Re: [Bell_quantum_foundations] Quantum probabilities from Kolmogorov axioms (alternative approach)

[Alexandre de Castro]

your sentence sounds somewhat nonsense. 

Em seg., 6 de jan. de 2025 às 09:20, Richard Gill <gill...@gmail.com> escreveu:

The probabilities you talk about cannot be “obtained" from Kolmogorov axioms alone. The inequality which you write down follows from arithmetic. Your starting point was 1/2 = 0.5 is smaller than 1/sqrt 2 = 0.7071… Arithmetic. 

And that is exactly the fact that Bell used,

On 6 Jan 2025, at 00:52, Alexandre de Castro <alx...@gmail.com> wrote:

In summary: Bell calculates the quantum probabilities (4) using Born rule and shows that they are not compatible with the local model of probability distribution (9) derived from the Kolmogorov axioms. However, it is possible to show that the same probabilities can be obtained directly from Kolmogorov's axioms

Em dom., 5 de jan. de 2025 às 20:31, Alexandre de Castro <alx...@gmail.com> escreveu:

Hi Richard.
We have discussed Bell's calculation and have, previously, reproduced his formulation.
Bell showed that the probabilities obtained by applying the Born rule are not compatible with local models of probability distributions, according to his conception of locality expressed in Eq. 9 (Bertlmann's socks). But we can show that it is possible to obtain from the Kolmogorov axioms those same probabilities obtained by Bell for any event that has probability ½ of occurring.

Em dom., 5 de jan. de 2025 às 13:46, Richard Gill <gill...@gmail.com> escreveu:

Alexandre, the contradiction derived in Bertlmann’s socks is a contradiction between certain physics assumptions and some simple algebra.

Richard

Sent from my iPhone

On 5 Jan 2025, at 16:16, Alexandre de Castro <alx...@gmail.com> wrote:



Dear colleagues,

Here, an alternative approach involving the Born rule. Feel free to analyze.

Consider that , then the condition   holds.

Take any event  that has a probability  of occurring.

Hence,

             

We then can write the inequality as:

             

Or even as: 

             

This inequality can be rewritten in the trigonometric form:

           

And considering the identity: 

We have: 

            

As a result:  

           

Thus, the probabilities obtained in Bertlmann's socks and the nature of reality, Pg 10) can be directly obtained from the probability axioms, without any contradiction.

 

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[Alexandre de Castro]

Mark,

considering the following calculation, can you show where Richard makes perfect sense?

In "Bertlmann's socks", consider Ineq.(9): 

The probability of being able to pass at C and not able at C  The probability of being able to pass C and not able at C  The probability of being able to pass at C and not able at C

This inequality can be written as: ,  where C, C, C and  corresponds to "able to pass" and "not able", respectively.

Let's represent the events as orthonormal vectors in an inner product space:

We can write the following:

By the Born rule:

Thus, Ineq.(9) requires: . As a result: 

Notice that , then the inequality  is equivalent to 

So, . Hence, , 

We then can write this inequality as: , or even as: 

And considering the identity: 

We have: . As a result: 

Alexandre

[Alexandre de Castro]

"Bell's mathematics is elementary and his logic is impeccable."

I agree. What is most interesting is that we can use Bell's formulation to show that a statement and its negation can both be true.

Em ter., 7 de jan. de 2025 08:33, Richard Gill <gill...@gmail.com> escreveu:

I have always said that Bell’s math is elementary and his logic is impeccable. He makes some physical assumptions and derives a logical consequence of them. In some very careful experiments we see that the consequence which he derived is not true. Hence the physics assumptions under which he derived it are not valid in those situations 

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On 7 Jan 2025, at 10:38, Alexandre de Castro <alx...@gmail.com> wrote:



"Alexandre, you didn't use any physics assumptions. You started with 0.5 < 0.7071… = sqrt(2), did some simple arithmetic, and at some point used the well known values of sin^2(22.5 degrees) and sin^2(45 degrees)., thereby recovering a true inequality also used by Bell. What you write down is a trivially true fact. Bell did something interesting with it."

but Bell's formulation is also quite simple.

It can even be considered trivial.
Just see below:

Em seg., 6 de jan. de 2025 às 19:46, Alexandre de Castro <alx...@gmail.com> escreveu:

Mark,

considering the following calculation, can you show where Richard makes perfect sense?

In "Bertlmann's socks", consider Ineq.(9): 

The probability of being able to pass at C and not able at C  The probability of being able to pass C and not able at C  The probability of being able to pass at C and not able at C

This inequality can be written as: ,  where C, C, C and  corresponds to "able to pass" and "not able", respectively.

