hidden variable theory can reproduce quantum mechanical predictions

for e.g. the singlet state”. You do not want to understand that only
Bohm's quantum mechanics, but not orthodox quantum mechanics predicts
violation of Bell’s inequalities. You do not want to understand that
according to the orthodox quantum mechanics operators acting on
different particles commute and therefore quantum mechanics cannot
contradict locality. You do not want to understand that all this story
with Bell's inequalities is a mass delusion provoked by Bohm, who,
without any reason, extended the Dirac jump to the particle that is
not measured, making the Dirac jump completely absurd.

With best wishes,

Alexey

ср, 27 апр. 2022 г. в 18:45, Chantal Roth <cr...@nobilitas.com>:

> To view this discussion on the web visit https://groups.google.com/d/msgid/Bell_quantum_foundations/71bcdadd-e687-404b-be2b-65996072f3c9%40www.fastmail.com.

[Bryan Sanctuary]

The outcomes are the experiments by Aspect, Gregor and they violate BI and I agree with their data.  -cos(a-b).  

I cannot provide a click by click build up because we must have a theory that can account for two incompatible elements of reality simultaneously.  QM cannot do it.  So to include click by click agreement, qm must be extended. Future work.

My role is to show you that spin has more than polarization, and that more fills the gap.  You want to stick with Bell's classical notions,  I said that at the end, if you want to reject helicity go ahead and then you get non-locality.  Up to you. 

If you want, it is up to you to do the click by click work.  I just present a counter example. 

Bryan

[Bryan Sanctuary]

point 1  I agree there are other issues with QM.  However I am talking about EPR (Bell's theorem stood in the way, now it is gone)

\point 2 shows me that you have not read the paper fully and jumped to conclusion  I say twice that the usual helicity is entirely different from hyperhelicity.  I would appreciate it if you would read before you react.  Look at the acknowledgement.

 the other points are a result of you not being clear on what I am saying,  Please read it there because I it is not worth adding again here.

Thanks for the other info which I will look at.

Bryan

[Richard Gill]

Dear Alexei

With all respect, I think you are talking utter nonsense.

Richard

Sent from my iPad

> On 27 Apr 2022, at 17:53, Алексей Никулов <nikulo...@gmail.com> wrote:
>
> Dear Richard,

[Jan-Åke Larsson]

No. Either you do it or there is no counterexample.

Simple as that.

/JÅ

[Алексей Никулов]

Dear Richard,

With all respect, I think you are extremely biased. You are biased,
including as a mathematician. You don't want to admit that obvious
mathematical mistakes were made in the derivation of the GHSZ theorem
and local realism was experimentally refuted on the basis of these
mistakes. The authors [1] made obvious mistakes precisely because Bohm
misled Bell, and Bell misled everyone including you. You don't seem to
understand why quantum mechanics predicts the violation of Bell
inequalities.

[1] D.M. Greenberger, M.A. Home, A. Shimony and A. Zeilinger, Bell’s
theorem without inequalities, Amer. J. Phys. 58, 1131 (1990).

With best wishes,
Alexey

ср, 27 апр. 2022 г. в 20:14, Jan-Åke Larsson <jan-ake...@liu.se>:

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[Richard Gill]

Bryan, if you could extend QM so as get click by click agreement in a local way you would effectively have described the algorithm for a computer program for a pair of separated computers which could simulate the quantum correlations in a local realistic way.

Unfortunately, this is impossible. The future work you envisage is doomed to failure. See my paper on Gull’s theorem (to appear soon in “Entropy”), 

https://arxiv.org/abs/2012.00719

Or show me the error! I will admit defeat if you can identify a fatal error in this paper. By the way, it is not about quantum mechanics, but about distributed computing. The maths is quite easy, it uses some well known results about Fourier transforms.

Bell’s theorem is a corollary.

Sent from my iPad

[sgl...@nist.gov]

Bryan,

I looked at your paper "Spin With Hyperhelicity" today.  Unfortunately, I was not able to understand much of it.  It would be helpful if there was a more detailed discussion of what exactly you mean when you say "local hidden variable" and why hyperhelicity is a local hidden variable theory.

Even though I'm not exactly clear on what you mean by "local hidden variable", it seems clear that you and Bell assign different meanings.  For the clarity of this discussion, it would help to distinguish Bell's LHVs from Sanctuary's LHVs, so maybe we could call them "BLHV" and "SLHV".  It seems that you are saying that SLHVs are not constrained by Bell's Inequalities.  I think that is not a disproof of Bell's proof that BLHVs are constrained by Bell's Inequalities because both statements "BLHVs are constrained by Bell Inequalities." and "SLHVs are not constrained by Bell Inequalities" can be true.

You have said that Bell's assumption is false.  Do you mean that actual LHVs in the real world do not have the same properties of BLHVs?  If that is what you mean, I would still think that the statement "All BLHVs are constrained by Bell's Inequalities" is true, even though BLHVs might not exist in the real world.  (I also think the statement "All unicorns have horns." is true.)

