My Challenge to All Bell-Believers --- Meet it or Beat it:

[Curiosity]

Yes, what he says is correct, but it is empty. There are no other local hidden variables models which reproduce the singlet correlations than models which can be cast in the form A (a, lambda) and B (b, lambda). Determinism is indeed irrelevant.

A local hidden variables model would (a) be local and (b) satisfy counterfactual definiteness. One could create a probability space with random variables A_a and B_b, for all directions a and b, such that A_a is the outcome which Alice would see if she chose setting a. Now define lambda = the pair of functions (A_a, B_b; a, b directions). Nature chooses a 0/1 valued function A_(.), and a function B_(.). The experimenter chooses settings a, b. The experimenter observes outcomes A_(a) and B_(b).

The no-conspiracy assumption says that nature and the experimenter are not constrained by one another.

I am not sure I understand. Are you saying your model includes the case when we do not assume deterministic functions A(.) but only probabilistic functions P_A(.)?

[gill1109]

Yes, what he says is correct, but it is empty. There are no other local hidden variables models which reproduce the singlet correlations than models which can be cast in the form A (a, lambda) and B (b, lambda). Determinism is indeed irrelevant.

A local hidden variables model would (a) be local and (b) satisfy counterfactual definiteness. One could create a probability space with random variables A_a and B_b, for all directions a and b, such that A_a is the outcome which Alice would see if she chose setting a. Now define lambda = the pair of functions (A_a, B_b; a, b directions). Nature chooses a 0/1 valued function A_(.), and a function B_(.). The experimenter chooses settings a, b. The experimenter observes outcomes A_(a) and B_(b).

The no-conspiracy assumption says that nature and the experimenter are not constrained by one another.

I am not sure I understand. Are you saying your model includes the case when we do not assume deterministic functions A(.) but only probabilistic functions P_A(.)?

I am not saying that, but it is true.
I'm saying that a local hidden variables model, including a stochastic local hidden variables model, allows the creation of a classical probability space (Omega, F, P) with random variables X_a, Y_b defined on it. Thus X_a is a function of omega in Omega. If you like, you can think of omega as being lambda. But if you like, you can also think of the set of all functions {X_a(omega), Y_b(omega) : a, b directions} which you find when you let omega range through Omega.


If we are just interested in the probability distribution of a random variable X we can forget about the underlying probability space Omega and just take the new probability space IR (the real line) with the induced probability measure P_X on it defined as follows: for Borel subsets B of IR, P_X(B) = P(X in B) := P({omega: X(omega) in B}).

This is basic stuff in the complete standard measure theoretic foundation of probability. The theory built by Borel and Lebesgue and completed by Kolmogorov. And standard terminology from the theory of stochastic processes. We can think of all the possible outcomes of Alice's measuring spin in direction a as a random function, with time variable a. X_a(omega) as a varies, for fixed omega, is called the sample path of the stochastic process. Of course we do not observe that sample path. Alice chooses a direction a and gets to see one point on that random graph, namely X_a(omega).

[Curiosity]

I think that Arthur Fine also proved that rejecting a deterministic model and using a probabilistic one is only an apparent generalization.
By the way, there are correct ways to reject the Bell theorem and non-locality. You only have to explain what Bell's assumption you are rejecting and why. See for instance https://arxiv.org/abs/1511.00729.

[gill1109]

I think that Arthur Fine also proved that rejecting a deterministic model and using a probabilistic one is only an apparent generalization.
By the way, there are correct ways to reject the Bell theorem and non-locality. You only have to explain what Bell's assumption you are rejecting and why. See for instance https://arxiv.org/abs/1511.00729.

Yes, you are absolutely right. Nowadays we say that Bell's more interesting "meta-theorem" (the metaphysical conclusions which he drew from his inequalities concerning the relation between quantum mechanics and relativity theory) is that QM is incompatible with locality [local relativistic causality], realism [counterfactual definiteness] and no-conspiracy [freedom]. Loophole-free experiments furthermore show by the same reasoning that not just QM theory or any theory with approximately the same predictions but also meticulously generated laboratory observations prepared under exacting conditions are incompatible with locality [local relativistic causality], realism [counterfactual definiteness] and no-conspiracy [freedom].

The paper your refer to uses violation of no-conspiracy. Arthur Fine knew this all very well, too. Bell knew it all too, but didn't use the same words.

Progress is nowadays being made using retrocausality and using superdeterminism. Lots of people working on those devices. This might solve the problems of harmonising quantum theory and relativity theory for the purpose of modelling the early universe, but I am certain that it is not going to solve the problem of merging quantum theory and relativity theory for the purpose of understanding the quantum correlations which are observed in rigorous "loophole free" laboratory experiments, ie with distances of the order of micrometers - kilometers and time corresponding to the distances (ie the times taken by "light in vacuum" to travel such distances).

[Joy Christian]

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In the last few months, there have been frequent hits on the opening post of this thread from the Einstein Centre's website: http://einstein-physics.org/.

In other words, the hits are to this link: viewtopic.php?f=6&t=275#p6681, which is to this thread.

My guess is that someone has posted a discussion on the Internet about my challenge to all Bell-believers that started this thread in 2016. That is pretty old and the challenge still stands.

But I would like to point out that now there is a serious theoretical counterpart to the challenge in the form of this paper: https://arxiv.org/pdf/1704.02876.pdf.

My conclusion in the paper is that

... what is ruled out by the Bell-test experiments is not local realism but the additivity of expectation values.

You will have to read the paper I have linked above to understand why that is the case.

So the challenge has reached its conclusion. For obvious reasons, no one has been able to defeat the challenge in five years, but the paper shows why that was an impossibility.
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[FrediFizzx]

There is more than one way to shoot down Bell's junk physics theory. I think the best way is to show a local model that predicts -a.b.




For sure, local realism is not ruled out by the experiments after that.
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[Joy Christian]

For sure, local realism is not ruled out by the experiments after that.

You are right, of course. The essence of the claim by Bell is that quantum correlations cannot be reproduced in a local-realistic model. But your simulation above, which supports the analytical 3-sphere model, clearly shows that Bell's claim is wrong. So that should be the end of the saga. A clear refutation by a constructive counterexample. But there is also a formal aspect to Bell's argument, with the core of Bell's so-called "theorem" supported by an application of probability theory. That formal aspect must also be defeated, and that can be decisive and convincing only by playing the Bell-believers' own formal game. So Bell's argument has now been defeated both by a constructive counterexample and a decisive formal argument.
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