## A new simulation of the EPR-Bohm correlations

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

### Re: A new simulation of the EPR-Bohm correlations

minkwe wrote:
Jochen wrote:OK, so how do you justify the existence of a joint PD? If I am allowed nonlocal signalling, then I can always alter the PD of one part of the system due to measurements done on the other, and no joint PD exists.

If you review my response carefully, you will see examples of how to do it. For example, the your state-machine with non-local disturbance, in which the measurements are always done in sequence A,B,C,D, would produce a joint PD. So long as the 4 numbers are jointly measured, it matters not one iota what physical mechanism is generating them, you will get a joint PD of outcomes and Bell's inequalities will apply.

The problem is that the sequential measurement you proposed does not generate the PD of the outcomes---in particular, it will be impossible to derive the correlations between different variables, as you effectively only measure single-observable marginals. Take a simple example where A and B are always perfectly correlated, but each +1 or -1 with 50% probability. Then, measuring sequences of the form A, B, A, B, ... will never tell you anything about the correlation, and you'll only recover the statement that A=+/-1 with 50% probability, and B=+/-1 with 50% probability, which is the same you would get if, say, both were perfectly anticorrelated, or not correlated at all. And again, the measurement of all quantities at once may be physically impossible.

minkwe wrote:original bell inequalities would have been violated by 3 spin-half particles, the goal-posts would not have needed to be shifted. The original Bell inequalities involve 3 simultaneous measurements at settings (a,b,c). That can be done for 3 spin-half particles directly, and the original Bell's inequalities will apply, shouldn't they?

Each Bell inequality is derived for a specific setting; thus, that Bell inequalities can't be violated in a setting they are not apt to is no great mystery, and in particular does not imply any shifting of goalposts. It's not any more mysterious than that in one system, observables A,B,C may be correlated, while in a different one, they might not be.

Otherwise, why would you expect a joint PD (A,B,C) to be present in this case, but absent in the case of only 2 particles, if you refuse to acknowledge that it is the joint measurement that determines whether you have a joint PD, so that when you measure the 3 simultaneously, you get a joint PD P(A,B,C), and when you measure only 2 you do not get a joint PD P(A,B,C). It does not matter what physical mechanism is generating the outcomes.

The reason is simply that in the two-particle case, not all of these observables are compatible, while in a three-particle setting, they are. But for compatible observables, a joint PD can always be found, and they can always be measured jointly.

minkwe wrote:
Jochen wrote:Take three coins, $C_1$, $C_2$, and $C_3$. If you flip the first and second together, they will always agree, giving both H = heads or T = tails with 50% probability. If you flip the second and third together, they will always land oppositely (again with 50% probability). If you flip the second and third together, they will always agree (50 % HH, 50% TT). Clearly, there does not exist a joint PD $P(C_1, C_2, C_3)$. Nevertheless, flipping each coin on its own is a perfectly ordinary stochastic process---for which, however, BIs can't be derived.

But your contrived example does not translate into a general truth.

No, but it suffices to refute your assertion that every statistical process always can be ascribed a joint probability distribution by exhibiting a stochastic process in which this is not the case.

The point was, that contrary to your claim that pre-determination of values is required, a random number generator which generates the 4 numbers (A,B,C,D) without any pre-determination, must obey the CHSH inequality because the outcomes represent a joint PD P(A,B,C,D). Therefore pre-determination is not required to obtain a joint PD. Do you agree or disagree?

I disagree: a random process does not always produce something which can be described by a joint PD, as is shown by the coin example.

You have a bigger burden than me. You are trying to argue that it is ALWAYS possible to reconstruct a joint PD for ALL local HV theories. Using specific contrived examples do not serve your purpose. I'm arguing that in some cases where you have a local HV theory, it is not always possible to reconstruct a joint PD from measured pairs. So I can use simple contrived examples to make my point effectively, you cannot.

I've given a general argument why any local HV theory can be described by a joint PD: the PD is simply a convex combination of all the value-assignments the theory makes, which exists if there are such value-assignments and there is no disturbance. You've tried to refute this by proposing that for a class of systems, a joint PD can always be found even though there is no value-assignment; I have against this general statement provided an example which refutes it, a system in this class of stochastic systems for which no joint PD can be found.

minkwe wrote:You do not say what you mean by "at variance" so I don't know how to answer a claim that is not substantiated. I use degrees of freedom it in the same way it is usually used. So please explain what you mean by "at variance".

I asked you to elaborate on how you used a term, because I would use it differently---to me, degrees of freedom are something like, for instance, the allowed number of independent motions of a molecule, the number of parameters to describe an object's motion, etc. You seem to apply the term to the freedom the experimenters have in a Bell test. Hence, I asked to clarify; no need to get all defensive.

minkwe wrote:So you misunderstood me. The fact that averages actually measured on separate sets of particles are always reproducible does not and cannot reasonably be taken to mean that those averages are the same ones represented by the terms in the inequality which were not measured on the same set of particles. It is a fact that the measured averages are reproducible. But that has nothing to do with the fact that the actually measured correlations are not the same as the unmeasured counterfactual ones from the same set of particles.

This is exactly what the assumption of hidden variables amounts to: if there are such hidden variables, then the statistical properties of the unmeasured ones are the same as the measured ones, since the particle or whatever system could not have known beforehand which ones would be measured, and hence, could not have arranged for the unmeasured ones to differ in any relevant way.

minkwe wrote:In the expression $Q = C_iB_i + C_iD_i + A_iB_i - A_iD_i$, for the particle pair $i$, three of the paired terms are counterfactual and one is actual.

But only at the measurement, by the free choice of the experimenter, is it decided which one is made actual. Hence, the statistics must agree for every choice they could make; but then, the inference from the above being below 2 for every single particle to it being below two on average even if not all terms are measured on every particle is valid.

The terms are not independent from each other, there are 4 independent values which are free to vary in that expression, and those 4 values are cyclically shared by the paired terms such that they are not independent.

Come again? The 4 independent values are not independent? I don't know how to parse this.

Once three of the paired terms are given, the fourth one is determined automatically. That is the origin of the relationship $Q$. The problem is that you are trying to take away the feature that gives you that relationship while at the same time claiming that the relationship continues to hold.