Scott

On Wednesday, April 27, 2022 at 6:19:26 AM UTC-6 bryancs...@gmail.com wrote:

Hi Scott

I do not think you have read my paper,

http://blog.mchmultimedia.com/2022/04/26/hyperhelicity-the-completion-of-spin/

Here is the NUTSHELL:    Bell says " if it agrees with quantum mechanics it will not be local"

Hyperhelicity is a LHV, that accounts for the violation of BI, Therefore I have  disproven Bell's Theorem by counter example.END OF STORY.

WIth that we do not have to waste our time talking about the issues you raise.  His theorem is toast.

In short, from now on there is no reason to even mention the theorem, let alone worry about its  proof. It is wrong. The reason it is wrong is he  made a bad assumption just like von Neuman did.

I have no interest in discussing anything of Bell's Theorem.  It is now relegated to the "Annals of Lost causes and Bad Ideas"  Bell's theorem are now only of historical interest and must be removed from physics

Do you agree?

Bryan

On Tue, Apr 26, 2022 at 11:15 PM 'sgl...@nist.gov' via Bell inequalities and quantum foundations <Bell_quantum...@googlegroups.com> wrote:

Bryan,

To understand what you mean when you say that you have disproved the statement "If [a hidden-variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local.", we need to have a mapping between all of the words in that statement and mathematical concepts.  If you think that the statement is false and Bell thinks that the statement is true, the disagreement could be caused by you and Bell having different interpretations of those words as mathematical concepts. To me, that quote seems like an informal summary of the statements 1, 2, and 3 that I mentioned earlier.  I think that Bell was trying to translate some formal statements about probability distributions into natural, English language.  When Bell says "If a [hidden variable theory] is local", I think that he simply means those theories that produce probability distributions that are constrained by Bell Inequalities.

Could the disagreement be that you think that "local hidden variable theory" is not a good description of those theories whose probability distributions obey Bell Inequalities?  Or do you think the disagreement lies elsewhere?

Scott

On Tuesday, April 26, 2022 at 5:11:35 PM UTC-6 bryancs...@gmail.com wrote:

Hi Scott

I state  Bell's THeorem:

 ``If [a hidden-variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local."

I really have never been interested in the veracity of BI  I went through the math years ago and am not interested in any challenge.  I accept and in fact really see them as Bell's achievement.  Its just that his theorem is wrong.  

I just posted my first paper.  I resolves the EPR paradox, it is here

http://blog.mchmultimedia.com/2022/04/26/hyperhelicity-the-completion-of-spin/

Thanks

Bryan

On Tue, Apr 26, 2022 at 7:04 PM 'sgl...@nist.gov' via Bell inequalities and quantum foundations <Bell_quantum...@googlegroups.com> wrote:

Bryan,

When you say that you have found an error in the proof of "Bell's Theorem", I am not certain about the precise theorem that you think is in error.  I wasn't able to find a statement of the theorem in your "Bell's Blunder" paper.

I can think of a few different possibilities for theorems related to Bell:

1. The marginal distributions produced by joint probability distributions obey some inequalities ("Bell Inequalities").

2. Quantum theory predicts that the marginal distributions produced by some entangled systems can violate the Bell Inequalities.

3. Spacelike separated measurements on entangled particles cannot be described by a fixed joint probability distribution.

I haven't stated any of those formally, but it would be helpful if you could specify which statement you object to.  Then we might work on where exactly you think the mathematical error lies.

Scott

On Tuesday, April 26, 2022 at 6:47:26 AM UTC-6 bryancs...@gmail.com wrote:

Hi Richard

I can understand why you are upset.  You are a Bellist and have great regard for the work John Stewart Bell, especially his Theorem.  I am attacking that but I am not denigrating his career at CERN (of which I know little) or his other successes or him personally.  However he made an enormous Blunder in the proof of his theorem and that is his legacy now.  Still, 60 years on,  people are using his Theorem to justify so much work that is misleading and incorrect, like the Big Bell Test*, and for quantum teleportation**.  It must change.

*BIG Bell Test Collaboration. "Challenging local realism with human choices." Nature 557.7704 (2018): 212-216.

**Bennett, C. H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., & Wootters, W. K. (1993). Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Physical review letters, 70(13), 1895.

The reason for Bell's error is he believed that spin is always polarized, and it is not.  That means to me, he could not image beyond his classical states--hence my comment about his Positivist attitude.   

The end result is that his theorem, and then the CHSH successful experiment, has seared into physics the absurd notion on non-locality.  I find it boggling that the world of Physics succumbed and accepted such nonsense in the first place, because, think of it, non-locality, EPR channels make no sense, and constitutes, as Alexey says, religion.

MY GOAL: This is an academic war about knowledge.  I will win but first I must fight. I did not fight until I had the ammunition.  My intention is to completely change the world view of spin from a two level vector observable to a four level hyperspin.  From this, gobsmacking consequences arise, like the Dirac equation does NOT produce anti-matter. (First time I told you that).

I know what I am up against:  a chemist with little credibility is telling physics they have spin wrong, Quantum Information Theory must change, and that antimatter is not produced!!  No wonder there is skepticism and disbelieve. 

