On 1 May 2022, at 15:59, Bryan Sanctuary <bryancs...@gmail.com> wrote:
Hi all
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You start your report by claiming no-one saw errors in your maths. That is not true. You claimed to have a counter-example to Bell’s theorem but you don’t.
Bell’s theorem states that no local hidden variables model, by which he means a deterministic model in which any randomness in measurement outcomes is attributed to statistical variation in initial values of unmeasured variables, can reproduce certain statistical QM predictions, or even approximately reproduce them. You did not refute Bell’s claim.You seem to imagine that Chantal or Pierre will be able to do that for you. This shows that you do not understand Bell’s maths, which shows that a computer network with nodes and links mimicking a Bell type experiment cannot reproduce quantum correlations. Bell’s theorem is a no-go theorem in theoretical computer science, subfield distributed computation, as well as a no-go theorem in physics, subfield foundations of quantum mechanics.
You seem to have your own notions of “local” and “realistic” though you fail to make them explicit. This means that you don’t even have any clear mathematical claim concerning your helicity ideas.
These are all major mathematical errors. Much more serious than any mistakes in computations within your chosen framework. Because of these serious errors, I, for one, have little motivation in checking those computations.
You have till New Year to gain support for your work from a majority of our peers. I don’t see much chance that you will succeed.
I'll comment on Richard's email.You start your report by claiming no-one saw errors in your maths. That is not true. You claimed to have a counter-example to Bell’s theorem but you don’t.PLEASE POINT OUT MY MATH ERRORS
--Jan-Åke Larsson
Department of Electrical Engineering SE-581 83 Linköping Phone: +46 (0)13-28 14 68 Mobile: +46 (0)13-28 14 68 Visiting address: Campus Valla, House B, Entr 27, 3A:482 Please visit us at www.liu.se |
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Hi Jan-ÅkeI was not shouting, I was just distinguishing with caps from Richard. I will use something different if it upsets you.I agree a statistical model would seal my case and that is now underway, but a local counter example dooms Bell's or anyone's theorem. That you reject my couterexample because a non-proven mechanism is laughable: I simply have to point to the "mechanism"for "quantum weirdness" that you embrace. If you do not like my counter example, then please explain the mechanism that you rely on, namely quantum weirdness.
In English we say you are a "pot calling the kettle black."
Here is local realism;These additional variables were to restore to the theory causality and locality. In this note that idea will be formulated mathematically and shown to be incompatible with the statistical predictions of quantum mechanics. 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.Any problems with this?
But, I do have a mechanism that I sent you: what is wrong with that?
If I know the starting point at separation, and the spin spins to the filter, it carries correlation. Please show my mechanism does not provide a local realistic and deterministic account of EPR correlation.Also Spin Helicity paper just introduces helicity. There is a lot more.Thanks for your comments. But I would give up teleportation (hey what is the mechanism?) and move on to reality.
On 2 May 2022, at 13:15, Bryan Sanctuary <bryancs...@gmail.com> wrote:
Department of Electrical Engineering
SE-581 83 Linköping
Phone: +46 (0)13-28 14 68
Mobile: +46 (0)13-28 14 68
Visiting address: Campus Valla, House B, Entr 27, 3A:482
Please visit us at www.liu.se
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Dear Richard, Alexandre drew attention to a problem with inequality (9) in "Bertlmann’s socks” [1]. I draw your attention once again that the equality (4) in the Bell article [1] cannot be correct
according to the orthodox quantum mechanics since results of observations of two particles cannot be different if operators acting on different particles commute. It is surprising to me
that it is necessary to convince a mathematician that the result of the actions of operators cannot depend on the order of their actions if these operators commute. Bell deduced the equality (4) in [1] since he followed Bohm’s quantum mechanics, according to which operators acting on different particles do not commute, rather than the orthodox
quantum mechanics, according to which operators acting on different particles commute. Only Bohm’s quantum mechanics can contradict locality and predicts the EPR correlation and
violation of Bell’s inequalities whereas the orthodox quantum mechanics cannot make this because of its principle that operators acting on different particles commute. It is necessary to know and understand this at least in order not to repeat the mistakes of the authors [2,3] of the GHZ theorem who followed orthodox quantum mechanics, in
order to prove that quantum mechanics contradicts locality. It is necessary also to understand that Bohm postulated the contradiction with locality with the help of an absurdity.
According to the equality (4) in the Bell article [1] the results of Alice's measurements depend on who will be the first to measure the spin projections of their particles, she or Bob.
Alice will see spin up with the probability 1/2 at measurements of the spin projections of her particles in any direction if she will measure first. But this probability sin^{2}(a-b)/2 will
depend, according to (4) in [1], not only from the direction “a” of measurement of the spin projection of her particles, but also from the direction “b” of measurement of the Bob
particles, if Bob will measure first. Are you not confused by this absurdity necessary to predict the violation of Bell's inequalities?
[1] J.S. Bell, Bertlmann’s socks and the nature of reality. J. de Physique 42, 41 (1981).
[2] 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).
[3] 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
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Dear Richard, You also wrote to me that you know that operators acting on different particles commute according to the orthodox quantum mechanics. Then why don't you understand that the orthodox
quantum mechanics cannot predict the violation of Bell's inequalities and that Bell's theorem contradicts the orthodox quantum mechanics?
With best wishes,
Alexey
Dear Richard, You do not understand logic rather than my statement. You know: 1) operators acting on different particles commute according to the orthodox quantum mechanics;
2) results of observations of two particles cannot be different if operators acting on different particles commute. From this knowledge of yours, it logically
follows that the results of observations of two particles cannot be different according to the orthodox quantum mechanics. But the results of observations of the first and second particles of the EPR pair are fundamentally different according to the equality (4) in the Bell article [1]. Consequently the equality (4), which provides the prediction of violation of Bell’s inequality, cannot be correct according to the orthodox quantum mechanics.
You wrote: “The quantum state of two separated particles is by definition a non-local thing”. Earlier, May 1 you wrote in the discussion about “Bell's Blunder”: “I would like to see
Alexei’s definition of “locality", and his definition of "quantum state ``''. I provided my definitions of “locality" and "quantum state” May 1. I wrote: “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 describes the knowledge that the first
measurement of spin projection in any direction of one of the two particles will give spin up with probability 1/2. According to the objective definition spin states of non-entangled
particles exist really in the real three-dimensional space”.
When you write that “The quantum state of two separated particles is by definition a non-local thing” you use the objective definition. But the objective definition cannot be applied to
the entangled spin states according mathematics, 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 entangled spin states can describe only the observer's knowledge of
the probability of the result of an upcoming observation. Schrodinger defined in 1935 the EPR correlation as entanglement of our knowledge. This definition is the only one possible
according to mathematics. Bohm considered in 1951 the EPR state as a non-local thing, contrary to logic and mathematics. Bohm misled not only most physicists, but even Bell.
Bohm and Bell were wrong rather than you.
[1] J.S. Bell, Bertlmann’s socks and the nature of reality. J. de Physique 42, 41 (1981).
With best wishes,
Alexey
Dear Richard, You surprised me! You claim that 1/2 is not different from sin^{2}(a-b)/2! I draw your attention that quantum mechanics predicts the same result for two measurements of single
particles which Bell predicted in equation (4) in “Bertlmann’s socks” [1] for two particles of the EPR pair. The first measurement of single particles along a direction with an angle “a”
relative to the given direction should give spin up with the probability 1/2 when particles are in random states. But the probability to observe spin down at the second measurements
will depend both the angles of the first “a” and second “b” measurements due to the Dirac jump which postulates ”that a measurement always causes the system to jump into an
eigenstate of the dynamical variable that is being measured” [2]. All particles jump into the same eigenstate in the direction with the angle “a” after the first measurement. The
probability to observe spin down at the second measurement in the direction with the angle “b” is calculated uniquely using the operators of finite rotations of the coordinate system,
see [3]. Therefore, quantum mechanics predicts for two measurements of single particles the probability 0.5sin^{2}(a-b)/2 predicted by equation (4) in “Bertlmann’s socks” [1]. I draw your attention that this prediction could be impossible without the Dirac jump, the operators of finite rotations of coordinate system and if the operators of measurements of spin
projections of the same particles in different directions “a” and “b” commute. According to the orthodox quantum mechanics the operators fail to commute when they act on the
same particle. Therefore the orthodox quantum mechanics predicts the violation of the trivial inequality (4) in section 4. THE ASSUMPTION USED AT THE DEDUCTION OF
THE GHZ THEOREM MAKES IMPOSSIBLE THE PREDICTION OF VIOLATION OF BELL’S INEQUALITIES of my manuscript “Physical thinking and the GHZ theorem”,
which you do not want to read. But the orthodox quantum mechanics cannot predicts violation of Bell’s inequality (equation (8) in my manuscript) because of two reasons: 1) operators acting on different particles
commute according to the orthodox quantum mechanics; 2) Dirac postulated that only measured particle jumps into an eigenstate of the dynamical variable that is being measured, and
therefore the spin state of other particles cannot change. The particles of the EPR pair (1) jump in the state (2) in my manuscript according to the Dirac jump. No correlation can be in this
case between results of measurements of the first and second particles. The EPR correlation can be only if the both particles jump in the state (3) in my manuscript when one of the
particles is measured. This jump, postulated by Bohm in 1951, not only contradicts the orthodox quantum mechanics, but also logically leads to the absurd, see section 6. THE
REJECTION OF REALISM RESULTS TO THE ABSURD in my manuscript. Bell wrote for physicists. Therefore, he did not explain in sufficient detail from which principles of quantum mechanics equation (4) in “Bertlmann’s socks” [1] is derived. Apparently
this has misled you. But, even many physicists do not understand the necessity of the Dirac jump and its sense.
[1] J.S. Bell, Bertlmann’s socks and the nature of reality. J. de Physique 42, 41 (1981).
[2] A.M. Dirac, The Principles of Quantum Mechanics (Oxford University Press, 1958).
[3] L. D. Landau, E. M. Lifshitz, Quantum Mechanics: NonRelativistic Theory (Volume 3, Third Edition, Elsevier Science, Oxford, 1977).
With best wishes,
Alexey
Dear Richard, I think that you are confusing quantum mechanics and theory of probability. Bell deduced equation (4) in “Bertlmann’s socks” from quantum mechanics rather than theory of
probability. I am not sure that Bell was knowing about marginal and conditional probability. But Bell was understanding that according to the expression for the EPR state
(1/2)^{1/2}|+-> - (1/2)^{1/2}|-+> the measurement of the first particle will give spin up (+) with the probability 1/2 = (1/2)^{1/2}^{2}. Consequently sin^{2}(a-b)/2 in equation (4) in
“Bertlmann’s socks” is the probability to observe spin up of the second particle. What does the marginal and conditional probability have to do with it? Can you deduce sin^{2}(a-b)/2
from the marginal or conditional probability? But do you know how Bell derived the probability sin^{2}(a-b)/2 to observe spin up of the second particle from Bohm's quantum
mechanics?
With best wishes,
Alexey
Dear Richard, I think you don't understand at all why Bohm's quantum mechanics predicts the violation of Bell's inequalities. What you wrote, you probably read from authors like M. A. Nielsen and
I. L. Chuang, who does not understand quantum mechanics. The expectation value E(AB) = - cos(alpha — beta), which you wrote, is deduced from equation (4) in “Bertlmann’s socks”.
But where do the values of 1/2 and sin^{2}(a-b)/2 in equation (4) come from? You do not take into account that even when the joint probability is determined the spin projection of
each particle is measured and the result depends on whether the measurement of one particle affects the state of other particles. Such an effect cannot be if the operators (rather than
observables) acting on different particles commute. The value sin^{2}(a-b)/2 cannot be in principle in equation (4) in “Bertlmann’s socks” since the probability to observe spin up of
the second particle in a direction “b” cannot depend on the direction “a”, in which the first particle was measured, if the measurement of the first particle does not the state of the second
particle.
You don't seem to understand very well that Bell's inequality was provoked by the quantum dispute between Einstein and Bohr about the EPR paradox. Einstein argued that measuring one particle cannot change the state of another particle, and Bohr disputed this. If most physicists understood quantum mechanics, they would have to understand that Einstein is right, since measuring one particle cannot change the state of another particle according to the principle of quantum mechanics that operators acting on different particles commute. But most physicists rather believe than understand quantum mechanics. Therefore they concluded that Bohr rather than Einstein was right. Only this blind faith can have provoked this comedy with EPR correlation and Bell inequalities.
With best wishes,
Alexey
Dear Richard,
The probability to observe one of the two particles of the EPR pair can depend on both settings only if the observation of one particle can change the state of another particle. You keep forgetting that the only point of Bell's inequalities is to determine whether the measurement of one particle affects the state of another particle. You state that such an effect should always be, according to your mathematics. But in this case, Bell's inequalities lose any sense. You don't want to understand that Bell's inequalities have nothing to do with probability theory and mathematics in general, since they are mathematically trivial. Bell's inequality is deduced under one condition: the turn of her analyzer by Alice cannot influence the result of the measurement by Bohm of his particle.
Mathematicians, for example you and Frank Lad (Department of Mathematics and Statistics, University of Canterbury, New Zealand) argue about Bell's inequalities only because they can't believe that quantum mechanics, which almost all physicists believe in, is absurd. Frank Lad submitted three manuscripts to the Special Issue "Violation of Bell’s Inequalities and the Idea of a Quantum Computer" https://www.mdpi.com/journal/entropy/special_issues/Bell_Inequalities : “Quantum violations of Bell's inequality: a misunderstanding based on a mathematical error of neglect”, “The GHSZ argument: a gedankenexperiment requiring more denken” and “Resurrecting the principle of Local Realism and the prospect of supplementary variables”. I was Guest Editor of this Special Issue. I managed with great difficulty to publish only one article of Frank Lad [1], since most believe in Bell's inequalities. Frank Lad was expressing his indignation at Bell's inequalities quite emotionally. As a mathematician, he did not understand that one should be outraged not by Bell's inequalities, but by quantum mechanics.
You, like most people, do not want to admit that quantum mechanics is absurd, although it is obvious. I will try to explain the absurdity of quantum mechanics to you using the example of the EPR pair. According to the expression
EPR = (1/2)^{1/2}|A+B-> - (1/2)^{1/2}|A-B+> (1)
the first measurement will give spin up (+) with the probability 1/2. For this reason 1/2 is in equation (4) in “Bertlmann’s socks”. I draw your attention that the amplitude in the expression (1) for the EPR pair cannot differ from (1/2)^{1/2} since we cannot know which particle A or B will be measured first.
Thus, the first measurement of spin projection in any direction of one of the particles will give spin up (+) with probability 1/2. This mathematical fact means that the particles A and B in the EPR state (1) cannot have eigenstates in any direction since the measurement in eigenstate should give spin up (+) with probability 1. Eigenstates of both particles will appear only after the first observation. Eigenstates will appear according to both the orthodox quantum mechanics and Bohm's quantum mechanics. But the eigenstates of the particle, which is not measured, will depend on which quantum mechanics is used.
The orthodox quantum mechanics postulated in 1930 the Dirac jump according to which only measured particle jumps ”into an eigenstate of the dynamical variable that is being measured” [2]. The particles A and B will jump to the states
Dirac = |A+z1>[ (1/2)^{1/2}|B-> - (1/2)^{1/2}|B+>] (2)
according to the Dirac jump when Alice will see that her particle deflects up along the direction z1 in which she measures spin projection. The expression (2) predicts no correlation between results of observations of the A and B particles. Quantum mechanics can predict the EPR correlation only if not only a measured particle but also another particle which is not measured will jump ”into an eigenstate of the dynamical variable that is being measured”. Bohm postulated such a jump only in 1951 under the influence of Bohr's claim that measurement of one particle can change the state of another particle. Therefore I call this jump as the Bohr jump in the manuscript "Physical thinking and the GHZ theorem". The particles A and B will jump to the states
Bohr = |A+z1>|B-z1> (3)
according to the Bohr jump when Alice will see that her particle deflects up along the direction z1. The expression (3) provides the EPR correlation: spin projections of the A and B particles in the z1 direction are opposite with probability 1. This expression provides the probability sin^{2}(a-b)/2 for the second particle in equation (4) in “Bertlmann’s socks” together with the operators of finite rotation of the coordinate axes which can be applied to non-entangled states such as (2) and (3), but not to entangled states (1).
Quantum mechanics, both orthodox and Bohm's, is absurd since it postulates that the mind of the observer creates eigenstates (2) or (3) at observation.
[1] Lad, F. The GHSZ Argument: A Gedankenexperiment Requiring More Denken. Entropy 2020, 22, 759. https://doi.org/10.3390/e22070759 ; https://www.mdpi.com/1099-4300/22/7/759
[2] A.M. Dirac, The Principles of Quantum Mechanics (Oxford University Press, 1958).
With best wishes,
Alexey
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