Again, the logic is: it holds for every particle; therefore, it holds statistically. But since the measurement is only decided after the HV-assignment, there is no way for things to be arranged such that the 'counterfactual' outcomes differ from the observed ones---since I could just as well have measured C and D instead of A and B, I can infer that it must be the case that C and D must have the same statistical properties whether I actually measure them or not; because otherwise, had I instead chosen to measure them, I would have observed statistics incompatible with the predictions of QM.

minkwe wrote:I already have written two local realistic simulations of EPRB experiments, which reproduce the QM correlations without any disturbance, and without non-locality. You can find them https://github.com/minkwe/epr-simple/, and https://github.com/minkwe/epr-clocked. But you are not going to understand what is going on there, if you do not understand my arguments.

I think I understand quite well what's going on there, and hence you should be able to anticipate my response: get rid of the nondetections in the first, or of the failures to produce particle pairs in the second, and then we can talk. A local realistic strategy should work just as well in the case of ideal detectors and sources.
Jochen

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### Re: A new simulation of the EPR-Bohm correlations

Joy Christian wrote:In that case let me suggest a toy example. Ideally I would like you to appreciate the non-trivial geometry and topology of the 3-sphere itself to understand what I am saying. But the next best thing is this toy example in the first appendix of this paper: http://arxiv.org/pdf/1201.0775.pdf. Please read the entire appendix if you can, but if you are impatient then just have a look at eqs. (1.57) to (1.59) on pages 22 and 23. Also, please understand that the toy example can only illustrate a point. It should not be taken too seriously. I am not asking you to believe that Alice and Bob are running around a Mobius strip every time they are performing an experiment.

Thanks, this is helpful. A few observations: it seems to me that you could get rid of the twist in the fiber, and simply have a hidden variable state carrying out a continuous rotation along its trajectory. But then, the experimenters' measurement directions (well, the only relevant z-direction) is seen to not be free: it must be given by the amount of rotation the hidden variable has undergone. So this is then, in essence, a superdeterministic model: the value of the correlations is explained by the fact that the experimenters aren't fully free to choose their measurement direction.

There's also the somewhat curious fact that the correlation between the experimenters is given solely in terms of their distance (a non-local quantity), which is ultimately what simultaneously determines their measurement directions and the value of the HV, but I guess this is maybe an artefact of the analogy.

If this is truly analogous to what determines the correlations in your full model, then I wouldn't really see it as a refutation of Bell's theorem---we'd merely be subject to unknown constraints (the nontrivially twisted fiber) that essentially invalidate the assumption of the experimenter's freedom. And it would be somewhat odd to me if this should be the case---quantum mechanics pays no mind to the topology of spacetime, yet explains the correlations perfectly well. That is, even in a universe with a wildly different shape, QM would predict the same correlations, while your model presumably wouldn't. And AIUI, the current data is most simply explained by a flat universe; so is it correct to say that for your model to be correct, that can't be the case?

Anyway, in the end, I think that only the full two-boxes simulation can really settle this question.
Jochen

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### Re: A new simulation of the EPR-Bohm correlations

FrediFizzx wrote:
Schmelzer wrote:I could do it easier, simply "right result = -ab". With a counterexample for Bell's theorem this has anyway nothing to do.

It is the same result as QM for EPRB via a classical local realistic model. Sorry that you can't see that. And it is actually not very complicated at all. What don't you understand?

Sorry, indeed, I do not have hallucinations yet. I see only a laughable collection of meaningless formulas of type $\lim_{e_0\to a, e_0\to b}$ which, it seems, even Joy does not try to defend anymore. What I don't understand are, for example, formulas containing terms like $\lim_{e_0\to a, e_0\to b}$.

FrediFizzx wrote:Does QM use the +/- 1 outcomes to get its theoretical prediction of -a.b for EPRB? No, it doesn't.

QM is not a local realistic theory, so it doesn't have to. Why you think that a strange set of formulas, which somehow gives -ab, has any relevance to Bell's theorem, I don't understand.
Schmelzer

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### Re: A new simulation of the EPR-Bohm correlations

Hi Jochen,

As I was afraid, you are taking the Mobius analogy too seriously and drawing conclusions that are not warranted --- at least for the actual 3-sphere model.

Before I address your specific comments, let me first summarize my general point of view so we can understand why we are seeing the same evidence so differently:

1) In my view quantum entanglement is an illusion. It is analogous to the phlogiston theory. It works beautifully, but in the end it is a fool's gold, not the real thing.

2) The strong correlations we observe in Nature are a direct consequence of the geometry and topology of the physical space we live in. They have nothing much to do with quantum entanglement per se. They are a direct consequence of the highly non-trivial and counterintuitive (but well known) spinorial properties of spacetime.

3) It is only when we ignore these properties in our investigations, we are led to the illusions of non-locality, non-reality, superdeterminism, backward causation, etc.

In the light of these remarks, it will not surprise you that I don't quite agree with your specific comments.

Jochen wrote:Thanks, this is helpful. A few observations: it seems to me that you could get rid of the twist in the fiber, and simply have a hidden variable state carrying out a continuous rotation along its trajectory. But then, the experimenters' measurement directions (well, the only relevant z-direction) is seen to not be free: it must be given by the amount of rotation the hidden variable has undergone. So this is then, in essence, a superdeterministic model: the value of the correlations is explained by the fact that the experimenters aren't fully free to choose their measurement direction.

In the toy model, as well as in the original 3-sphere model, the experimenters are completely free to choose their measurement directions. Getting rid of the twist in the fiber in the toy model is equivalent to switching from S^3 to R^3 geometry in the 3-sphere model. In R^3 your observations are correct, but the whole point of my model is that we do not live in R^3. We live in S^3, and the EPR-B correlations we observe in Nature are the proof of this fact. In S^3 it is not the superdeterminism or non-locality but the geometry, topology, and the spinorial properties of the physical space that lead to the existence of strong correlations. This is quite evident from both the toy analogy and the original 3-sphere model. This evidence is also illustrated in my latest simulation where the strong correlations are shown to reduce to the linear correlations when S^3 is reduced to R^3 (i.e, to its tangent space --- see the last but one plot).