Let's represent the events as orthonormal vectors in an inner product space:

[Eugen Muchowski]

Richard Gill schrieb am Dienstag, 7. Januar 2025 um 12:33:41 UTC+1:

I have always said that Bell’s math is elementary and his logic is impeccable. He makes some physical assumptions and derives a logical consequence of them. In some very careful experiments we see that the consequence which he derived is not true. Hence the physics assumptions under which he derived it are not valid in those situations 

The physical assumption Bell made need to be challenged.

The following refers to entangled photons in the singlet state, but are also applicable to spin 1/2 particles. 

It is well known that the singlet state, like all Bell states, is not separable. This means that the state of each of the two photons is not only not known, but that a separate state of each of the two photons does not even exist. The reason for this is the indistinguishability of the photons that form the entangled state. If there is no defined state of a single photon from the entangled state, then there is also no definable measurement result A(a, l) or B(b, l) before measurement. If there were measurement results A(a, l) / B(b, l) defined before measurement, then these could only result from the states of the individual photons, which, however, do not exist because of the non-separability (physically the indistinguishability of the particles in singlet state). The conclusion is that Bell's assumption that measurement results have to be of the form A(a, l) / B(b, l) in order to reproduce the QM correlations is wrong. Because of this wrong assumption Bell's inequality fails to correctly describe the relationships between expectation values with polarization entangled photons. 

[GeraldoAlexandreBarbosa]

Please see the attached jpg.

Geraldo A. Barbosa, PhD

KeyBITS Encryption Technologies LLC

https://www.keybits.tech/

1540 Moorings Drive #2B, Reston VA 20190

E-Mail: GeraldoABarbosa@keybits.tech 

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

On Tue, Jan 7, 2025 at 5:13 AM Richard Gill <gill...@gmail.com> wrote:

Alexandre, you did not use any physics assumptions. You started with 0.5 < 0.7071… = sqrt(2), did some simple arithmetic, and at some point used the well known values of sin^2(22.5 degrees) and sin^2(45 degrees)., thereby recovering a true inequality also used by Bell. What you write down is a trivially true fact. Bell did something interesting with it. 

Sent from my iPhone

On 6 Jan 2025, at 21:54, Alexandre de Castro <alx...@gmail.com> wrote:



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[Alexandre de Castro]

Geraldo, 
in attachment, I show in detail how this arithmetic leads to a problem with Bell's formulation.

[Mark Hadley]

Dear Alexey,

I have  explained to you before that QM predicts the correlation correctly and unambiguously using the same probability rule as it does for everything else:

Prob = Tr( \rho P)

Where P is the projection operator for the relevant correlation and \rho is the state operator.

It's as simple as that. The prediction does not need an observer and it does not need a wave function collapse.

If you add anything else to the simple rule above, then you will create unnecessary and unwelcome problems and probably inconsistencies elsewhere.

Learn how to calculate QM probabilities before you post anything else.

Cheers

Nark

On Wed, 8 Jan 2025, 20:51 Алексей Никулов, <nikulo...@gmail.com> wrote:

Dear Colleagues

I must once again draw your attention to my article [1], which proves that Bell's inequality does not make sense. Bell made two mistakes that provoked mass delusion. 1) Bell did not understand that the no-go theorem proposed by von Neumann in 1932 has proved that quantum mechanics cannot describe some quantum phenomena, for example the Stern – Gerlach effect, without the absurd claim that the mind of the observer can create a quantum state at observation; 2) Bell did not understand that the orthodox quantum mechanics cannot predict the EPR correlation since the observer can create a quantum state only the particle which he observes according to the Dirac jump or wave function collapse. The EPR correlation was invented in 1951 by Bohm, with the help of a more absurd claim that an observer can create a quantum state not only of the particle he is observing, but also of another particle that he cannot observe.

Quantum mechanics is one of the mass delusions of 20th century physicists. Another mass delusion is the theory of superconductivity. The mass delusions have become possible because science has become mass. The mass man rather believes in successful theories than understands them. The opinion of the masses now prevails in science, which is expressed in particular through the Hirsch index https://en.wikipedia.org/wiki/H-index . The mass man, as a rule, pays attention to publications by authors who have a fairly large Hirsch index and articles with many links. This psychology of the mass man was particularly evident in relation to Bell's publications, which almost no one noticed in the early years.

It should be noted that Hirsch himself, Professor of physics at University of California, San Diego https://jorge.physics.ucsd.edu/jh.html , is quite negative about his index, as he wrote in the article [2]. Hirsch aptly compares in this article [2] the attitude of most theorists to the famous BCS theory of superconductivity (https://en.wikipedia.org/wiki/BCS_theory , Nobel prize in Physics 1972) with the attitude of the characters of the fairy tale "The Emperor's New Clothes" by Hans Christian Andersen to the emperor's new clothes. The validity of this comparison is proved by the fact that for many years no one noticed that the BCS theory contradicts the second law of thermodynamics.

Hirsch argues in the recent article [3] that one of the following two alternatives has to be valid: (1) The Meissner effect violates the second law of thermodynamics, and is consistent with the BCS theory of superconductivity, as argued by Nikulov. (2) The Meissner effect is consistent with the second law of thermodynamics, establishes the invalidity of the BCS theory of superconductivity. Hirsch tries to prove that the second alternative should be valid. But in order to show that the Meissner effect is consistent with the second law of thermodynamics Hirsch uses in [3] a false analogy of the Gorter cycle with the Carnot cycle and makes contradictory statements. I draw attention to Hirsch's mistakes and contradictions in the manuscript “The Meissner Effect Violates the Second Law of Thermodynamics” submitted to the journal Physica C. This manuscript is available at SSRN https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5077185 .

[1] Alexey Nikulov, Physical Thinking and the GHZ Theorem. Found. Phys. 53, 51 (2023). DOI: <https://doi.org/10.1007/s10701-023-00693-y>, https://link.springer.com/article/10.1007/s10701-023-00693-y

[2] J. E. Hirsch, Superconductivity, what the H? The emperor has no clothes. APS Forum on Physics and Society Newsletter, January 2020, p. 4-9; arXiv: https://arxiv.org/abs/2001.09496 

[3] J.E. Hirsch, Does the Meissner effect violate the second law of thermodynamics? Physica C, Volume 629, 15 February 2025, 1354618, doi: https://doi.org/10.1016/j.physc.2024.1354618 ; https://www.sciencedirect.com/science/article/pii/S0921453424001825?via%3Dihub .

With best wishes,

Alexey

ср, 8 янв. 2025 г. в 20:11, GeraldoAlexandreBarbosa <geraldo...@gmail.com>:

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[Thomas Ray]

What Gill means is that you started with P(1/2) for a physical event without observing it.  Bell's theorem depends on an experimental set-up for a series of physical outcomes with predicted probabilities for occurence.  This maintains scientific correspondence between theory and result.  

https://www.researchgate.net/publication/383561991_The_Ferryman's_Dilemma

Tom

[Alexandre de Castro]

I have used exactly the same formulation as Bell. See, please, my last message.

[Austin Fearnley]

QM uses a singlet formula which shares a composite spin state between two entangled particles separated by any distance.
The use of this formula ensures non-locality and non-realistic treatment of elementary particles by QM: at least judging by comparison with local and realistic behaviour apparent in the macroscopic world.
Fortunately for QM,  Bell experiments since 2015 appear to show that the world is behaving in a non-local way and maybe our perception of reality needs to be revised.

The results of a Bell experiment can fit into the four cells of a two rows by two columns table.  For a and b detector polarisation settings differing by 45 degrees, the correlation for the table is -0.707. This result immediately relates to Malus's Law and I have a paper showing that one obtains a correlation of -0.707 using my version of retrocausality where the proportions in the cells were calculated using Malus's Law.

Why is there a connection between Malus and Bell?  
First, I cannot get the quantum result from Malus without also using retrocausality and I used a catch-phrase 'Malus + Retrocausality --> Bell'.
It seems very strange to me that the proportions in the Bell results table agree with Malus calculations as the Bell experiment is not set up as a Malus experiment.
In a Malus experiment the particles in an incoming beam have a common polarisation, for example passing the beam through polaroid sunglasses prior to the measurement at the detector.  This does not happen in a Bell experiment: where entangled pairs of particles are generated at a source and there is expected to be a random polaristion angle for any pair. That randomness is why retrocausality is needed.  Or QM is needed as QM does give the correct result.

I need to add that I do not like any retrocausal method other than my version.  My version does not allow any H.G. Wells type of time travel.  It does not even allow particles to be 'sent back in time' as mentioned in the May 2024 New Scientist. My version requires preons and I suspect retrocausality needs further acceptance of preons before gaining headway.  

[Alexandre de Castro]

Bell's formulation results in sin^2(45 degrees) <= 2sin^2(22.5 degrees) and sin^2(45 degrees) >= 2sin^2(22.5 degrees) at the same time. By the Explosion Principle, we can infer anything.

Thus, in Bell's test experiments, the CHSH inequality will continue to result in > 2, however, any inferences from those results can be considered valid.

To view this discussion visit https://groups.google.com/d/msgid/Bell_quantum_foundations/5d581692-93c2-441e-845e-6d0f2c56b84bn%40googlegroups.com.

[Richard Gill]

No. We can infer that at least one of his assumptions is wrong. 

Sent from my iPad

On 11 Jan 2025, at 05:11, Alexandre de Castro <alx...@gmail.com> wrote:



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[Alexandre de Castro]

Well, but P[a+,b-] \in [0,1] is not an assumption.

[Алексей Никулов]

Dear Mark,

Your point of view is the typical point of view of mass man that prevailed before Bell's inequalities became popular. Bell's publications were ignored for many years precisely because of this point of view of the mass man, who ignored the contradiction of quantum mechanics with realism, because most scientists could not understand the sense of this contradiction. Because of this disregard for the obvious contradiction by the former mass man, the modern mass man has the illusion that quantum mechanics contradicts realism due to the EPR correlation and violation of Bell inequalities. Thus, your point of view has provoked senseless modern controversies about Bell's inequalities and even the 2022 Nobel Prize in Physics. The modern mass man ignored the fact that Einstein protested against the rejection of realism by the creators of quantum mechanics and said about ’spooky action at a distant’ long before Bell's inequalities appeared.

In fact, you urge to do not think and only to calculate. Most theorists treated quantum mechanics that way without your instruction. But there was always a minority of those who continued to think and understand. Einstein understood as early as 1927 that because of Born's proposal, quantum mechanics should predict the possibility to see one particle in several places at once, i.e. obvious absurd, without a wave function collapse at the first observation. You still don't understand the obvious logic that Einstein understood.

Einstein, who understood the necessity of the postulate about the wave function collapse five years before von Neumann or about the Dirac jump three years before Dirac, also understood that this postulate contradicts locality and realism. He said in 1927, in his speech in the debate at the 5th Solvay Congress [3] this postulate about an instantaneous and non-local change in the quantum state "leads to a contradiction with the postulate of relativity". The contradiction of quantum mechanics with the theory of relativity is a consequence of the fact that the postulate about the wave function collapse cannot logically be understood otherwise than as the postulate about the instantaneous and non-local change in the quantum state under influence of the change in the observer's knowledge, after the first observation, about the probability of the result of the second observation.

J. von Neumann understood that the wave function collapse occurs under an influence of the mind of the observer. Heisenberg justified the postulate of the jump at observation by a discontinuous change in our knowledge: "Since through the observation our knowledge of the system has changed discontinuously, its mathematical representation also has undergone the discontinuous change and we speak of a ’quantum jump’" [4]. But the former mass man did not want to understand this absurdity of quantum mechanics. Therefore the modern mass man has the illusion that quantum mechanics contradicts realism due to the EPR correlation and violation of Bell inequalities. The modern mass man does not want to understand that the orthodox quantum mechanics cannot predict the EPR correlation and violation of Bell inequalities, although this fact is proven in my article [5].

[1] J. von Neumann, Mathematical Foundations of Quantum Mechanics. Princeton, NJ Princeton University Press. 1955; Mathematishe Grundlagen der Quantem-mechanik. Springer, Berlin, 1932.

[2] A.M. Dirac, The Principles of Quantum Mechanics. Oxford University Press. 1930.

[3] A. Einstein, Electrons et photons. Rapports et discussions du cinquieme Gonseil de physique- Bruxelles du 24 au 29 octobre 1927 sous les auspices de 1' Institut International de physique Solvay, p. 253—256. Paris, Gautier-Villars et Gie, editeurs 1928.

[4] W. Heisenberg, Physics and Philosophy. George Allen and Unwin Edition, 1959.

[5] Alexey Nikulov, Physical Thinking and the GHZ Theorem. Found. Phys. 53, 51 (2023). DOI: <https://doi.org/10.1007/s10701-023-00693-y>, https://link.springer.com/article/10.1007/s10701-023-00693-y

With best wishes,

Alexey

чт, 9 янв. 2025 г. в 00:06, Mark Hadley <sunshine...@googlemail.com>:

[Bryan Sanctuary]

Dear all,  

I have been following these discussions a bit.  I have a question which maybe someone can answer. Everyone says that Quantum Mechanics is a statistical theory. How can Nature build order from randomness? It seems to me that all this discussion about probabilities does not address this point.

Happy New Year to you all. 

Bryan

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[Mark Hadley]

You are in good company. As Einstein said "god does not play dice" 

But then learnt that would violate causality.

At that point 99% if physicists gave up understanding QM and got on with their calculations.

And 0.9% lived in denial and continued to work on causal models.

Actually I believe that god does not play dice and that BI gives us an enormous clue about where to look for a solution.

Cheers

Mark

[Bryan Sanctuary]

Hi Mark,

Ok, you believe the Old One does play dice. I do not. What would convince you He does not to play dice?  

Also, I would be happy to hear your comment on how a random theory can produce order.

Bryan

[Mark Hadley]

I said the opposite.

I don't believe that god plays dice.

My own theories are based on causal structures. 

Cheers

Mark

[Bryan Sanctuary]

😁

Bryan Sanctuary reacted via Gmail

[Austin Fearnley]

 "How can Nature build order from randomness? It seems to me that all this discussion about probabilities does not address this point."  [Bryan]

It is decades since I read Prigogine's Order out of Chaos.  I was too busy earning a salary then to spend more time on it and I still do not understand it.  

"Thermodynamics is about heat and its transformation into other forms of energy — basically involving statistical descriptions of atomic and molecular movements. Irreversible thermodynamic processes go in only one direction, usually toward more disorder. However, during the 1960s Ilya Prigogine developed a theory about dissipative structures, which maintains that long before a state of equilibrium is reached in irreversible processes, orderly and stable systems can arise from more disordered systems. The result has been applied in a great many areas."  (Based on Nobel Award Ceremony speech.)

Penrose's CCC idea of a cyclic universe necessarily involves returning from disorder (end point & high entropy) back to order (start point & low entropy).  The start point has all the stuff of the universe in the form of bosons and makes use of Bose-Einstein Condensates to allow all the stuff to be in a single, shared state, as bosons are gregarious.  The end point has all stuff in the universe in the form of fermions which obey Pauli's Exclusion Principle so they are in a countless number of states as the fermions elbow each other out of their way. At this point in his public lecture, Penrose seems to be a little apologetic about asking people to accept the sudden transition from extremely high entropy back to extremely low entropy.  I liked that transition, though, as it fitted my work (viXra:1609.0329) on the Rasch Model. The most robust Rasch metric is found when the objects to be put on a scale are close together, and least robust when objects are far flung. Closeness allows an introduction of error whereas far distances removes error to the point where a physical, ratio-scale metric will fail to occur.  


"Actually I believe that god does not play dice and that BI gives us an enormous clue about where to look for a solution."  [Mark]

Not sure if I understand quantum dice correctly.  Classical dice usage implies randomness, but not if one were able to measure all the microscopic bumps and contacts and use that information to produce deterministic results.  Therefore classical dice are also synonymous with determinism in principle, though not in practice.  Quantum dice, on the other hand, are not deterministic in principle.  This is because QM is non-local / non-real confirmed by BT experiments. [I suggest that quantum dice contain information from the future and so cannot be entirely determined from the past.]  Also, elementary particle interactions are affected by stuff in the vacuum which are seemingly impossible to use as data to make the interactions deterministic.  Tables of known elementary particle decays are available and there are at least a dozen decay routes for the pions.  Some years ago I tested my preon model by translating all these decays into preon interactions.  This used some stuff from the vacuum to input/output preons in the interactions.  So I could explain all the interactions in terms of preon content but not predict which outcome would arise.


"nature is built on and with quantum dice."  [Richard]

Some years ago I made a computer program to calculate preon cotents of elementary particles using classical dice throws of preons.  I put it on my wordpress website but soon afterwards wordpress banned my file type.  Someone from the far east tried to uses the program last week but it is inaccessible.  I can output the preon content of all the elementary particles by throwing classical dice, but many of the output combinations are not known in nature, so there are many thrown away by the program.

On Monday, January 13, 2025 at 5:05:16 AM UTC Richard Gill wrote:

Mark, I am completely with you! In my opinion: nature is built on and with quantum dice. Life, including human life, is biology; biology is chemistry and physics; chemistry is quantum dice. It builds molecules. Quantum randomness and gravity built the structure of the universe.

Sent from my iPad

On 12 Jan 2025, at 19:49, Mark Hadley <sunshine...@googlemail.com> wrote: