Do nonlocal entities fulfill assumptions of Bell theorem?

[brucep]

Cool stuff about random walks! Statistical mechanics always go a little over my head, but it's pretty cool that you can recover Anderson localization and the Born rule by just maximizing entropy over classical paths. Also, the plots are pretty, which is always one of my primary criteria for evaluating papers outside my field.

Back to the topic at hand, though, I think I may finally see your confusion. I certainly agree that solitons have information about both spins spread throughout all of space, but that's not enough. In fact, let's go a step further and consider the most powerful classical measurement possible: observe data that tells you the exact, pre-measurement state of both particles, then apply some function to that data that outputs one of two outcomes. Such a measurement is still not enough to violate Bell's inequality, because each observer only knows the pre-measurement state of the particles. To reach quantum-mechanical levels of correlations, each measurement outcome needs to depend not only on the states of the particles, but also on what measurement the other observer chose to make. Solitons provide a clear mechanism for the former, but no mechanism for the latter, as far as I can tell.

Beyond that, I'm running up against the limits of how precisely I can explain why Bell's inequality applies to solitons. Bell's inequality (or at least, the two-particle version of it) requires measurements of spin at 45-degree angles to one another, so for me to get any more specific, you'll have to provide some model of solitons that supports more than two directions of spin. Otherwise, all I can say is that your arguments seem to stem from defining "locality" differently from Bell, and if you actually go through any proof of Bell's theorem, you'll never find any steps that stop being correct for solitons.


I didn't know they'd done Bell inequality violations with neutrons - nifty!

As for that link, Bryan Sanctuary seems to be a big fan of Joy Christian's work. In reading his blog, I think I've actually come to a better understanding of where Christian's primary error is. The math is obtuse enough that I can't say for sure, but I think that both authors are looking at direct correlations between spins, rather than correlations between measurements of spins. By applying fancy models of the spins, they come up with more complicated formulas for spin-spin correlations, which can exceed Bell inequality bounds. But in doing so, they sacrifice the connection between their formulas and experimental results. In Bell inequality experiments, some physics leads to Alice's and Bob's binary measurement outcomes, which they write down in their lab notebooks. That's where the physics stops. To look for Bell inequality violations, they punch the numbers into Matlab and calculate a well-defined correlations function. Does that function really capture the correlations between the spins themselves? Maybe not, but Bell's theorem doesn't care, because it puts bounds on the correlation function as traditionally defined. That's what I meant before when I said that Bell's theorem is really about statistics, rather than physics.

(Addendum: I think the most convincing argument that Sanctuary is making this mistake comes near the top of post 009b, where he says Bell's original equation 1 is mistaken. He says that because spin can point in any direction, the functions A and B should not be restricted to having values of plus/minus one. But A and B are measurement outcomes, so they can only be plus/minus one by definition, independent of any physics.)

Nice post. Very informative. Everything that hasn't been physically measured is still a prediction which hasn't been empirically confirmed or falsified. If you separate your model from the empirical side of science you're no longer doing science. I don't feel this way about quantum gravity since the domain is insane for the empirical side.

 

[Q-reeus]

(Addendum: I think the most convincing argument that Sanctuary is making this mistake comes near the top of post 009b, where he says Bell's original equation 1 is mistaken. He says that because spin can point in any direction, the functions A and B should not be restricted to having values of plus/minus one. But A and B are measurement outcomes, so they can only be plus/minus one by definition, independent of any physics.)

I think you may have misinterpreted Joy and Bryan there. Their analyses always predict binary outcomes. Joy's picture though requires we live in an S^7 reality (with S^3 as subset). Whenever I tried to pin him down to observable classical physics consequences of an implied constant spacetime torsion (or, elsewhere in his writing, constant curvature), nothing sensible to me came back.

Brian otoh seems to require only that quantum spin has this anyon character. The prospect of that model demolishing quantum weirdness (read: magic) suggests it should be given every chance possible. Whether apparent lack of interest indicates lack of merit or an entrenched mindset is debatable.

 

[Jarek Duda]

Taking a very different approach, Bryan Sanctuary claims to be able to reconcile locality and realism with Bell by modelling particle spin (or rather 2D spins) differently to the standard way:
http://quantummechanics.mchmultimedia.com/2011/quantum-mechanics/009-disproof-of-bells-theorem/
Given Fednis48 is evidently the best informed here re Bell inequalities, it might be interesting to get his take on that.

Thanks, very interesting, especially leading to weaker inequalities while considering direction of spin, instead of +-1 values of Bell:

Regarding neutron, they have magnetic dipole moment, what also means nonlocality - their influence (magnetic field) drops with 1/r^3.

Back to the topic at hand, though, I think I may finally see your confusion. I certainly agree that solitons have information about both spins spread throughout all of space, but that's not enough. In fact, let's go a step further and consider the most powerful classical measurement possible: observe data that tells you the exact, pre-measurement state of both particles, then apply some function to that data that outputs one of two outcomes. Such a measurement is still not enough to violate Bell's inequality, because each observer only knows the pre-measurement state of the particles. To reach quantum-mechanical levels of correlations, each measurement outcome needs to depend not only on the states of the particles, but also on what measurement the other observer chose to make. Solitons provide a clear mechanism for the former, but no mechanism for the latter, as far as I can tell.

So what does "local" in Bell's theorem means?

Beyond that, I'm running up against the limits of how precisely I can explain why Bell's inequality applies to solitons. Bell's inequality (or at least, the two-particle version of it) requires measurements of spin at 45-degree angles to one another, so for me to get any more specific, you'll have to provide some model of solitons that supports more than two directions of spin. Otherwise, all I can say is that your arguments seem to stem from defining "locality" differently from Bell, and if you actually go through any proof of Bell's theorem, you'll never find any steps that stop being correct for solitons.

So imagine an infinite tank of superliquid (no viscosity), in which e.g. due to theremal fluctuations there were created two swirls of opposite angular momentum due to Noether theorem (preferably of topological nature like fluxons to be unable to unwind).
These swirls go to infinity, affecting the entire field with e.g. 1/r^3 dipole-like behavior.
For the measurement purpose, imagine some kind of Stern-Gerlach setting - enforcing them to finally choose parallel or anti-parallel alignment.
Should they fulfill Bell inequalities?

ps. You have written that superdeterminism is a way to avoid Bell inequity problem - doesn't the use of Langrangian formalism for field theory with the solitons solve the problem?
My view on Bell's correlations, like for Born rules in MERW picture, is through the action-optimizing formulation of Largangian mechanics: there is a pre-measurement state in the past and post-measurement state in the future - getting the squares of probabilities for the measurement values.
We can analogously see quantum computers, like Shor's algorithm - its strength lies in the selection measurement - which influence kind of go back to the "classical function", restricting the orignal ensemble/superposition:

Regarding Maximal Entropy Random Walk (MERW), it was my original motivation a few years ago to start overcoming the need of mysticism to explain physics, e.g. Feynman's ""If you think you understand quantum mechanics, you don't understand quantum mechanics.", "Shut up and calculate".
MERW basically says that disagreement between stochastic models and thermodynamical prediction of QM, seen for example in Anderson localization, is only a consequence of only approximating the maximal entropy principle, which gives the meaning to the statistical physics considerations.
MERW is nonlocal in QM-like style (Born rules, leading to QM round state) due to using ensemble of paths which depend also on distant situation - but it doesn't mean that the particle has this knowledge. Instead, it is a statistical physics effective model: only gives us prediction of the safest assumption of e.g. probability distribution, assuming some hidden complex dynamics.
So while looking at a point, we consider all trajectories going through this point, their statistics gives the MERW stochastic propagator.
It is essentially different than QM (e.g. no interference - de Broglie's clock is missing), but recreates its thermodynamical prediction, including first localizing in near low energy excited state, then deexcitng to the ground state:

 

[Schmelzer]

Taking a very different approach, Bryan Sanctuary claims to be able to reconcile locality and realism with Bell by modelling particle spin (or rather 2D spins) differently to the standard way:
http://quantummechanics.mchmultimedia.com/2011/quantum-mechanics/009-disproof-of-bells-theorem/

He claims but delivers nothing. Showing the front page of a paper of two Anti-Bell cranks is nothing, Joy Christian is a known crank, reference to him gives nothing, the other guy I don't know. but doubt that it is worth to be studied. I have been unable to find a reasonable formula which describes his hidden variable model. It may be, of course, hidden in some of his videos, but to check them all would be too much loss of time.

Anyway, one claim is clearly wrong, namely that there is no nonlocal hidden variable explanation of QM. It is wrong, because there is even a deterministic one, de Broglie-Bohm theory. So, should we consider seriously guys who don't even know what dBB theory delivers?

 

[Schmelzer]

Brian otoh seems to require only that quantum spin has this anyon character. The prospect of that model demolishing quantum weirdness (read: magic) suggests it should be given every chance possible. Whether apparent lack of interest indicates lack of merit or an entrenched mindset is debatable.

Whatever it requires, it has to present somehow the local hidden variables $$\lambda$$ and the functions $$A(a,\lambda)\in \{-1,1\}$$ which predict the observed measurement outcomes, or to argue why they do not exist despite the EPR argument. I have been unable to find the corresponding formulas. (If you find them in a video, please link the video and give the time when the formula appears.)

 

[Q-reeus]

He claims but delivers nothing. Showing the front page of a paper of two Anti-Bell cranks is nothing, Joy Christian is a known crank, reference to him gives nothing, the other guy I don't know. but doubt that it is worth to be studied. I have been unable to find a reasonable formula which describes his hidden variable model. It may be, of course, hidden in some of his videos, but to check them all would be too much loss of time.

Anyway, one claim is clearly wrong, namely that there is no nonlocal hidden variable explanation of QM. It is wrong, because there is even a deterministic one, de Broglie-Bohm theory. So, should we consider seriously guys who don't even know what dBB theory delivers?

Try toning down use of the 'crank' label. You in particular are well aware of use and abuse of 'psychological impact' techniques.
I don't know if Han Geurdes has it right, but if you wish to pick him apart, his site and papers are not hidden away: http://leidenuni.academia.edu/HanGeurdes
And the same sentiment applies to Bryan Sanctuary. Basic concept is set out here:

Maybe you try pointing to where iyo the very first actual fatal error occurs.
[well....that one fizzled out with little to go on. Best to look through articles at his site:
http://quantummechanics.mchmultimedia.com/category/local-reconciliation-epr-paradox/]
As for him being ignorant of DBB theory, that I severely doubt. Without knowing where he allegedly states such, as a general observation, context can be all-important as to determining actual intent.

 

[Schmelzer]

Maybe you try pointing to where iyo the very first actual fatal error occurs.

No problem.

Best to look through articles at his site:
http://quantummechanics.mchmultimedia.com/category/local-reconciliation-epr-paradox/]

Ok, in https://www.academia.edu/7930924/Concrete_incompleteness_and_Bell_s_theorem I did not have to read much:

The measurement functions A(a,λ) and B(b,λ) represent the outcomeof measurements. The outcome not only depends on the unitsetting parameters a and b ∈ R^3, but also on hidden λ. The restriction is: |A| ≤ 1 and |B| ≤ 1.

False, the restriction is A, B in {-1,1}.

As for him being ignorant of DBB theory, that I severely doubt. Without knowing where he allegedly states such, as a general observation, context can be all-important as to determining actual intent.

Ok, no problem, 2.04 of

is the place where he states "no one has been able to find a nonlocal hidden variable theory to explain the data, and no one ever will".