Jochen wrote:There's also the somewhat curious fact that the correlation between the experimenters is given solely in terms of their distance (a non-local quantity), which is ultimately what simultaneously determines their measurement directions and the value of the HV, but I guess this is maybe an artefact of the analogy.

It is just an artefact of a rather crude analogy. In the actual 3-sphere model it is not the distance but the locally defined torsion tensor that determines the strong correlation. See, for example, some of the mathematical details I provide here: http://libertesphilosophica.info/blog/o ... lations-2/.

Jochen wrote:If this is truly analogous to what determines the correlations in your full model, then I wouldn't really see it as a refutation of Bell's theorem---we'd merely be subject to unknown constraints (the nontrivially twisted fiber) that essentially invalidate the assumption of the experimenter's freedom. And it would be somewhat odd to me if this should be the case---quantum mechanics pays no mind to the topology of spacetime, yet explains the correlations perfectly well. That is, even in a universe with a wildly different shape, QM would predict the same correlations, while your model presumably wouldn't. And AIUI, the current data is most simply explained by a flat universe; so is it correct to say that for your model to be correct, that can't be the case?

It should be clear from my comments above that what you say here is not true, either for the toy analogy or for the original 3-sphere model. The experimenter's freedom is not at all compromised in the model, because we cannot get rid of the twist, either form the fiber in the toy analogy or from the torsion in the 3-sphere. We are stuck with it, and observe the strong correlations as a consequence. If quantum mechanics predicts the same correlations in a universe with a wildly different shape (which seems quite speculative to me), then that is a weakness of quantum mechanics, not its strength. The current data indeed favours flat universe at the cosmological scale, but that does not rule out non-flat geometries at the terrestrial scales. Moreover, the quaternionic 3-sphere I am talking about has a vanishing spatial curvature but non-vanishing torsion. So even at the cosmological scale there is no direct contradiction between what the data favours and what I am claiming.

Jochen wrote:Anyway, in the end, I think that only the full two-boxes simulation can really settle this question.

The matter is already settled analytically. Eq. (B10) of this paper is an incontrovertible proof of my claim. Thus, strictly speaking, no simulation is necessary. But of course you are entitled to be convinced only if a "full two-boxes simulation" is provided, according to your specifications. I myself am quite happy with my Eq. (B10).
Joy Christian
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### Re: A new simulation of the EPR-Bohm correlations

Schmelzer wrote:I see only a laughable collection of meaningless formulas of type $\lim_{e_0\to a, e_0\to b}$ which, it seems, even Joy does not try to defend anymore. What I don't understand are, for example, formulas containing terms like $\lim_{e_0\to a, e_0\to b}$.

I am not your teacher. I am under no obligation of teaching you elementary mathematics. In any case, I have already answered your question once. Take it or leave it:

Joy Christian wrote:
Schmelzer wrote:
Joy Christian wrote:To see how wrong and naïve the claim of "always -1 correlation" is, you may wish to consult equation (A.9.15) on page 244 of this paper.

Sorry, but I'm unable to make sense of the limiting operator $\lim_{e_0\to \pm a, e_0\to\pm b}$

Equation (A.9.15) describes a limit of a geometric product of two different quaternions, which belong to S^3. And since S^3 remains closed under multiplication, the product is also a unit quaternion, as shown in equations (A.9.16) and (A.9.17). Also worth noting is that quaternionic S^3 is necessarily "flat", with constant but non-vanishing torsion. The limits in these equations simply describe the limits in which the scalar part of the product quaternion reduces to +/-1 while the bivector part reduces to zero, as shown in equations (A.9.17) to (A.9.19). The purpose of this demonstration is to show that the geometry and topology of the 3-sphere is highly non-trivial.
Joy Christian
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### Re: A new simulation of the EPR-Bohm correlations

Joy Christian wrote:1) In my view quantum entanglement is an illusion. It is analogous to the phlogiston theory. It works beautifully, but in the end it is a fool's gold, not the real thing.

Does this entail, for instance, the insecurity of quantum cryptography, or the impossibility of building large-scale quantum computers? If so, what will you do if they in fact are built?

In the toy model, as well as in the original 3-sphere model, the experimenters are completely free to choose their measurement directions.

Well, but their choice doesn't really matter, does it? In the toy model, the correlations depend only on the relative orientation along the dimension (locally) orthogonal to the Möbius band, which is beyond the experimenters' control; the components lying in the band are basically just discarded. No?

In S^3 it is not the superdeterminism or non-locality but the geometry, topology, and the spinorial properties of the physical space that lead to the existence of strong correlations.

I'm not sure I really see the difference. Basically, you introduce additional degrees of freedom, and then have those, rather than the experimenters' choices, determine the measurement outcomes. So in a sense, the free choice of the experimenter is disregarded and replaced with a 'measurement' that is not under the experimenter's control.

It is just an artefact of a rather crude analogy. In the actual 3-sphere model it is not the distance but the locally defined torsion tensor that determines the strong correlation. See, for example, some of the mathematical details I provide here: http://libertesphilosophica.info/blog/o ... lations-2/.

I've got a question about that, too: locally, a nontrivial fiber bundle is always equivalent to a product manifold between base and fiber, so how can any local measurement know about the global twist?

Also, regarding your paper http://arxiv.org/abs/1201.0775, in footnote 2, you say that the probability distribution of A and B factorizes, due to them being independent variables; but if that's the case, then the correlator factorizes also, and the value of the CHSH quantity is constrained by 2. Both can't be right: the probability distributions can't factorize and still violate CHSH (or any BI).

And another question: what must be the case in order for Bell inequalities to not be violated in your setup? The correct correlation for the singlet state is -a.b, but for a separable state, you just get $\langle AB \rangle = \langle A \rangle \langle B\rangle$, which doesn't violate any inequalities. How is that represented within your scheme?

Finally, how about inequalities not given in terms of correlations, but of probabilities (or even entropic inequalities)---have you had a look at those? How do you calculate, e.g., $p(A=+1 \wedge B=+1)$?

The matter is already settled analytically. Eq. (B10) of this paper is an incontrovertible proof of my claim. Thus, strictly speaking, no simulation is necessary. But of course you are entitled to be convinced only if a "full two-boxes simulation" is provided, according to your specifications. I myself am quite happy with my Eq. (B10).

Well, the equation may be all right for all I know, but the question is whether it actually corresponds to the correlation between two actual measurements, or is just a fancy way of calculating -a.b. An explicit simulation would certainly clear up the doubts there.
Jochen

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### Re: A new simulation of the EPR-Bohm correlations

minkwe wrote:I already have written two local realistic simulations of EPRB experiments, which reproduce the QM correlations without any disturbance, and without non-locality. You can find them https://github.com/minkwe/epr-simple/, and https://github.com/minkwe/epr-clocked. But you are not going to understand what is going on there, if you do not understand my arguments.

In case you don't understand minkwe's arguments, http://arxiv.org/abs/1507.00106 tries to explain these simulations.
Schmelzer

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### Re: A new simulation of the EPR-Bohm correlations

Jochen wrote:The problem is that the sequential measurement you proposed does not generate the PD of the outcomes---in particular, it will be impossible to derive the correlations between different variables, as you effectively only measure single-observable marginals. Take a simple example where A and B are always perfectly correlated, but each +1 or -1 with 50% probability. Then, measuring sequences of the form A, B, A, B, ...

You did not understand what I said. Again, you have a 4xN spreadsheet with columns labelled A,B,C,D. You press A, write the outcome on row 1, col 1, then press button B, and write the outcome in col 2 row 1, and next C, and next D. When you reach the end, you jump to row 2 col 1 and repeat ad nauseum. Your 4xN spreadsheet is a joint PD of outcomes P(A,B,C,D). It does not matter what process is generating the outcomes. The point is simply that disturbance or nonlocality is irrelevant. You can obtain a joint PD of outcomes even if you have non-locality or disturbance, so long as you measure the outcomes jointly.

Jochen wrote:And again, the measurement of all quantities at once may be physically impossible.

That is my point! it is the fact that the quantities can not be measured at once that is important, not whether you have non-locality or disturbance.

Jochen wrote:Each Bell inequality is derived for a specific setting; thus, that Bell inequalities can't be violated in a setting they are not apt to is no great mystery, and in particular does not imply any shifting of goalposts. It's not any more mysterious than that in one system, observables A,B,C may be correlated, while in a different one, they might not be.

It is in fact a shifting of goal posts. If I give you 3 spin-half particles and instruct that you only measure two of them each time, we are back to the Bell's inequalities. You would say the inequality is violated because of non-locality or disturbance? Do you think the outcomes from such a system will violate the Bell's inequalities? If you do, then why should adding a third measurement eliminate the presence of non-locality or disturbance, unless the whole thing is just a ruse.

Jochen wrote:The reason is simply that in the two-particle case, not all of these observables are compatible, while in a three-particle setting, they are. But for compatible observables, a joint PD can always be found, and they can always be measured jointly.

Please think about what you are saying here. If I give you 3particles each time but forbid you from measuring more than two of the 3, would you say Bell's inequalities apply or not. Don't you see the contradiction? Unless you are now suggesting my instruction to you about what you shouldn't do, mystically changes whether the particles will disturb each other or communicate non-locally.

Jochen wrote:No, but it suffices to refute your assertion that every statistical process always can be ascribed a joint probability distribution by exhibiting a stochastic process in which this is not the case.

Again, you are ascribing to me arguments I've never made. It is you who is arguing that pre-determination is necessary in order to have a joint PD. All I've done is give you one counter-example in which pre-determination was absent and yet a joint PD was obtained. That is absolutely not the same thing as saying every statistical process can always generate a joint PD. I don't think you are reading my argument carefully. You have a harder burden of proof if you claim something is necessary, I simply have to show you one counter-example, and that is what I've done.

Jochen wrote:I disagree: a random process does not always produce something which can be described by a joint PD, as is shown by the coin example.

Again, please read my argument carefully. This is simple logic. It does not matter whether a random process can "always" produce a joint PD. If you argue that pre-determination is necessary to obtain a joint PD, then you mean that pre-determination must always be present for a joint PD to be possible. If I show you just one case in which a random process produced a joint PD without predetermination, your argument is toast.

Jochen wrote:I've given a general argument why any local HV theory can be described by a joint PD: the PD is simply a convex combination of all the value-assignments the theory makes, which exists if there are such value-assignments and there is no disturbance. You've tried to refute this by proposing that for a class of systems, a joint PD can always be found even though there is no value-assignment; I have against this general statement provided an example which refutes it, a system in this class of stochastic systems for which no joint PD can be found.

This is a complete mis-characterization of the argument. I've argued that the only requirement to obtain the inequalities is the assumption of a joint PD, which is tightly coupled with how the measurements are performed. Rather, you've tried to argue that in addition to "joint PD", locality and no-disturbance are necessary. I've argued by giving you specific examples where a joint PD could be obtained if the measurements are performed jointly, even with non-locality and disturbance, effectively debunking your argument that locality and no-disturbance are necessary. Now you think my argument is that a joint PD is always possible. That couldn't be further from the truth. You have not countered my argument at all.

minkwe wrote:I asked you to elaborate on how you used a term, because I would use it differently---to me, degrees of freedom are something like, for instance, the allowed number of independent motions of a molecule, the number of parameters to describe an object's motion, etc. You seem to apply the term to the freedom the experimenters have in a Bell test. Hence, I asked to clarify; no need to get all defensive.

You said my use of the term was "at variance" without saying how, so I'm entitled to understand what you mean in order to respond to it. I still do not see anything in your response that justifies your claim that anything I said was "at variance". I'm using degrees of freedom in the standard way it is used in statistics and mathematics:

Wikipedia wrote:In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary. The number of independent ways by which a dynamic system can move, without violating any constraint imposed on it, is called number of degrees of freedom.

Jochen wrote:
minkwe wrote:So you misunderstood me. The fact that averages actually measured on separate sets of particles are always reproducible does not and cannot reasonably be taken to mean that those averages are the same ones represented by the terms in the inequality which were not measured on the same set of particles. It is a fact that the measured averages are reproducible. But that has nothing to do with the fact that the actually measured correlations are not the same as the unmeasured counterfactual ones from the same set of particles.

This is exactly what the assumption of hidden variables amounts to: if there are such hidden variables, then the statistical properties of the unmeasured ones are the same as the measured ones, since the particle or whatever system could not have known beforehand which ones would be measured, and hence, could not have arranged for the unmeasured ones to differ in any relevant way.

Not at all. Hidden variables do not imply that at all. That is what I've been explaining to you all along, the measured ones are not from the same particles as the unmeasured ones in the inequality. The relationship between the measured and unmeasured ones in the same set of particles is not the same relationship between measured ones in one set, and measured ones in another set. The symmetry inherent in the structure of a coin that links the H to the T such that when you measure one you definitely does not get the other, does not exist between the H of one coin and the T of another coin. A single coin toss has just one degree of freedom. Two separate tosses have 2 degrees of freedom. And the difference between those two scenarios exists irrespective of hidden variables. This is the point I don't think you've appreciated.

minkwe wrote:In the expression $Q = C_iB_i + C_iD_i + A_iB_i - A_iD_i$, for the particle pair $i$, three of the paired terms are counterfactual and one is actual.

But only at the measurement, by the free choice of the experimenter, is it decided which one is made actual. Hence, the statistics must agree for every choice they could make; but then, the inference from the above being below 2 for every single particle to it being below two on average even if not all terms are measured on every particle is valid.

Jochen wrote:
The terms are not independent from each other, there are 4 independent values which are free to vary in that expression, and those 4 values are cyclically shared by the paired terms such that they are not independent.

Come again? The 4 independent values are not independent? I don't know how to parse this.

You parse it by understanding the difference between the 4 independent values $A_i, B_i, C_i, D_i$, and the 4 cyclically dependent paired terms $C_iB_i , C_iD_i , A_iB_i , A_iD_i$.

Jochen wrote:Again, the logic is: it holds for every particle; therefore, it holds statistically. But since the measurement is only decided after the HV-assignment, there is no way for things to be arranged such that the 'counterfactual' outcomes differ from the observed ones

Again, you haven't understood. The measurements which are always performed are statistically reproducible. But that does not translate to the counterfactual ones being the same as the measured ones. If I toss a coin, I get H, the counter-factual outcome is constrained by symmetry of the coin to be T. It must be in this case. But If I toss one coin and get H, there is absolutely nothing which constrains a second toss even of the same coin to be T. It is a mathematical error to think a relationship you derived by relying on the symmetry to relate the actual outcome to counterfactual outcomes, can always be extended to separate pairs of actual outcomes, where that symmetry is absent.

---since I could just as well have measured C and D instead of A and B, I can infer that it must be the case that C and D must have the same statistical properties whether I actually measure them or not; because otherwise, had I instead chosen to measure them, I would have observed statistics incompatible with the predictions of QM.

But that line of argumentation is fallacious as I've explained and that is why it must be rejected. The QM predictions are for measured outcomes, not counterfactual ones, so that fact that the counterfactual unmeasured ones are not the same as the QM ones does not amount to a contradiction with QM. QM only cares and makes predictions about stuff that is actually measured.

Jochen wrote:
minkwe wrote:I already have written two local realistic simulations of EPRB experiments, which reproduce the QM correlations without any disturbance, and without non-locality. You can find them https://github.com/minkwe/epr-simple/, and https://github.com/minkwe/epr-clocked. But you are not going to understand what is going on there, if you do not understand my arguments.

I think I understand quite well what's going on there, and hence you should be able to anticipate my response: get rid of the nondetections in the first, or of the failures to produce particle pairs in the second, and then we can talk. A local realistic strategy should work just as well in the case of ideal detectors and sources.

You think you know but I think you don't. Please explain and justify why you think I should change the models before we can talk. Do you claim that the models are non-local? Then explain how simulations which can be run on separate computers without any communication are non-local.

If on the other hand, you are ready to admit that I have presented 2 examples of completely local realistic models reproducing the QM predictions, which Bell's inequalities do not apply to, then it means you have at least begun to understand my claim that it is not always possible to produce a joint PD, even for completely local realistic HV models.

So what is it going to be?

1) You continue to claim that local HV theories must always produce joint PD, in which case you show me the disturbance or non-locality in my simulations
2) You admit that I'm right, that local HV theories do not always have to produce a joint PD, in which case Bell's inequalities do not apply to cases in which they do not, such as epr-simple/epr-clocked.
minkwe

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### Re: A new simulation of the EPR-Bohm correlations

Jochen wrote:
Joy Christian wrote:1) In my view quantum entanglement is an illusion. It is analogous to the phlogiston theory. It works beautifully, but in the end it is a fool's gold, not the real thing.

Does this entail, for instance, the insecurity of quantum cryptography, or the impossibility of building large-scale quantum computers? If so, what will you do if they in fact are built?

Yes, it does.

If large-scale quantum computers are ever built --- exhibiting exponential speed up unambiguously, by utilizing quantum entanglement as a fundamental, irreducible concept --- then I will obviously be proven wrong. Being proven wrong is a part of doing science. There is no shame in it. I will be surprised, however, to find out that Nature is not only subtle but also malicious.

Jochen wrote:
In the toy model, as well as in the original 3-sphere model, the experimenters are completely free to choose their measurement directions.

Well, but their choice doesn't really matter, does it? In the toy model, the correlations depend only on the relative orientation along the dimension (locally) orthogonal to the Möbius band, which is beyond the experimenters' control; the components lying in the band are basically just discarded. No?

Again, you are taking the toy model far too seriously. I brought it up to counter a specific claim, namely that AB is always equal to -1 in my one-page paper. The toy model explains why that claim is wrong and naïve within the context of my original model. Beyond that the toy model should be taken with a large pinch of salt. In the 3-sphere model it is quite evident that experimenters are completely free to choose their measurement directions at will. Their "free will" is not compromised.

Jochen wrote:
In S^3 it is not the superdeterminism or non-locality but the geometry, topology, and the spinorial properties of the physical space that lead to the existence of strong correlations.

I'm not sure I really see the difference. Basically, you introduce additional degrees of freedom, and then have those, rather than the experimenters' choices, determine the measurement outcomes. So in a sense, the free choice of the experimenter is disregarded and replaced with a 'measurement' that is not under the experimenter's control.

I am afraid I do not agree. The measurement results in the 3-sphere model are functions only of a and b, chosen freely, and the orientation of the 3-sphere, which is the hidden variable: $A(a, \lambda)$. Nor does the probability density $\rho$ depend on a and b. This is already quite clearly demonstrated in my very first paper on the subject: http://arxiv.org/abs/quant-ph/0703179. Thus it is simply wrong to say that there is any restrictions on what a and b the experimenters can choose. Remember also that locally S^3 is identical to R^3. The experimenters have no way of knowing before computing the joint correlation whether they are operating within S^3 or R^3.

Jochen wrote:
It is just an artefact of a rather crude analogy. In the actual 3-sphere model it is not the distance but the locally defined torsion tensor that determines the strong correlation. See, for example, some of the mathematical details I provide here: http://libertesphilosophica.info/blog/o ... lations-2/.

I've got a question about that, too: locally, a nontrivial fiber bundle is always equivalent to a product manifold between base and fiber, so how can any local measurement know about the global twist?

You are quite right. Locally S^3 = S^2 x S^1, or equivalently SU(2) = S^2 x U(1). Alternatively, one can say that locally S^3 is identical to R^3, which is its tangent space, just as locally S^2 (our earth, for example) is identical to R^2 (our football field, for example). Thus the local experimenters or their measurement results know nothing about the global twists in S^3. It is only by comparing their results with the results obtained at a remote station that they would be in for a surprise!

Jochen wrote:Also, regarding your paper http://arxiv.org/abs/1201.0775, in footnote 2, you say that the probability distribution of A and B factorizes, due to them being independent variables; but if that's the case, then the correlator factorizes also, and the value of the CHSH quantity is constrained by 2. Both can't be right: the probability distributions can't factorize and still violate CHSH (or any BI).

In the Clifford-algebraic representation of S^3 the probability distribution of A and B factorizes but the correlator does not, because of the geometric product of A and B. And this is the stumbling block for many people who are not familiar with geometric algebra, and have not studied how I manage to have my cake and eat it too.

Jochen wrote:And another question: what must be the case in order for Bell inequalities to not be violated in your setup? The correct correlation for the singlet state is -a.b, but for a separable state, you just get $\langle AB \rangle = \langle A \rangle \langle B\rangle$, which doesn't violate any inequalities. How is that represented within your scheme?

Good question. A separable state in my model is represented by spin bivectors $\cal A$ and $\cal B$ that are always orthogonal to each other, so that $\langle AB \rangle = \langle A \rangle \langle B\rangle=0$.

Jochen wrote:Finally, how about inequalities not given in terms of correlations, but of probabilities (or even entropic inequalities)---have you had a look at those? How do you calculate, e.g., $p(A=+1 \wedge B=+1)$?

There are lots of inequalities floating around, and I am a lone researcher with rather limited resources. So, no, I haven't looked at many of these inequalities. I have done explicit calculations only for the EPR-B, GHZ-3, GHZ-4, and Hardy states, and I have a general, formal theorem for ALL quantum correlations. In any case, all one really needs is the EPR-B case, because if quantum mechanics cannot provide a complete description for even such a simple case, then it is best to look beyond it.

Jochen wrote:
The matter is already settled analytically. Eq. (B10) of this paper is an incontrovertible proof of my claim. Thus, strictly speaking, no simulation is necessary. But of course you are entitled to be convinced only if a "full two-boxes simulation" is provided, according to your specifications. I myself am quite happy with my Eq. (B10).

Well, the equation may be all right for all I know, but the question is whether it actually corresponds to the correlation between two actual measurements, or is just a fancy way of calculating -a.b. An explicit simulation would certainly clear up the doubts there.

Eq. (B10), plus this event-by-event simulation of the model, already provides substantial support for my program. But you are not satisfied with it. Fair enough.
Joy Christian
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### Re: A new simulation of the EPR-Bohm correlations

Schmelzer wrote:
minkwe wrote:I already have written two local realistic simulations of EPRB experiments, which reproduce the QM correlations without any disturbance, and without non-locality. You can find them https://github.com/minkwe/epr-simple/, and https://github.com/minkwe/epr-clocked. But you are not going to understand what is going on there, if you do not understand my arguments.

In case you don't understand minkwe's arguments, http://arxiv.org/abs/1507.00106 tries to explain these simulations.

In case anyone is decieved by Gill's antics, the careful reader will note that Gill is not analyzing the data from my programs as he claims but from carricatures of it that he has "roughly" rewritten himself in R.

Note the appendix:

Gill wrote:I plan in a later revision to add the actual mathematical formulas of the two simulation models. For
the time being, the reader is referred to the original Python code and accompanying explanations
by the author Michel Fodje, and to rough (and unauthorised) translation of these into the R language
by myself

My python code is available at the links I provided above. Completely open source and free for anyone to download. Anyone can run the simulations themselves and analyze the data themselves. You don't have to use my own analysis code. You could write yours. But it is highly dubious for someone to claim that they are testing output from my programs, when in fact they are using a completely unnecessary "rough and unauthorized" translation of the programs.

There is nothing wrong with trying to understand what the program does by trying to rewrite it in different languages. But it is not honest scientific practice to claim :

Gill wrote:I analyse the data generated by M. Fodje’s simulation programs epr-simple and epr-clocked

when in fact, the paper does not present any such analysis of output from my programs but rather "Gill's unauthorized modifications".

Another interesting tidbit is Gill's mind-reading abilities where he writes :

Gill wrote:Michel Fodje mistakenly (thinking of the polarization measurements in
quantum optics) took the angles 0 and 45 degrees for Alice’s settings, and 22.5 and 67.5 for Bob. I have
changed these to 0 and 90 for Alice, and 45 and 135 for Bob, as is appropriate for a spin-half experiment.

He doesn't realize that I can use whatever angles I like, and match what QM predictions for whatever angles I chose, nor does he realize that my simulation works with both spin-1 and spin-half particles. This is usually what happens when people have an agenda they are trying to propagate.

At least, to his credit, Gill admits that Bell's and CHSH inequalities do not apply to those simulations, just like I've been insisting from the beginning.
Last edited by minkwe on Thu Jul 02, 2015 10:28 am, edited 2 times in total.
minkwe

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### Re: A new simulation of the EPR-Bohm correlations

minkwe wrote:Another interesting tidbit is Gill's mind-reading abilities where he writes :

Gill wrote:Michel Fodje mistakenly (thinking of the polarization measurements in
quantum optics) took the angles 0 and 45 degrees for Alice’s settings, and 22.5 and 67.5 for Bob. I have
changed these to 0 and 90 for Alice, and 45 and 135 for Bob, as is appropriate for a spin-half experiment.

He doesn't realize that I can use whatever angles I like, and match what QM predictions for whatever angles I chose, nor does he realize that my simulation works with both spin-1 and spin-half particles. This is usually what happens when people have an agenda they are trying to propagate.

I noticed that nonsense from Gill. He is an expert on conjuring up such junk, with a confidence that can only come from utter unawareness of his own incompetence.
Joy Christian
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### Re: A new simulation of the EPR-Bohm correlations

Schmelzer wrote:
FrediFizzx wrote:
Schmelzer wrote:I could do it easier, simply "right result = -ab". With a counterexample for Bell's theorem this has anyway nothing to do.

It is the same result as QM for EPRB via a classical local realistic model. Sorry that you can't see that. And it is actually not very complicated at all. What don't you understand?

Sorry, indeed, I do not have hallucinations yet. I see only a laughable collection of meaningless formulas of type $\lim_{e_0\to a, e_0\to b}$ which, it seems, even Joy does not try to defend anymore. What I don't understand are, for example, formulas containing terms like $\lim_{e_0\to a, e_0\to b}$.

We were talking about the GAViewer code. Not what you presented above.
Schmelzer wrote:
FrediFizzx wrote:Does QM use the +/- 1 outcomes to get its theoretical prediction of -a.b for EPRB? No, it doesn't.

QM is not a local realistic theory, so it doesn't have to. Why you think that a strange set of formulas, which somehow gives -ab, has any relevance to Bell's theorem, I don't understand.

Why does a local realistic theory have to use +/- 1 outcomes to obtain a result of -a.b? Of course it doesn't have to any more than QM. If a classical local realistic model gives the same result as QM for EPRB, then Bell's theorem is of course nonsense. In fact, the QM experiments for EPRB support the local realistic model. That you think the formulas are "strange" indicates that you simply don't understand them. So let's work on an understanding. For the GAViewer code above, what don't you understand?
FrediFizzx
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### Re: A new simulation of the EPR-Bohm correlations

minkwe wrote:At least, to his credit, Gill admits that Bell's and CHSH inequalities do not apply to those simulations, just like I've been insisting from the beginning.

You are flogging a dead horse. No one has ever claimed that the straight CHSH inequality applies to your simulations, and this has been well known since Pearle (1970). By the way, did you find some time to compute the CH inequality I showed you?
Heinera

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### Re: A new simulation of the EPR-Bohm correlations

Heinera wrote:...did you find some time to compute the CH inequality I showed you?

The CH inequality you "showed" on the other thread is erroneous, as I pointed out to you there.

Not surprisingly, the correct CH inequality is "violated" local-realistically, as I show in this simulation: http://rpubs.com/jjc/84238.
Joy Christian
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### Re: A new simulation of the EPR-Bohm correlations

Schmelzer wrote:
FrediFizzx wrote:Does QM use the +/- 1 outcomes to get its theoretical prediction of -a.b for EPRB? No, it doesn't.

QM is not a local realistic theory,...

How do you know that QM is not a local realistic theory? Isn't that an unfounded assumption?
FrediFizzx
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### Re: A new simulation of the EPR-Bohm correlations

Heinera wrote:You are flogging a dead horse. No one has ever claimed that the straight CHSH inequality applies to your simulations

How can inequalities which apply to ALL local HV theories have any exceptions which are local HV theories ??? My simulations are all local and realistic. None of you has argued otherwise. The outcomes are produced in completely local manner. None of you has argued against that. All I'm argued is that Bell's inequalities do not apply to all local HV theories as Bell claimed. I've given 2 examples which are completely local realistic, which reproduce the QM predictions. I claim the inequalities do not apply to my simulations nor to the QM predictions, contrary to Bell's claim. Whether Pearle knew about this or not is irrelevant. The fact is, Bell screwed up when he said:

Bell wrote:In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that a theory could not be Lorentz invariant.[4]

I've simply proven that Bell's statement is false, by presenting 2 counter examples. Can you admit that? If not please show exactly where in my simulation the setting of one instrument influences the reading of another instrument. Had Bell known that his inequalities and theorem did not apply to all HV theories, he wouldn't have written what he wrote.

How his worshippers prefer to do the ritual dance of goal-post shifting. There is always some other inequality, or some other theorem they'd rather talk about instead of the one under discussion.

Therefore, I'm not trying to flog a dead horse. I'm flogging the jockeys who are in denial and are continuously trying to ride the poor thing.
Last edited by minkwe on Thu Jul 02, 2015 3:08 pm, edited 1 time in total.
minkwe

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### Re: A new simulation of the EPR-Bohm correlations

minkwe wrote:
Heinera wrote:You are flogging a dead horse. No one has ever claimed that the straight CHSH inequality applies to your simulations

How can inequalities which apply to ALL local HV theories have any exceptions which are local HV theories ???

Bell's original inequality, as well as CHSH, asume that all particles are detected, and that they can always be correctly paired. That's why these inequalities are not used to analyze experiments anymore, but are superseded by inequalities that do not make these assumptions.. You know this very well; by pretending otherwise you simply show dishonesty.
Heinera

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### Re: A new simulation of the EPR-Bohm correlations

Ben6993 wrote: "The use of a final strong measurement seems to imply that what I have written above is incorrect and that an individual particle is followed and labelled across its interactions. And how are the weak results for a single particle checked against the final strong result. And how does the strong measurement at the end differ from the weak measurements en route?"
Joachim wrote: "TBH, I haven't really grasped the role of the strong measurement in the end myself... And as I said, I'm not ready to vouch for the quality of the paper."

OK, I have read up a liitle on weak measurement theory and accept that the aim is to make repeated weak measurements on the same particle.

I like the idea of weak measurements and it seems not to fit in with spooky effects of one particle on another. Weak measurements appear to be via field interactions and a strong measurement is via a particle interaction. So we have (say) an electron field for the first partner of a pair and a number of weak measurements are made on it without disturbing much its spin state.

But at what stage in the sequence of weak measurements on the same electron does the spooky chance decision arise that the particle is (say) left-handed? {I don't believe in such spookiness myself.} Presumably on the first weak measurement Thereafter the electron field is fixed in a left-handed form for all further weak measurements, and at the final confirmatory strong measurement the field collapses to a particle and after which the electron has a right-handed spin state.

What if we let the weak measurements or perturbations of/on the field gradually grow stronger. Say the earliest very slight perturbations have no discernible effect on the weak measurement device. I am trying to locate the first weak measurement which triggers the random decision to choose a fixed spin handedness for that particle but that would be difficult to label for very very weak perturbations. .... I can't see spin handedness as a random decision based on a very tiny perturbation. Also, what if the electron field early on encountered a magnetic field and underwent a minor perturbation. Would not that spookily fix the electron's handedness? Isn't it unlikely that the electron field had a completely pristine environment before the first weak measurement. Isn't it likely that the electron field's handedness gets fixed very early on in its lifetime before any weak measurements are made? Surely the spookiness does not await a human measurement intervention.

Suppose, instead, that the electron field is replaced by a composite field of an electron and its partner positron. This field contains the mix of left and right spin states. But the weak measurement sequence has to be acting on a single particle not on the pair. The first weak measurement must contain the spooky instant of choice of spin and also select which particle is being treated out of the pair field

The whole idea of weak measurements, which to me are field interactions, seems to make field collapse [as in a strong measurement] unimportant w.r.t. spookiness. The spooky choice [were it to exist, which I do not believe] is likely to have been made much earlier by slight random field perturbations during time of flight. E.g. by encountering a virtual particle pair en route.
Ben6993

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### Re: A new simulation of the EPR-Bohm correlations

Dear Jochen and other, see Richard Gill new paper http://arxiv.org/abs/1507.00106
He wants to contribute to the ongoing discussion.
helgus

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### Re: A new simulation of the EPR-Bohm correlations

minkwe wrote:How can inequalities which apply to ALL local HV theories have any exceptions which are local HV theories ???

You can't answer this question can you? Now who's pretending? Who's being dishonest?
I claim that my simulations are fully local realistic. And your response to that is what exactly? You pretend to argue against that but have absolutely no counter argument, just empty barks.

I claim that Bell's inequalities do not apply to my simulation, nor to the predictions of QM, nor to the results of EPRB experiments. What is your response to that exactly? You want to shift the goal-post to point to other inequalities instead of the ones we are discussing. Making dubious claims to have tested my code against other inequalities. While your friends are there insisting that Bell's inequalities must apply because of statistics, blah, blah, blah.

The horse is dead, Bell messed up. Admit it and stop trying to ride a dead horse.

Heinera wrote:Bell's original inequality, as well as CHSH, asume that all particles are detected, and that they can always be correctly paired.

And whose problem is it if they make nonsensical impractical assumptions, fit for abstract mathematics but completely uninteresting for physics? Why would the inequalities need to be monkey-patched, if the assumptions were justified in the first place?

Bell said:
Bell wrote:In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that a theory could not be Lorentz invariant.[4]

Let me fix that for him
Bell Should Have wrote:In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, it is not necessarily the case that there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. But most likely, it could be that either not all particles are detected, or it is not always possible to reliably pair detected particles. Therefore, the idea of a signal which must propagate instantaneously, or the idea of a theory that is not Lorentz invariant is silly, if not premature.

Ladies and Gentlemen, behold, the celebrated Bell's theorem from the Bell worshipers.

What physical principle or experimental result enable you to claim that all particles must be detected? No answer.
What physical principle or experimental result enable you to claim that all it must always be possible to reliably pair particles? No answer.
So what chemical does a person have to be inhaling to claim a local realistic model which reproduces all the essential features of an experiment, and reproduces the results of the experiment, contains a "flaw" that should be fixed to make it as much unlike the experiment as possible? Just because experiments/simulations do not fit the box which you can fit in your brain does not mean the experiments/simulations are flawed or have "loopholes"! You should look inward. It is Bell's theorem that has loopholes and needs to be fixed and you will see how completely irrelevant the inequalities are. You will get

$\rho(a, c) -\rho(b, a) - \rho(b, c) \le 3$
$\rho(a,b) + \rho(a,b') + \rho(a',b) - \rho(a',b') \leq 4$

Heinera wrote:No one has ever claimed that the straight CHSH inequality applies to your simulations

Let us see ...
Denis Rosset et al 2013 wrote:"Considering a generalization of usual Bell scenarios where external quantum inputs are provided
to the parties, we show that any entangled quantum state exhibits correlations that cannot be
simulated using only shared randomness and classical communication, even when the amount and rounds
of classical communication involved are unrestricted."
-- Denis Rosset et al 2013 New J. Phys. 15 053025

Gill wrote:The results also show that Hess and Philipp's (2001a,b) recent claims are mistaken that Bell's theorem fails because of time phenomena supposedly neglected by Bell.
...
In the mean time, there have been more challenges to Bell (1964) in
which an attempt is made to exploit time dependence and memory effects;
see Hess and Philipp (2001a,b). I was unable to interest Walter Philipp in
a bet: “our results are mathematically proven and a computer simulation is
unnecessary”. The present paper provides another mathematically proved
http://arxiv.org/pdf/quant-ph/0110137v4.pdf

Now who is being dishonest? Making claims they know to be false?

I wonder, if everything I'm saying has been known since 1970, and I'm simply pretending and being dishonest? Why is a "big shot" "mathematical statistician" like Gill paying so much attention to me that he can't stop mentioning my name everywhere and he's now writing an article about my simulations? You should ask him that question.
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