If in a meek and mild way I posted somewhere, my work would be ignored.  How long did Bell's 1964 paper sit unnoticed?  By delaying the repudiation of non-locality, billions of research funds are being wasted and myriad research projects will result in misleading ideas.  If I am to change the field of Quantum Information and stop teleportation nonsense, I have to attack Bell's Theorem. I also must be assertive.  I only bet you to get attention, and, of course, the certainty that I will win.  

There will be casualties in my attack, like your papers being retracted, and the gurus who have hyped the field for so long will convert to local realism, or retire. I have no qualms about personal consequences: hey it has had a number of negative effects on me by sticking to my values.  

In my short Bell's Blunder paper, please tell me where I am not truthful, obfuscating or wrong.  So far you have nothing credible so I surmise that if I give you that LHV part, and you accept this as a counter example, then Bell's Theorem is disproven,

Finally, in this, my intention is absolute honesty and integrity.  I would never think of "putting any words" in any one's mouth.  Any other approach than honesty will fail and I will lose.  Hence I am forceful, assertive, but guided by truth, justice and the (well I'll not finish that).

I guess there are various editions of speakable, with the pages not the same.  Sorry about that. I attach the page with Bell's quote"  The others are there somewhere in your edition, I hope you find them.  I made nothing up:  Bell said:

"If [a hidden-variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local."  Bell, John S., (1987). Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press. p. 65. 

Brest wishes,

Bryan

On Monday, April 25, 2022 at 7:42:52 PM UTC-4 Richard Gill wrote:

Dear Bryan

You are categorically and emphatically wrong. I will write to you personally with exact with quotes from Bell, proving this.

You refer to two page numbers of your edition of “Speakable and unspeakable”. Please send me a pdf/photo of each of those pages, or quote a salient sentence from each.

You apparently utterly mistake Bell’s intention. You say Bell could only think classically. His main work at CERN was top level orthodox QM work. The point of his foundational work was to prove that classical thinking could not explain certain QM predictions. He succeeded in showing exactly why this was so.

In other words: you agree with Bell. Feynman already said: we already knew this! It’s not interesting, not useful!

You could have more success with your mission if you would stop maligning Bell by putting claims into his mouth which he never made. It gives everyone a license to ignore the “meat” in your work.

Richard

Sent from my iPhone

On 25 Apr 2022, at 16:03, Bryan Sanctuary <bryancs...@gmail.com> wrote:



Thanks for your comment Richard:  

First you say:

“Bryan is mistaken. Bell did not assume that the outcomes +/-1 always exist from source to destination. He only assumed that the outcomes appear upon measurement.”

My response:

This is categorically and emphatically untrue.  Bell’s random variables only take values of +/-1, all the time, everywhere, no question. The immediate consequence of your statement is that qubits, superpositions of +/-1, only exist upon measurement! That will upset quantum computing programmers.  Second that means that the singlet state is not (|up>|dn> - |dn>|up>).  This expression is the only one I have seen for the singlet: flags always flying whether measured or not. Third spin is measured in a Stern-Gerlach experiment to have values of only |+/-1>, which is exactly what Bell uses. Sorry Richard, nice try.

I challenge you to point out anywhere in the literature that you have a spin, or a spin function, that is NOT composed of polarized up/dn states.  I doubt you can.

Bell’s assumption is a result of Bell not being able to think quantum mechanically.  I see that in his papers.  He is tied to classical thought, just like his useful inequalities. He forced his classical system (socks) to be non-classical and the result is non-locality. It is that simple. Non-locality is the only consequence in the absence of other elements of reality.

Second you say:

“So instead of adding classical hidden variables, Bryan seems to be adding unobservable quantum observables: |+><-| and |-><+| are operators acting on the Hilbert space  C^2, but they are not self-adjoint. Their eigenvalues are purely imaginary.”

My response:

This is exactly what I am saying.  The coherences are unobservable (LHiddenV) which is why they have been missed for 100 years. Indeed, the states are non-Hermitian, but Richard is wrong, all the eigenvalues are real +/-1.  They are not imaginary at all. Finally, the non-Hermiticity breaks up into two spaces, which are complementary and carry Hermitian operators (polarizations) and anti-Hermitian operators (coherences).

My space is not is Hilbert Space C^2 but a single space of 4x4 gamma matrices that describe a single spin which is embedded in spacetime.

I should point out that Bell’s Blunder is the first of very sobering results which you will find quite unsetting. It is interesting that you cannot come up with any other points of contention in that little Blunder paper.  You will find, as I finally get these out, that one by one your notions will fall until finally you will convert to local realism.

On Monday, April 25, 2022 at 12:36:28 AM UTC-4 Richard Gill wrote:

Bryan writes:

“The error in Bell’s Theorem [11] is his assumption that his random variables always carry the values of ±1. This is not supported by the existence of LHV. Bell assumed polarization, |±⟩ ⟨±|, always exists from the source to detection: the flags are always flying. However, the flags only appear upon the measurement of spin. In contrast, for coherence, |±⟩ ⟨∓|, the flags are furled, and describes a spin in isotropy. [11] Bell, J. S. (2004). p. 139 or 147, Speakable and unspeakable in quantum mechanics: Collected papers on quantum philosophy. Cambridge university press.”

Bryan is mistaken. Bell did not assume that the outcomes +/-1 always exist from source to destination. He only assumed that the outcomes appear upon measurement.