If these two errors are considered fatal is, of course, a personal decision, but if somebody makes such an extraordinary claim like that a well-known essentially mathematical theorem is false, I do not really care about the level of fatality of his errors, and one false claim seems sufficient for the crank classification.

 

[Jarek Duda]

What is the problem with dBB interpretation?
https://en.wikipedia.org/wiki/Pilot_wave
We just take Schrodinger equation and perform Madelung substitution: psi = sqrt(rho) * exp(i*S), getting continuity equation for density rho and Hamilton-Jacobi for action S, with Planck-order corrections from interaction with the pilot wave.
Everything is local here, like in Couder's experiments of soliton-like corpuscles with coupled clock causing waves around: in interference the corpuscle travels one path while its coupled 'pilot' wave travels all paths - affecting the trajectory ( http://prl.aps.org/abstract/PRL/v97/i15/e154101 ).
For orbit quantization the particle's internal clock needs to find resonance with the field - to get low energy uniform oscillations of the field ( http://www.pnas.org/content/107/41/17515 ):

So looking at such picture of particles as Couder's walking droplets or in the language of fields: breathers - solitons with internal oscillations (de Broglie's clock/zitterbewegung), what exactly "missing piece" does the Bell's theorem suggests?

 

[Schmelzer]

What is the problem with dBB interpretation?
... Everything is local here,

No, dBB interpretation is nonlocal. It is local only in the one-particle theory. Already in the two-particle case, the velocity of the particle $$\dot{q}_1(t)$$ is defined via the guiding equation by the wave function $$\psi(q_1,q_2, t)$$ and the actual position $$q_2(t)$$ of the other particle at the same time t.

 

[Jarek Duda]

Oh I see - so the multiple particle Schrodinger equation requires multiple dimensions (psi(x1,x2,...)), which I can believe require some nonlocality.

However, Couder/soliton picture suggests a more intuitive approach to description of multi-particle system: they are a part of the same field, where also their coupled 'pilot' waves propagate:

This is clearly a local picture, governed e.g. by some Euler-Lagrange equation (super(?)deterministic what is supposed to solve the Bell issue?) - what does such picture lack comparing to the real microscopic physics?

There is the question of equivalence of two approaches to describe multiple particle systems:
- multi-particle Schrodinger equation, which goes toward QFT while the number of particle can vary,
- soliton (particle) models - which directly allow for varying number of solitons/particles.
How would a description of scattering of solitons look like? In this case we would need to consider ensemble of scenarios - Feynman diagrams, getting something similar to perturbative QFT ... don't we?

 

[Schmelzer]

There are no equations in the video, and the picture shows only the one-particle case, so obviously the case of many particles is not handled too.

BTW, Euler-Lagrange equations are standard physics and have nothing to do with superdeterminism. What one needs to overcome the violation of BI is locality (or better Einstein causality, because it makes no sense to name a theory with, say, a maximal speed of, say, 1000 c "nonlocal" while naming one with c as the maximal speed "local").

 

[Jarek Duda]

I apology, so here are multiple droplets:

There are lots of papers with equations for them, but clearly this is not exactly the microscopic physics - only very nice intuitions, including double slit experiment - which as Feynman said:
"… In this chapter we shall tackle immediately the basic element of the mysterious behavior in its most strange form. We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way and which is at the heart of quantum mechanics. In reality it contains the only mystery. We cannot make the mystery go away by explaining how it works . We will just tell you how it works.…"

The main differences with real physics are:
- there is used external clock, while particles have internal clock (de Broglie's clock/zitterbewegung), which has already been observed for electron: http://link.springer.com/article/10.1007/s10701-008-9225-1
- droplets are not exactly a part of the field (solitons), while e.g. electron is among others a singularity (regularized in soliton models) of electric field,
- there is missing charge quantization, what can be realized by using topological charge as electric charge (Gauss-Bonnet theorem as Gauss law),
There are various approaches of this type - my favorite is of prof. Faber (slides: https://dl.dropboxusercontent.com/u/12405967/soliton.pdf )

Regarding non-locality, as we have discussed and Fednis48 has agreed, e.g. spin of a particle is not a local property - instead, this information propagates with speed of light from creation of the pair (like rotation around a vortex in superfluid) - the spin information is smeared over the entire universe ... and can affect the Bell-like localized spin during the measurement.

 

[Schmelzer]

So the video are words which one can ignore. That a double slit experiment can be reproduced is plausible, even if, I would guess, not with what is shown in the video - one would need many drops with the same wave, most of them hitting the wall, while what was shown were different waves with different drops. If this guess is correct is something I cannot even try to find out without the equations.

That you can create nice pictures with several drops is clear, there is no physical difference, if one drop can do this, why not several. But the equation of what we see would be one wave in three-dimensional space (sorry, two-dimensional) and not in configuration space which would be six- (or, reduced to a plane, four-) dimensional.

Regarding non-locality, as we have discussed and Fednis48 has agreed, e.g. spin of a particle is not a local property - instead, this information propagates with speed of light from creation of the pair (like rotation around a vortex in superfluid) - the spin information is smeared over the entire universe ... and can affect the Bell-like localized spin during the measurement.

This does not help at all. The point is that nothing in Bell's theorem requires the hidden parameters to be local. All what is forbidden by locality is that the information which measurement (which direction) is measured at A (the choice of a) is used to choose what is observed at B. In the function $$B(b,\lambda)$$ all what matters is that a is not used. $$\lambda$$ may be whatever you like, it can live in some stringy 26-dimensional universe somewhere else with no connection at all to any localization in 3D, it can be predefined and known everywhere, whatever. Spin, shmin, whatever, it doesn't help.

 

[Fednis48]

I think you may have misinterpreted Joy and Bryan there. Their analyses always predict binary outcomes.

I may have misinterpreted Christian's work, but I'm increasingly convinced that I have Sanctuary's number. I went back and read his blog a little more carefully, and what's missing is any description of how his anyonic spins get translated into an actual, binary measurement outcome at the end. Section 009b is particularly flagrant in this regard; after confusing the spin itself with its measured value in criticizing Bell's original equation 1, he repeatedly comes back to the theme of spherical geometries having strong correlations and stresses the idea that Bell was ignoring important options by restricting A and B to values of $$\pm 1$$. Honestly, a true disproof of Bell's theorem would only need to contain two lines: an expression for the distribution of the hidden variable, and a function that maps its value and a measurement setting to a binary outcome. Sanctuary's multi-page explanation does not even contain the latter (as far as I can tell), so I'm convinced he's just gotten himself confused through too much math with not enough sanity checks.

Whatever it requires, it has to present somehow the local hidden variables $$\lambda$$ and the functions $$A(a,\lambda)\in \{-1,1\}$$ which predict the observed measurement outcomes, or to argue why they do not exist despite the EPR argument. I have been unable to find the corresponding formulas. (If you find them in a video, please link the video and give the time when the formula appears.)

This.^^^^^^

So what does "local" in Bell's theorem means?

Its means that no measurement can alter the outcome of another, spacelike-separated measurement.

So imagine an infinite tank of superliquid (no viscosity), in which e.g. due to theremal fluctuations there were created two swirls of opposite angular momentum due to Noether theorem (preferably of topological nature like fluxons to be unable to unwind).
These swirls go to infinity, affecting the entire field with e.g. 1/r^3 dipole-like behavior.
For the measurement purpose, imagine some kind of Stern-Gerlach setting - enforcing them to finally choose parallel or anti-parallel alignment.
Should they fulfill Bell inequalities?

Yes, they should. Even beyond Stern-Gerlach, the most powerful measurement one could perform on such a system would be to carefully measure the fluid dynamics to determine the exact angular momentum of both swirls. Angular momentum is a 3-vector, so now we can drop the physics of solitons and just say the hidden variable is a 3-vector $$\vec{J}$$, and both Alice and Bob know it precisely. Your task is now to find a probability distribution over $$\vec{J}$$ and four functions $$M_i(\vec{J})=\pm1,i\in[1,4]$$such that
$$\langle M_1 M_2\rangle-\langle M_1 M_4\rangle+\langle M_2 M_3\rangle+\langle M_3 M_4\rangle>2$$.
By Bell's theorem, this can't be done.

ps. You have written that superdeterminism is a way to avoid Bell inequity problem - doesn't the use of Langrangian formalism for field theory with the solitons solve the problem?
My view on Bell's correlations, like for Born rules in MERW picture, is through the action-optimizing formulation of Largangian mechanics: there is a pre-measurement state in the past and post-measurement state in the future - getting the squares of probabilities for the measurement values.
...
MERW is nonlocal in QM-like style (Born rules, leading to QM round state) due to using ensemble of paths which depend also on distant situation - but it doesn't mean that the particle has this knowledge. Instead, it is a statistical physics effective model: only gives us prediction of the safest assumption of e.g. probability distribution, assuming some hidden complex dynamics.
So while looking at a point, we consider all trajectories going through this point, their statistics gives the MERW stochastic propagator.

I may be misunderstanding something, but if you have to consider all the trajectories that take you from point a to point b, how do you know where the particle was at some point partway along its trajectory? The whole point of a realistic hidden variable is that it has a well-defined value at all times, and measurement just tells us what that value is. If you have to specify a point of measurement to calculate the dynamics, you're abandoning realism.

 

[Jarek Duda]

Schmelzer, the video shows for example that Feynman was wrong - that we can have interference in double slit experiment also for classical object with wave-particle duality.
This is only one of many issues which were believed to have no explanation ...

Returning to Bell theorem, which is clearly violated by the nature - instead of concluding that physics makes no sense, there is just an error in its assumptions - for example too simplistic representation of spin: which in fact is not a local zero/one value, but due to Noether theorem, an information delocalized in a complex way over the entire field.

 

[Schmelzer]

Schmelzer, the video shows for example that Feynman was wrong

If you refer to some video, link to the video and time.

- that we can have interference in double slit experiment also for classical object with wave-particle duality.

The point that "particle and wave" can explain the double slit is a famous point made by Bell. So nothing new.

Returning to Bell theorem, which is clearly violated by the nature - instead of concluding that physics makes no sense, there is just an error in its assumptions - for example too simplistic representation of spin: which in fact is not a local zero/one value, but due to Noether theorem, an information delocalized in a complex way over the entire field.

First of all, physics makes sense. There is at least one interpretation, dBB theory, which avoids all the esoterical nonsense.

Then, Bell's theorem does not make assumptions about spin at all. What is -1 or +1 is the macroscopic outcome of the experiment. This outcome may have been caused by the spin, but is not the spin. And this macroscopic outcome being -1 or +1 is not a hypothesis, but a simple observable fact.

 

[Jarek Duda]

Regarding Couder's double-slit experiment with classical objects having wave-particle duality, see e.g.: http://prl.aps.org/abstract/PRL/v97/i15/e154101
Sure this picture is probably nothing new: that the corpuscle travels one path, while its pilot/theta wave travels all paths, causing interference - I am only saying that it is against what Feynman has said.
And this simple picture allows to remove lots of mysticism from QM, like retrocausality from Wheeler's experiment - http://redshift.vif.com/JournalFiles/V16NO2PDF/V16N2CRO.pdf :

Regarding Bell - we know that nature violates his inequalities, so we need to find an erroneous assumption in his way of thinking.
Let's look at a simple proof from http://www.johnboccio.com/research/quantum/notes/paper.pdf
So let us assume that there are 3 binary hidden variables describing our system - let us call them A, B, C.
We can assume that the total probability of being in one of these 8 possibilities is 1:
Pr(000)+Pr(001)+Pr(010)+Pr(011)+Pr(100)+Pr(101)+Pr(110)+Pr(111)=1
Denote by Pe as probability that given two variables have equal values:
Pe(A,B) = Pr(000) + Pr (001) + Pr(110) + Pr(111)
Pe(A,C) = Pr(000) + Pr(010) + Pr(101) + Pr(111)
Pe(B,C) = Pr(000) + Pr(100) + Pr(011) + Pr(111)
summing these 3 we get Bell inequalities:
Pe(A,B) + Pe(A,C) + Pe(B,C) = 1 + 2Pr(000) + 2 Pr(111) >= 1
Now denote ABC as outcomes of measurement in 3 directions (differing by 120 deg) - taking two identical (entangled) particles and asking about frequencies of their ABC outcomes, we can get
Pe(A,B) + Pe(A,C) + Pe(B,C) < 1 what agrees with experiment ... so something is wrong with the above line of thinking ...

The problem is that we cannot think of particles as having fixed ABC binary values describing direction of spin.
We can ask about these values independently by using measurements - which are extremely complex phenomena like Stern-Gerlach.
Such measurement doesn't just return a fixed internal variable.
Instead, in every measurement this variable is chosen at random - and this process changes the state of the system.

Here is a schematic picture of the Bell's misconception:

The squares leading to violation of Bell inequalities come e.g. from completely classical Malus law: the polarizer reduces electric field like cos(theta), light intensity is E^2: cos^2(theta).
http://www.physics.utoronto.ca/~phy225h/experiments/polarization-of-light/polar.pdf

 

[Schmelzer]

Bell's theorem is a theorem, with clearly stated assumptions. If A then B. We can, then, observe if B holds. If it does not hold, it follows that A does not hold, that means, one of the assumptions has to be wrong. But this does not mean that there is a certain "misconception" somewhere in the theorem.

What you name "misconception" is nothing but an intermediate step of the proof. The logic here is A -> "misconception" -> B. It is quite typical to present a reduced version, "misconception" -> B, as Bell's theorem, then to claim "oh, the misconception is wrong, forget about this". But the full theorem also contains the derivation A -> "misconception" of this misconception. From assumptions which have nothing at all to do with spins. This first part is the EPR argument. All we need for this is an assumption about Einstein causality - the outcome of the measurement at A does not depend on what is measured - b - at B. And, then, the EPR criterion of reality: If we can predict, with certainty, the result of an experiment without disturbing it, then something exists in reality which predefines this result. You see, spin is not even mentioned in these assumptions, and even quantum theory is not mentioned.

To identify what is wrong is quite easy. It is Einstein causality. Everything else would mean to give up common sense and to accept mysticism, to accept, in particular, correlations which are unexplainable in principle. For the simple reason that we don't want to accept the straightforward explanation that there is a superluminal causal influence.

 

[Jarek Duda]

As I have sketched a proof, the following statement is true:
(*): "Assuming the system have some 3 fixed binary descriptors (ABC), then frequencies of their occurrences fulfill
Pe(A,B) + Pe(A,C) + Pe(B,C) >= 1 (Bell) inequality"

By misconception I have meant applying it to situation with spins: assuming that the internal state uniquely defines a few applied binary values.
In contrast, this is a probabilistic translation (measurement) and it changes the system.
Beside probabilistic nature, while asking about all 3, their values would depend on the order of questioning - ABC are definitely not fixed in the initial system, what is required to apply (*).

 

[Schmelzer]

So, you have made your own version of Bell's theorem, one which consists only of the second part, "misconception" -> B. You have not criticized Bell's theorem, where this "misconception" is derived from some other assumptions. Assumptions which do not refer to spin or quantum theory at all.

That means, your considerations are quite irrelevant for a discussion of Bell's theorem.