Bryan sees spin from a quantum-mechanical point of view. He argues that all these years, we have been missing something connected to complementarity. We have missed:

“that spin components do not commute, that quantum mechanics reveals ‘inverse’ spaces. What, then, is the inverse space for spin angular momentum? All we know of spin is its measured vector polarizations, |±⟩ ⟨±|. It turns out that the inverse spin space is the coherencies expressed by, |±⟩ ⟨∓|. These support other spin properties which account for the missing correlation”

So instead of adding classical hidden variables, Bryan seems to be adding unobservable quantum observables: |+><-| and |-><+| are operators acting on the Hilbert space  C^2, but they are not self-adjoint. Their eigenvalues are purely imaginary.

Sent from my iPad

On 24 Apr 2022, at 23:34, Bryan Sanctuary <bryancs...@gmail.com> wrote:



Hi all

Here is a link to my view of the error Bell made in his Theorem,

http://blog.mchmultimedia.com/2022/04/24/bells-blunder/

Bryan 

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[Bryan Sanctuary]

Hi Chantal

I agree.  I will post a small summary of that issue and give a "rationale" for what happens from source to filter.  It needs a programmer who can reproduce the mechanism.

Good to hear from you,

Bryan

[Chantal Roth]

Hi Bryan,

I'd be happy to help - if you can explain it in simple terms so that I can actually program it though :-).

*If* the program works, it will be easy to convince anyone... (even Richard :-))

Best wishes,

Chantal

To view this discussion on the web visit https://groups.google.com/d/msgid/Bell_quantum_foundations/25aa5499-80ae-4bc9-8cc0-5c100f5f263dn%40googlegroups.com.

[Richard Gill]

Bryan, a programmer cannot generate the singlet correlations on a network of three computers (playing the parts of source, measurement station 1, measurement station 2) without using communication between the measurement station computers. Or breaking other rules (measurement outcomes +/-1, no post-selection, no control of the settings)

Sent from my iPhone

On 29 Apr 2022, at 13:27, Bryan Sanctuary <bryancs...@gmail.com> wrote:



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[Bryan Sanctuary]

Hi Scott,

The math in the paper is correct mainly because it is  based upon calculating expectation values.  Those equations can be calculated in the usual way using spin states.  The only new feature is defining the helicity as a second spin property and it is not Hermitian but anti-Hermitian. 

My LHV, helicity, is a new element of reality.  This property exists and is carried on the particle.  Its influence acts within the particle only.  All forces associated with the particle drop off with an inverse law on separation,  The helicity is hidden because it cannot be measured.  And it is a qm operator, or quantum variable. Hence a LHV and the two particles in an EPR pair cannot influence each other after separation.  It is a product state with no entanglement.

I use locality , and LHV, as the same as EPR used.  There can be no influence between Alice and Bob, hence local.

Non-local hidden variables require that the polarizations at Alice and Bob are connected in a way that is not explained, but accounts for the violation of BI.  The teleportation paper (Bennett et al) calls these "EPR channels"  and others "quantum channels" but they are never explained them and there is no evidence.  Non-local HV are supposed to make up for what is missing in the experiment.  I find no clear definition.  People say they violate Special Relativity.

Bell uses classical LHV in his inequlalities paper, and defines them as not influencing Alice and Bob.

To get the meaning of Non-local HV you must look at the Bertlmann sock proof and the socks (classical polarizations) must maintain connectivity through a non-local interaction.  It is not specified how beyond quantum weirdness.  No one knows what non-local hidden variables are.

True Bell is all classical but he models a spin based upon the experimental observation that spin has 2 states with outcomes +/-1.  I see no other value his random classical variables can take. 

I hope this helps 

Bryan

[Bryan Sanctuary]

I will post the description today.  If anyone can do it, you can!!

Bryan

[Richard Gill]

Bryan forgets there are two filters. The source sends information to filter 1 and to filter 2. The settings come from outside. According to Gull’s theorem it can’t be done, without cheating. 

Of course I will believe it if someone actually succeeds in this “impossible task”. 

https://gill1109.com/2021/12/22/the-bell-game-challenge/?amp=1

Sent from my iPhone

On 29 Apr 2022, at 13:41, Chantal Roth <cr...@nobilitas.com> wrote:



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[Bryan Sanctuary]

What if the particle carries a complex phase??

Bryan

[Richard Gill]

Bryan, the particles can carry pink unicorns as far as I’m concerned (as long as each unicorn has a horn on its head and a maiden sitting on its back). Or octonions. Or elements of some esoteric Clifford algebra. 

There are no restrictions on *what* is programmed. The restrictions concern the inputs, outputs, and possible communication channels.

Take a look at my proof of Gull’s theorem.

Sent from my iPhone

On 29 Apr 2022, at 13:56, Bryan Sanctuary <bryancs...@gmail.com> wrote:

What if the particle carries a complex phase??

To view this discussion on the web visit https://groups.google.com/d/msgid/Bell_quantum_foundations/ff3838a8-f9e0-4128-872b-ef90efb2cdban%40googlegroups.com.

[Алексей Никулов]

Dear Richard,
Yesterday, Editors of “Annalen der Physik” rejected my manuscript
"Physical thinking and the GHZ theorem" an hour after its submission.
They don't like my manuscript any less than you do. Nevertheless I
must explain to you shortly what obvious mathematical mistakes of the
authors [1] of the GHZ theorem I pay attention to in my manuscript.

The purpose of the GHZ theorem is to prove the incompatibility of the
predictions of quantum mechanics with the assumption of locality and
reality [1]. But, the principle of quantum mechanics is used in
deducing this theorem, according to which quantum mechanics cannot
contradict locality. The authors [1] assume, when deducing the
expectation value (8) in the Appendix F, that measurement of spin
projection of one of the four particles in the GHSZ state (7), for
example 1, does not change the spin states of other particles 2, 3, 4.
The result of measuring the spin projection of each particle does not
depend on the order of measurement of the particles according to the
Appendix F of [1]. The authors of the book [2] justify in section 6.6
“The Greenberger-Horne-Zeilinger Theorem” the independence of the
measurement results of different particles, when deriving the GHZ
theorem, by the well-known principle of quantum mechanics that the
operators can fail to commute only if they act on the same particle.

But quantum mechanics cannot contradict locality according to this
well-known principle since measurement of one particle of the EPR
(Einstein – Podolsky - Rosen) pair cannot change the quantum state of
other particles, if operators acting on different particles commute.
Result of measurements of the first and second particles of the EPR
pair cannot be different in this case. Therefore the expression (B4)
in the Appendix B, according to which the probability to observe spin
up of the first particle of the EPR pair differs fundamentally from
the probability to observe spin up of the second particle, cannot be
correct according to the principle of quantum mechanics that operators
acting on different particles commute. Thus, the Appendix B
contradicts the Appendix F in the work [1].

This contradiction appeared because the authors [1], when deducing the
expectation value (B5) in the Appendix B, followed John Bell. On the
other hand they used the principle of quantum mechanics, operators
acting on different particles commute, when deriving the GHSZ theorem
in the Appendix F of [1], since Bell did not draw readers' attention
to the mathematical fact that quantum mechanics can predict violation
of Bell's inequalities only if this principle was rejected.

Perhaps John Bell himself did not notice this mathematical fact, since
he was following David Bohm in the deduction of Bell’s theorem. David
Bohm also did not draw readers' attention to the mathematical fact
that the correlation between the results of measurements of the spin
projections of two particles of the EPR pair (the EPR correlation),
which he postulated, is possible only if operators acting on different
particles do not commute. I consider it necessary to finally draw
readers' attention to the important mathematical fact that the
principle of quantum mechanics, operators acting on different
particles commute, must be rejected so that predictions of the EPR
correlation and violations of Bell’s inequalities could be possible.

I also consider it necessary to pay attention to the contradictions in
the predictions of the measurement results given by the expression (7)
in [1] for the GHSZ state and by the expression (F2a), used to derive
the expectation value (8) for this state in the Appendix F. The
expression (7) predicts that the first measurement of spin projection
in any direction of one of the four particles will give spin up with
the probability 1/2, whereas the expression (F2a) predicts that this
probability depends on the angle between the measurement direction and
a direction in which this spin state is eigenstate.

This contradiction appeared because the authors [1] did not take into
account the mathematical fact that spin states of several particles
cannot be eigenstates if they are entangled. This mathematical fact
follows from the mathematical definition of entangled states: several
particles are entangled if their state cannot be described as the
product of the states of each of these particles. The spin state of
each of the non-entangled particles, written for a certain direction,
can be expressed in terms of the angles between this direction and a
direction in which this spin state is eigenstate.

But the spin states of entangled particles cannot be mathematically
expressed through these angles. Therefore the angles in the expression
(8) of [1] for the expectation value don't make sense. According to
the expression (F1) and contrary to mathematics, all four particles in
the GHSZ state (7) have eigenstate in the same direction. But the
authors chose this direction arbitrarily. Therefore the angles in
expression (8) of [1] for the expectation value depend on the
subjective choice of the authors.

[1] D.M. Greenberger, M.A. Home, A. Shimony and A. Zeilinger, Bell’s
theorem without inequalities, Amer. J. Phys. 58, 1131 (1990).

[2] G. Greenstein and A. Zajonc, The Quantum Challenge. Modern
Research on the Foundations of Quantum Mechanics, 2nd edn. Jones and
Bartlett, Sudbury, 2006.

With best wishes,
Alexey

пт, 29 апр. 2022 г. в 15:30, Richard Gill <gill...@gmail.com>:

> To view this discussion on the web visit https://groups.google.com/d/msgid/Bell_quantum_foundations/4E89664E-9502-47A6-AE46-DF29284B7973%40gmail.com.

[Bryan Sanctuary]

Hi  Jan-Åke

Just to be clear, can you be more specific about your statement:

There is no dispute that a quantum description can give the outcomes.

Do you just mean the usual entangled calculation, like my equation (7) in the paper?  If  not, please provide the description you mention.

Bryan

, 

On Wednesday, April 27, 2022 at 10:05:34 AM UTC-4 Jan-Åke Larsson wrote:

Dear Bryan

Bell poses the question: "Can there exist a local hidden variable model?" (you call it "classical")  His theorem proves that the answer is "No".

(He proves that one can not hammer your "square peg" into your "round hole".)

There is no dispute that a quantum description can give the outcomes. All of us understand that it can.

But that is not the kind of model Bell asks his question about. 

Your paper is not a counterexample.

Best
Jan-Åke

On ons, 2022-04-27 at 09:55 -0400, Bryan Sanctuary wrote:

Hi Jan-Åke

Helicity is local, hidden and a variable.  It accounts for the correlation as a LHV.  Bell is disproven, it is math.

I disagree that I must use Bell's classical description to describe a quantum system.  I do not have to pay any attention to Bell's work.  All I have to do is agree with the experimental results and I do:  I account for the violation using helicity.  Then others can scratch their heads and wonder why it disagrees with Bell.  You want to stay classical.  I want to be quantum. 

Bell's approach does not include coherence.  It is classical and you want me to hammer a square peg into a round hole like Bell did.  It will not work, so you must give up Bell and turn to quantum LHV

The Born rules works, of course, for coherences.  I did not say it did not.  I like von Neumann  better which is much easier for me than states.  The two are equivalent so I do not need to use the Born rule.

Hope you accept these arguments.

Bryan

On Wed, Apr 27, 2022 at 9:40 AM Jan-Åke Larsson <jan-ake...@liu.se> wrote:

On ons, 2022-04-27 at 06:19 -0700, Bryan Sanctuary wrote:

Hi  Jan-Åke

Thank you.  "Outcomes at Alice and Bob":  I calculate the EPR correlation, that is enough.   I am not counting clicks but simply agreeing with the coincidence experiments and the violation.  That is all that is necessary at this stage. 

No it is not, it is necessary to describe measurement outcomes using a local hidden variable model, and statistics thereof. 

Bell's theorem is specifically about the possibility of providing such descriptions.

If you do not provide such a description, then your claim fails.

I mention that I use von Neumann's projective measure, equation (4).  My state operators are Eq. 2 and 3 are pure states.  So that should answer your question about statistical averages.

"I can calculate the correlation directly from a vector expression (the singlet quantum state)"  

I am not sure I understand, the singlet is not viable after the local pair separate if that is what you  mean.  Can you explain more about this please?

The singlet is the quantum-mechanical description of the entangled spin state of the combined pair system even when the pair has separated.

Born's rule gives the probabilities of the measurement outcomes, for such a system.

We know this is a good description because it describes the outcome statistics well.

The Born rule is ok for polarizations, but it has a hard time with coherences  I use, as I said, von Neumann and the quantum trace accounts for pure and mixed states. 

Born's rule, as used in modern textbooks, works well with mixed states.

So you disagree that hyperhelicty does not provide a counter example.  Why not? 

Because it does not provide a local hidden variable model.

The paper you posted will not convince me, nor Richard, nor any of the other people you mention.

Like Richard wrote, your description may be correct (or may not), but either way it does not contradict Bell's result.

Best
Jan-Åke

Look forward to your reply

Bryan

> On 27 Apr 2022, at 05:15, 'sgl...@nist.gov' via Bell inequalities and quantum foundations <Bell_quantum...@googlegroups.com> wrote:
>
> If

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[Richard Gill]

The following message got held up by Google Groups' spam filter. The web interface has been changed and I was unable to approve it. So I send it to you all, myself.

From: pierre <pier...@free.fr>
Date: Apr 29 03:14PM +0200

Hello everyone.

It would be great if it works.
I tried to do this for 2 years..
I'm curious about the method used.

"What if the particle carries a complex phase??"

It's not a problem, as long as it's calculable.

Pierre

[pierre]

Hello everyone.

It would be great if it works.
I tried to do this for 2 years..
I'm curious about the method used.

"What if the particle carries a complex phase??"

It's not a problem, as long as it's calculable.

Pierre

[sgl...@nist.gov]

Bryan,

Bell gave various informal descriptions of BLHVs in various writings, and he had a formal, mathematical definition of BLHVs in terms of properties of probability distributions.

I don't know of any writing from Einstein, Podolsky, and Rosen in which they discuss local hidden variables.  As far as I can tell, EPR's notion of "element of reality" seems quite distinct from BLHVs because BLHVs are hidden, but EPR's elements of reality can be predicted with certainty.  EPR's paper seems to be about properties that can be measured rather than hidden properties.

So, I'm confused about how to interpret "I use locality , and LHV, as the same as EPR used.".  It would be most helpful if you could give a formal, mathematical definition of SLHVs in the same spirit as Bell's formal definition in terms of probability distributions.  Then we could compare their mathematical properties.

Scott

[Richard Gill]

Bryan’s equation (7) is

⟨AB⟩ = Tr A†Bρ,

an equation which I never saw before.

Are A, B and rho operators on a single particle Hilbert space for spin or polarization, H = C^2 ? Or what?

I think that the usual QM calculation is 

<A_1 B_2> = Tr ( rho (A x 1) (1 x B) ) = Tr(rho A x B)

where “x” stands for tensor product, the Hilbert space is C^2 x C^2, “1” is the identity operator on C^2, A and B are one-particle spin observables, A_1 := A x 1, B_2 = 1 x B, rho is the two particle density matrix 

rho = | Psi >< Psi |

|Psi> is e.g. the normalized singlet state vector, an element of C^4

Can anyone enlighten me?

Sent from my iPhone

On 29 Apr 2022, at 22:24, Bryan Sanctuary <bryancs...@gmail.com> wrote:

Hi  Jan-Åke

To view this discussion on the web visit https://groups.google.com/d/msgid/Bell_quantum_foundations/989fc7af-cec0-4db8-ad07-7332f4c84af2n%40googlegroups.com.

[Jan-Åke Larsson]

Yes, your presumption is correct. 

The trace expression also works for mixed states, not only pure states like the singlet state.

This is how the subject is tought nowadays, and this is the way we write Born's rule now.

(Bryan likes to call this "von Neumann", I don't care what name one uses so long as it is clear what mathematical expression is meant.)

Best

Jan-Åke

[Jan-Åke Larsson]

Correct, the standard trace expression involving the entangled state.

There is no dispute that a quantum description can give the (statistical description of the) outcomes. All of us understand that it can.

But that is not the kind of model Bell asks his question about. 

Quantum mechanics (involving the Born rule) allows us to write down a click-by-click simulation using standard random variables, but this is nonlocal when comparing to Bell's mathematical description. Bells theorem proves that it has to be, there is no other way out.

Your model is less descriptive than quantum mechanics, since it provides no mechanism for a click-by-click simulation.

This is a severe deficiency and actually, there is no basis for your claim that this is a model that describes the experiment.

You can calculate the correlation, nothing else. 

Also, you do not write what you mean with "local realist". since for certain it cannot be Bell's notion. Because of this, it is unclear to me how your "local realist quantum" description is "local realist quantum" and standard quantum mechanics is not "local realist quantum" in your sense.

Your paper is not a counterexample.

/JÅ

[Bryan Sanctuary]

Look up Hilbert Schmidt space and the definition of the inner product.

Bryan

[Richard Gill]

Bryan 

I know what a Hilbert Schmidt inner product is and all that. I’m a mathematician. 

My question is, what is the relation between your formula and mine?

Tell me what is your Hilbert space and what are rho, A and B in your formula. Is this a one particle formula or two particles? Are A and B operators on C^2 or on C^2 x C^2 ?

Richard

Sent from my iPhone

On 30 Apr 2022, at 13:37, Bryan Sanctuary <bryancs...@gmail.com> wrote:



[Bryan Sanctuary]

I don't have time today to spend on this, sorry.

 The ops A, B are usual qm ops on an h*xh normed vector ,Hilbert, space with inner product defined my way which is usual. 

Look at how I use them to get the props of the operators I use.  Works too. Trivial to relate to the usual vectors over h which give the same result. 

I will let you relate this to your approach.

[Richard Gill]

Dear Alexei, dear friends,

I would like to see Alexei’s definition of “locality", and his definition of "quantum state”.

Bell defined locality only in the context of what he called realistic models, by which he meant essentially deterministic models. Models in which effective randomness is just the expression of underlying chaotic processes. Hence apparently random outcomes are random through the randomness of initial conditions. 

If you trust and use quantum mechanics then you have no use for local realism. You can come up with a mathematical definition of “locality” within the quantum mechanical framework and argue that regular quantum mechanics is local. See for instance the qBist position, or maybe one should say qBist positions, since not all qBists agree: https://plato.stanford.edu/entries/quantum-bayesian/

But are the usual real numbers physically meaningful when we come up with models in which we claim to have “explained” some phenomenon by the hundredth and more decimals in the mathematical representation of an initial position or initial momentum? According to Nicolas Gisin, the so-called real numbers are themselves the hidden variables of classical physics. https://arxiv.org/abs/1909.04514

It seems to me that these foundational discussions are perhaps useful for those trying to come up with a Grand Unified Theory of Everything. Such a theory might “explain” the origins of the universe but it might not be a very useful theory for the quantum optics lab or for quantum information engineering. It might even be considered hubris to imagine that such a theory could exist *and* be comprehensible to our primate brains. Though I am glad that some people look for it. When very smart people fail to find such a theory despite enormous efforts, one has gained information. The nature of the failure might suggest which a priori ideas we are using need to be reconsidered.

Richard

On 30 Apr 2022, at 21:50, Алексей Никулов <nikulo...@gmail.com> wrote:

I am extremely surprised that the respected authors [1-3] did not
understand that if the results of measurements do not depend on the
order of measurements of particles, then quantum mechanics cannot
contradict locality since in this case the measurement of one particle
cannot change the quantum states of other particles.

[Алексей Никулов]

Dear Richard,
My definition of “locality" does not differ from the definition given
by D.M. Greenberger, M.A. Home, A. Shimony and A. Zeilinger on p. 1132
of the article [1]. The authors [1] followed the definition given in
the EPR article: “Since in the time of measurement the two systems no
longer interact, no real change can take place in the second system in
consequence anything of that may be done to the first system” [2].
Bohr disputed locality precisely in this EPR definition [3]. Bell also
used the EPR definition. He wrote in [4] “It is the requirement of
locality, or more precisely that the result of a measurement on one
system be unaffected by operations on a distant system with which it
has interacted in the past, that creates the essential difficulty”.
This definition is also in the book [5]: “Locality: The EPR argument
makes use of an assumption termed locality: the assumption that
anything that happens at a given location has only local effects.
Nothing that happens at A can have any effect on the state of affairs
at B. Locality is an essential component of the EPR argument, for
without this hypothesis it is possible to imagine that Alice's
measurement could have forced Bob's particle into a new state. Thus,
without the locality assumption, we cannot conclude that the spin of
the particle heading toward Bob existed independently of Alice's
measurement”, see p. 145.
The authors [5] were not right when they wrote that “without the
locality assumption, we cannot conclude that the spin of the particle
heading toward Bob existed independently of Alice's measurement”.
Firstly, according to quantum mechanics, it is wrong to think that
spin existed before observation. Quantum mechanics describes the
observable, not the existing. Secondly, Alice's measurement cannot
have forced Bob's particle into a new state according to the principle

of quantum mechanics that operators acting on different particles

commute. The locality assumption is redundant since it is logically
deduced from this well-known principle of the orthodox quantum
mechanics.
I am extremely surprised that the respected authors [1,5] did not
understand that the orthodox quantum mechanics cannot contradict
locality because of the principle that operators acting on different
particles commute. This principle of quantum mechanics was used at the
deduction of the GHSZ theorem [1]. The authors of the book [3] wrote
in section 6.6 “The Greenberger-Horne-Zeilinger Theorem”: “We know
that the three operators Sx(a), Sy(b), and Sy(c) commute. (This is
because each acts on a different particle. Only if Sx and Sy act on
the same particle do they fail to commute.) Thus, we can apply them to
the GHZ state in any order”. Quantum mechanics cannot predict the EPR
correlation and violation of Bell’s inequalities if results of
measurements do not depend on the order of measurements of particles.
Therefore, orthodox quantum mechanics cannot contradict locality.
Only Bohm’s quantum mechanics contradicts locality. Bohm in 1951 [6]
extended the Dirac jump on the particle which is not measured,
contrary to the principle of orthodox quantum mechanics that operators
acting on different particles commute. I draw attention in my
manuscript “Physical thinking and the GHZ theorem” (editors already
two journals rejected this manuscript) that only Bohm’s quantum
mechanics, but not orthodox quantum mechanics can predict the EPR
correlation and violation of Bell’s inequalities.
It is obvious from the expressions (B4) in the Appendix B of [1] that

quantum mechanics can predict violation of Bell’s inequalities only if

operators acting on different particles do not commute. Probabilities
to observe spin up of the first particle (1/2 for any direction)
differ fundamentally from probabilities to observe spin up of the
second particle (the probability depends on the angle between the
directions of measurements of spin projection of the first and second
particles). It is surprising that the respected authors [1] did not
understand that such a difference is in principle impossible, if

operators acting on different particles commute.

The mass delusion about quantum mechanics was provoked, first of all,
by the fact that the quantum state has two different definitions:
subjective and objective. According to the subjective definition,
proposed by Born, the quantum state describes the observer's knowledge
of the probability of the result of an upcoming observation. For
example, the EPR state (see (1) in [1] for example) describes the
knowledge that the first measurement of spin projection in any
direction of one of the two particles will give spin up with the
probability 1/2. According to the objective definition spin states of
non-entangled particles exist really in the real three-dimensional
space.
It should be emphasized that the objective definition can apply only
to non-entangled spin states, since entangled spin states, such as the
EPR state and the GHSZ state, cannot be eigenstates and the operators
of finite rotations of coordinate system are not applicable to them,
see my manuscript “Physical thinking and the GHZ theorem”. The

contradictions in the predictions of the measurement results given by
the expression (7) in [1] for the GHSZ state and by the expression
(F2a), used to derive the expectation value (8) for this state in the

Appendix F became possible because the authors did not take into
account this mathematical fact. The expression (F2a) in [1] predicts
that measurement of spin projection of each particle in the GHSZ state
in the direction which the authors chose arbitrarily will give spin up
with the probability of 1. This prediction, determined by the
arbitrariness of the authors, contradicts the prediction of the GHSZ
state, (7) in [1], according to which the measurement of any particle
in any direction will give a spin up with a probability of 0.5.

[1] D.M. Greenberger, M.A. Home, A. Shimony and A. Zeilinger, Bell’s
theorem without inequalities, Amer. J. Phys. 58, 1131 (1990).

[2] A. Einstein, B. Podolsky, and N. Rosen, Can QuantumMechanical
Description of Physical Reality be Considered Complete? Phys. Rev. 47,
777 (1935).
[3] N. Bohr, Can Quantum-Mechanical Description of Physical Reality be
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[4] J.S. Bell, On the Einstein-Podolsky-Rosen paradox, Physics 1, 195 (1964).
[5] G. Greenstein and A. Zajonc, The Quantum Challenge. Modern
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With best wishes,
Alexey

вс, 1 мая 2022 г. в 09:59, Richard Gill <gill...@gmail.com>: