Parrott's mathematical nonsense

[FrediFizzx]

From Retraction Watch,

The expectation of a random variable X will be denoted E(X). Bell’s argument starts with a simple algebraic manipulation showing that for any lambda,

A(a, lambda) B(b lambda) + A(a lambda) B(b’, lambda) + A(a’, lambda) B(b, lambda) – A(a’, lambda) B(b’, lambda)

is between -2 and +2. Everyone agrees that this is correct, including you and Dr. Christian. Taking the expectation of this expression and using the fact that the expectation of a sum of random variables is the sum of the expectations, i.e., E(X + Y) = E(X) + E(Y), shows that

E(A(a)B(b)) + E(A(a)B(b’)) + E(A(a’) B(b)) – E(A(a’)B(b’)) (1)

is between -2 and 2. This is a valid operation because all of the random variables are defined on the same probability space. The bounds of -2 and 2 for (1) is the conclusion of Bell’s theorem.

That is all fine and dandy but that is not what quantum mechanics and the experiments do when they say they have violated Bell-CHSH. They use independent expectation terms where the bound is |4|.

Of course, if (1) is between -2 and 2, it is also between -4 and 4 ! But the bounds of -4 and 4 are not “tight” bounds, in physics jargon. (In mathematics, we say that the bounds of -4 and 4 are not attained.) Christian’s “simple proof” would be correct if he also showed that the bounds of -4 and 4 are attained. But that cannot be proved under the hypothesis that all the random variables are defined on the same probability space. (Actually, the -4,4 bounds can’t even be attained in quantum mechanics; the tight bounds under that assumption are
+- 2 sqrt(2). )

Now I have never ever heard the terminology "loose" and "tight" bounds before. Talk about making up jargon...

Anyways, it is easy to prove that the bound is |4| for CHSH when the terms are independent like that for QM and experiments by simple mathematical inspection.

+ 1 +1 +1 -(-1) = 4
+(-1) +(-1) + (-1) - (+1) = -4

But wait a minute... guess what? It is impossible for QM and the experiments to do the CHSH string of expectations when they are dependent. So what was Bell doing comparing apples to oranges? It is a bunch of mathematical nonsense and you would think a mathematician should know better than to fall for it. Bell-CHSH has never ever been violated by QM nor the experiments. It is just mathematically impossible.
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[Joy Christian]

***

Good points, Fred. I just posted the following reply to Jay on Retraction Watch:

Hi Jay, your post above is disappointing. You are being led astray by the followers of Bell, as they always tend to do. They tend to obfuscate the physical issue by introducing completely unnecessary concepts from “statistics”, “probability”, “tight bounds”, “loose bounds”, etc. None of this is necessary to understand the basic error made by Bell, which I have exposed quite clearly in physical terms, without getting bogged down in unnecessary jargon borrowed from outside physics. I hope we are not trying to become mathematical acrobats but trying to understand physics. And physics shows quite clearly that Bell made a serious blunder.

***

[FrediFizzx]

***

Good points, Fred. I just posted the following reply to Jay on Retraction Watch:

Hi Jay, your post above is disappointing. You are being led astray by the followers of Bell, as they always tend to do. They tend to obfuscate the physical issue by introducing completely unnecessary concepts from “statistics”, “probability”, “tight bounds”, “loose bounds”, etc. None of this is necessary to understand the basic error made by Bell, which I have exposed quite clearly in physical terms, without getting bogged down in unnecessary jargon borrowed from outside physics. I hope we are not trying to become mathematical acrobats but trying to understand physics. And physics shows quite clearly that Bell made a serious blunder.

***

Yes, it is all quite simple so I don't know why Jay is struggling with it so much.

[thray]

Not expecting my post to make it out of RW moderation, my reply to Jay:

Jay,

"Hidden variables and local realism are excluded in the quantum limit but are permitted in the classical limit? Now I am just thinking out loud again."

That militates against your own research, of resolving the boundary between quantum and classical domains, by microscale time dilation.

There's no profit in playing Richard Gill's game, unless or until he specifies his measure space. Of course, that would disable his argument, no matter which physical space he chooses.

Bell's theorem assumes non-locality, and Bell-Aspect proves what it assumes. Yes, it is as simple as that.

[thray]

<blockquote cite="Richard Gill">
<cite>Richard Gill</cite>
<p>Jay, you are stuck because you are still missing *probability*. </p>
<p>You are still not making use of the law of large numbers, and you are still not making use of the definition of expectation value. Without them, you stay stuck.</p>
<p>Let those sample sizes converge to infinity, apply the law of large numbers (probability theory), use the definition of “local hidden variables” and the definition of expectation value (probability theory).</p>
<p>Result: the expectation value E(a, b) equals the integral over lamdba of A(a, lambda) B(b, lambda) rho(lambda) d lambda.</p>
<p>Now (only now!) add three such integrals and subtract the fourth. </p>
<p>The rest should be plain sailing.</p>
</blockquote>

Richard, everyone already understands this.

What you are missing is a measure space, without which expectation values have no meaning, and the law of large numbers is a mathematical artifact. You are proposing boundaries, without boundary conditions, requisite to any analytical framework.

Time to retire this straw man.

[FrediFizzx]

Not expecting my post to make it out of RW moderation, my reply to Jay:

Jay,

"Hidden variables and local realism are excluded in the quantum limit but are permitted in the classical limit? Now I am just thinking out loud again."

That militates against your own research, of resolving the boundary between quantum and classical domains, by microscale time dilation.

There's no profit in playing Richard Gill's game, unless or until he specifies his measure space. Of course, that would disable his argument, no matter which physical space he chooses.

Bell's theorem assumes non-locality, and Bell-Aspect proves what it assumes. Yes, it is as simple as that.

I didn't see your posts show up at RW so it looks like the moderators have decided to help suppress the truth with Joy being the only one being able to post. But here is some more nonsense from Parrott over there in response to Joy,

I think we are potentially very close to agreement ! If I interpret the above correctly,
Dr. Christian agrees that Bell’s theorem is mathematically correct but somehow doesn’t apply to actual experiments.

His objection seems to be that in actual experiments which approximate mathematical expectations like E(A1, B2) by observed averages, the various expectations (such as E(A1, B2) and E(A2, B2) ) need to be approximated in *different* experiments because the world is actually governed by quantum mechanics, which does not allow simultaneous measurement of A1, and A2. This is true.

What you are saying is NOT completely true. First of all, Bell's theory is just a word statement based on a false interpretation of the inequalities. There is no proof that it is actually correct so I am sure that Joy doesn't agree that it is mathematically correct. Now... Bell's inequalities are mathematically correct and I am sure we all agree on that. Second; you make the automatic assumption that the world is governed by quantum mechanics in the case of the EPR-Bohm scenario. That is not scientific. Joy's local realistic model for EPR-Bohm shows that that assumption is not necessarily true. The fact of the matter is that the EPR-Bohm scenario itself does not allow simultaneous measurement of A1, A2, etc. whether it be quantum or classical because you only have one particle pair at a time. The particle's properties are changed by the measurement process. Though granted people claim that as a quantum mechanics effect.

Because of that the *experimental approximation* to a CHSH sum like

E(A1, B1) + E(A1, B2) + E(A2, B1) – E(A2, B2)

indeed could be larger than Bell’s bound of 2, even though the sum as just written (which involves mathematical expectations, not experimental approximations to them) cannot exceed 2.

That is baloney. That string of expectations is NOT what QM and the experiments use in their evaluations. They use,

E(A1, B1) + E(A2, B2) + E(A3, B3) – E(A4, B4)

Or something very similar to that. It is easy to see from that that the bound is |4| mathematically.

However, by taking sufficiently large sample sizes, the probability that the experimental approximations for the above sum exceed 2 + epsilon (for given positive epsilon) can be made arbitrarily small. (Richard Gill has already emphasized this.) If Dr. Christian disagrees with this, I hope he will say so clearly, because it would further the discussion.

If that is the only objection to the observed experimental violation of Bell’s inequality, then it boils down to the question of whether the sample sizes were large enough to make the probability of violation small enough. That would require detailed analyses of the experiments. Normally, the experimenters would furnish such analyses (often in the form of statement that the results obtained lie a stated number of standard deviations from the result predicted by a local realistic model).

More baloney because of the use of the wrong expectation string of terms.

If there is some other objection to Bell’s conclusion or to claims that experiments violate it (so that a local realistic model is ruled out, up to some small probability that the violation is a statistical fluke), then it has not been expressed clearly enough to penetrate this thick skull.

It is very simple. It is mathematically impossible for ANYTHING to violate Bell's inequalities. I am not sure how you can call yourself a mathematician if you can't get that simple fact through your "thick skull". Neither QM nor any of the experiments have ever "violated" Bell's inequalities. And they have never ever violated an inequality that is appropriate for them.
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[FrediFizzx]

Now it is Graft posting more of his nonsense at Retraction Watch.

Specifically, since the events like A(a1) and A(a2) cannot possibly exist simultaneously in any possible physical world — classical or quantum — Bell’s argument is based on absurdity.

The fact that the different measurement arrangements cannot be run simultaneously is irrelevant and does not refute the validity of CH/CHSH. I show that in section 2.3 of https://arxiv.org/abs/1404.4329.

It totally refutes the validity of Bell-CHSH because that means they HAVE TO USE a DIFFERENT inequality to say they "violate" Bell-CHSH and the simple fact is that neither QM nor the experiments have ever violated any of the Bell inequalities. Apples and oranges. I wouldn't recommend that anyone bother to read Graft's junk physics paper at the link above.
'

[Joy Christian]

Now it is Graft posting more of his nonsense at Retraction Watch.

Specifically, since the events like A(a1) and A(a2) cannot possibly exist simultaneously in any possible physical world — classical or quantum — Bell’s argument is based on absurdity.

The fact that the different measurement arrangements cannot be run simultaneously is irrelevant and does not refute the validity of CH/CHSH. I show that in section 2.3 of https://arxiv.org/abs/1404.4329.

It totally refutes the validity of Bell-CHSH because that means they HAVE TO USE a DIFFERENT inequality to say they "violate" Bell-CHSH and the simple fact is that neither QM nor the experiments have ever violated any of the Bell inequalities. Apples and oranges. I wouldn't recommend that anyone bother to read Graft's junk physics paper at the link above.
'

I have just posted the following reply to Graft's comment at Retraction Watch:

The argument presented in the paper by Graft is both misleading and misguided. It amounts to using a completely different inequality — one with the bounds of -4 to +4 — when comparing actual experimental results, thus abandoning the bounds of -2 to +2 derived theoretically, and then claiming that Bell-CHSH inequality with the bounds of -2 to +2 has been “violated”, when in fact no such thing has happened, or shown to happen.

***

[Joy Christian]

***
In this forum we have of course repeatedly debunked the kind of nonsense Gill, Graft, and Parrott are promoting over at Retraction watch. Here is an old remark by Michel Fodje (written on 17 March 2014) that clearly exposes the insanity behind the silly misconceptions of Gill, Graft, and Parrott: viewtopic.php?f=21&t=34#p948

To appreciate one particularly troubling insanity in modern physics, consider the so called "experimental evidence" that realism is "untenable".

We set out assuming that a single particle pair has simultaneous values for 4 observables A, B, C, D. And this assumption is supposed to be the realism assumption. We then derive a relationship between those observables in the form of inequalities.

But unfortunately we are only able to measure two of those observables since we only have 2 particles in a pair. But maybe if we measure A, B on our initial particles, and C, D on two different particles then we can use those outcomes. It turns out, the outcomes we obtain in such a manner violate the inequalities we obtained by making our realism assumption. So we conclude with straight faces that therefore A, B, C, D do not simultaneously exist and therefore the realism assumption is false.

If this was not so insane, it would be funny. What we have in fact proven is the obvious and trivial result that the A, B, C, D that we measured are not all simultaneous values from a single particle pair. Duh, we measured them from different particle pairs, why would any sane scientist expect properties measured on different particle pairs to all belong to the same pair in first place? Maybe if we use statistics we can try to obscure the fact that we measured the wrong outcomes and therefore cannot legitimately use them in our original inequality.

***

[FrediFizzx]

I have just posted the following reply to Graft's comment at Retraction Watch:

The argument presented in the paper by Graft is both misleading and misguided. It amounts to using a completely different inequality — one with the bounds of -4 to +4 — when comparing actual experimental results, thus abandoning the bounds of -2 to +2 derived theoretically, and then claiming that Bell-CHSH inequality with the bounds of -2 to +2 has been “violated”, when in fact no such thing has happened, or shown to happen.

I posted a similar comment that the moderators did not let thru. Looks like you are on your own over there but we will try to support you from here.

[FrediFizzx]

More Parrott nonsense from RW

I completely disagree with your reading of my comments. What I am saying is that the claim by Bell and his followers that the bounds of -2 and +2 on the CHSH sum of expectation values cannot be exceeded by any local-realistic theory is simply wrong. In my comments I have explained precisely why their claim is wrong. Specifically, since the events like A(a1) and A(a2) cannot possibly exist simultaneously in any possible physical world — classical or quantum — Bell’s argument is based on absurdity. Consequently the correct local-realistic bounds on the CHSH sum of expectation values are not -2 to +2 as erroneously claimed by Bell and his followers, but are in fact -4 to +4 (or -2sqrt(2) to +2sqrt(2) if we do not ignore the geometry and topology of the physical space we live in). Is that now clear enough?

It’s not clear to me. The *hypotheses* of Bell’s theorem assume a mathematical model based on a probability space from which a “hidden variable” lambda is drawn. The response functions like your A(a1), A(a2), etc. are assumed to be random variables defined on that probability space. (They are not “events” as defined in probability theory, but I assume that your use of this incorrect terminology was simply a slip. I assume you meant “random variables instead of “events.) Any collection of random variables on a probability space can be simultaneously measured.

Bell also assumed an EPR-Bohm scenario so they are also "events". And in an EPR-Bohm scenario, they can't be measured simultaneously. Bell mistake number one.

That’s rather long-winded, so let me summarize: You say “since the events like A(a1) and A(a2) cannot possibly exist simultaneously in any possible physical world … , Bell’s argument is based on absurdity”. But Bell’s argument does *not* claim that A(a1) and A(a2) can be simultaneously observed *in the real world* (as opposed to in the hypothetical world of the mathematical model). The question is whether the hypothetical model can reproduce the correlations that we see in the real world. The conclusion of Bell’s theorem is that it cannot.

But since Bell's hypothetical mathematical model is flawed from the get go, why should anyone care if it produces the correlations of QM? What good is a hypothetical model if it doesn't fit the real world? Fortunately we do now have a local-realistic model that does produce the predictions of QM.

That said, I certainly can imagine a real world in which A(a1) and A(a2) could be simultaneously observed. That is the “classical” world that I believed in before learning about Bell’s theorem. I can only scratch my head at your statement that “events like A(a1) and A(a2) cannot possibly exist simultaneously in any possible physical world” . I cannot imagine what could lead to such a belief.

You forget that Bell's model was based on EPR-Bohm. Typical Bell fanatic misdirection. Of course in a macroscopic non-EPR-Bohm scenario those events could be simultaneously observed but that is not what we are analyzing here.
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[Joy Christian]

***
I also replied to Stephen Parrott similarly on Retraction Watch:

A(a1) and A(a2) are possible events in spacetime. They are clicks of the detectors located in spacetime. They cannot possibly exist simultaneously in any possible physical world, because a1 and a2 are mutually exclusive directions in the physical 3-space. Since (as you say) you do not understand this, it is unlikely that you will see the flaw in Bell’s logic I have exposed.

***

[FrediFizzx]

Parrott is back on RW after he said he was quitting the discussion. Typical for Bell fanatics.

This is becoming increaslingly silly. The expression A(a)*[B(b) + B(b’)] is not a probability.

I agree. At the referenced link, Christian says (and has said many times in many places)

“But since b and b’ are two mutually exclusive measurement directions that Bob could have chosen corresponding to two physically incompatible experiments, no event such as A(a)*[ B(b) + B(b’) ] can possibly exist in any possible physical world.”

I am going to try to explain why this is wrong. Since this is the *premise* for most of his arguments against Bell’s theorem, those arguments are also wrong.

First of all, I am going to ignore his incorrect terminology which calls A(a)*[B(b) + B(b’)] an “event”. It is a random variable, not an “event” (defined in all probability texts as a subset of a sample space). What he means (I assume) is that in the usual quantum-mechanical application, B(b) and B(b’) cannot be observed simultaneously. No one disputes this. But it is irrelevant to Bell’s theorem.

It is completely relevant. The only reason you say it is irrelevant is that you have no argument otherwise.

It is easy to imagine “possible physical worlds” in which anything observable can be observed simultaneously with anything else. Bell’s theoem *assumes* such a “classical” world and derives certain consequences such as the CHSH inequality. If the consequences like CHSH are violated in *our* physical world, that shows that our physical world cannot be the “local realistic” one assumed by Bell’s theorem. Someone asked what is the content of Bell’s theorem, and that is its content.

Again, you keep forgetting the context of Bell's model -- the EPR-Bohm scenario. Nothing else physically matters. Since nothing has ever violated Bell's model, the content of Bell's theory is junk.

Here is a physical example. To understand why it is relevant to Bell’s context, it is important to understand that Bell’s theorem has nothing to do with spin, quantum mechanics, or our “real world”.

That is such a stupid statement I just am scratching my head that you actually believe it. If it has nothing to do with those things, then why does Bell's model follow an EPR-Bohm scenario?

My car has two odometers (so-called “trip odometers”) to observed two different distances traveled. For example, one distance might be the distance since the last gasoline fillups, and the other the distance traveled on a given day. However, this twin trip odometer is constructed so that these two distances *cannot be observed at the same time*. A switch toggles between them.

Although in the world of my car, those two distances cannot be observed simultaneously, it is perfectly possible to imagine a car with two trip odometers which *could* be observed simultaneously.

In the world of my car, if I am driving along, and I look at at noon to see how far I have gone today, I will get one number. If at the same time I look to see how far I have gone on the current tank of gas, I will get a probably different number. There is no possible way that I can
get these two numbers at the same time. But there is nothing physically impossible about a car which *could* deliver the two numbers at the same time.

Talk about irrelevant!!! Your example is complete and pure nonsense relating to Bell's junk physics theory.
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[FrediFizzx]

Some more nonsense on RW from Parrott,

Jay,
Think of the probability space as an urn containing slips of paper. The slips are the “hidden variable”. On each slip is written something like “If Alice chooses *a*, return +1, if a’, return -1; if Bob chooses *b*, return -1, if b’, return +1. In all there are 2^4 = 16 possible slips.
The proportion of each is its probability.

Stephen, let me stop right here, to make sure I am understanding this, and please forgive me insofar as I do like to start with concrete data and then work back to the abstract conclusions. I see eight slips which are:
a -> +1 (if Alice Chooses a then return +1)
a -> -1 (etc. for the rest)
a’ -> +1
a’ -> -1
b -> +1
b -> -1
b’ -> +1
b’ -> -1
But you say there are 2^4 =16. What eight slips am I overlooking? Thanks, Jay

Jay is already on to the nonsense but is not sure.

One slip has four “binary” numbers on it. An example is:

If a, then 1, if a’ then -1, if b then -1, if b’ then -1.

If we agree that the order is always as just given, we can simplify the notation by writing

(1, -1, -1, -1)

instead of the above. So there are 2x2x2x2 = 16 slips, namely (+1, +1, +1, +1),
(+1, +1, +1, -1), etc. Your first slip (if a then 1) is not a “slip” according the the definition just given.

_______________________________________________________________________

The historical “hidden variable” terminology seems to me unfortunate. A much cleaner approach is to speak of a typical “lambda” (value of hidden variable or outcome in a probability space) as a four-tuple

lambda := (i, j k, m) with each entry either +1 or -1 .

This describes the set of outcomes very concretely as a 16-element set. The seemingly more complicated integral formulation is easily seen to be essentially equivalent. The probability
of the above typical outcome can be denoted

p( i, j, k, m)

instead of the more complicated integral notation of the traditional “hidden variable” approach.

The probability that Alice chooses to measure *a* and gets outcome -1 while Bob measures
*b’ * and gets +1 is then

sum_{j, k} p(-1, j , k, +1) (equation (1) )

which is a generalization of a so-called “marginal” probability.

If we assume that Alice cannot simultaneously observe *a* and *a’ * and Bob cannot observe
*b* and *b’ * , then physically we are given only four such “marginal” probabilities instead of the full p(i, j, k, m). But (and this is the important point), we *cannot assume* that the given “marginals” are true marginals obtained as in equation (1). If they always *can* be so obtained, we say that there is a “(local) realistic” model. This is equivalent to the historical “hidden variable” terminology.

Because there is no reason to assume that such given “marginals” are obtained as the true
marginals of equation (1), it is better to use a different name for them such as “pseudo marginals”. The rules of quantum mechanics furnish four such pseudo marginals. Can they always be obtained as the true marginals of equation (1), for some p( i , j , k , m) ?

It turns out that they *cannot* always be so obtained. It turns out that a *necessary* condition that they be so obtained is that they satisfy the CHSH inequalities. This is one way to state Bell’s theorem, in my view a much cleaner way than the language of “hidden variables”.

One reason that it is cleaner is that one can present a Bell denier with four quantum pseudo marginals (presented as 2×2 matrices) which do not satisfy CHSH and challenge him to produce a p(i , j, k, m) which reproduces them as true marginals. This is a a very concrete problem which could probably be solved by computer, and if he can’t do it one has to question his claims.

A computer solution requires solving a linear system for the 16 probabilities p( i , j , k, m) , which of course any computer algebra system can do. What makes it slightly tricky is that one needs a solution with all p( i , j , k , m) non-negative. I don’t know if there are packages that can always do this. One way to definitively solve the present Bell “controversy” (which of course is not a real controversy among the vast majority of physicists) would be to explicitly produce p( i , j , k , m) for four quantum marginals which do not satisfy CHSH. (See p. 164 of Asher Peres’ book on quantum mechanics for such marginals expressed in different language.) That would also make history. No journal would dare reject it.

If a computer expert like you could do that, there could be no argument that Bell’s theorem is incorrect. Moreover, although obtaining p( i , j , k, m ) would require programming, readers would not have to rely on its correctness because the solution could easily be checked directly with standard computer algebra systems such as Maple, or even by hand.

The above is so stupid that I have only one thing to say. It is impossible for anything to violate Bell-CHSH including QM.
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[Joy Christian]

***
Stephen Parrott is coming around to understanding the problem. I have just posted the following on Retraction Watch:

If you assume from the start that it is self-contradictory for Alice to access both A(a) and A(a’) simultaneously, as Christian does and you seem to, then you will not be able to prove Bell’s theorem. That it is not possible according to quantum mechanics does not make it self-contradictory.

And my reply to him:

I am pleased to note that at least one proponent of Bell’s theorem has accepted the fact that if it is self-contradictory for Alice to access both A(a) and A(a’) simultaneously, then it is not possible to prove Bell’s theorem.

But contrary to the claim by Stephen Parrott, quantum mechanics has nothing to do with the fact that Alice cannot access A(a) and A(a’) simultaneously. A(a) and A(a’) are only counterfactually possible measurement results, along two mutually exclusive detector directions, a and a’. Since a and a’ are classical, macroscopic directions, no experimenter has the ability to align his or her detector along both a and a’ simultaneously. Therefore, regardless of any physical theory — classical or quantum — it is self-contradictory for Alice to access both A(a) and A(a’) simultaneously. Consequently, as acknowledged by Stephen Parrott, it is not possible to prove Bell’s theorem.

***

[thray]

Awaiting "moderation" on RW:

Stephen Parrott wrote: "...'local realistic theory' has a precise mathematical meaning as the urn model, which is easily seen to be mathematically equivalent to any of the historical formulations."

Patently false.

Here's what Karl Hess (Einstein was Right!) has to say about it:

"Bell uses for his elements of reality the picture of things that can be drawn out of an urn. Of course, Bell knew that photons have both particle-like and wavelike properties, as do all the other elementary particles or 'entities'. His assumptions show, however, that both his lambda and the measurement equipment do not have general dynamic properties. The measurement equipment is explicitly described by settings a, b, c ... that are randomly chosen but otherwise static, and general time dependencies contained in lambda are excluded, because of the assumption that lambda and the settings are independent mathematical variables. Space-time data, which are also elements of reality, go beyond the mere existence of particles (or wavicles, the entities of quantum mechanics mechanics that also exhibit wavelike properties) and provide us with the relations of these particles to each other and to an objective world. It is very important to realize that the description of the *dynamics* of the particles requires these additional man-made elements of reality." (p. 101)

Clearly, no static (probabilistic) model can capture all the elements of reality. And so much for the claim of Richard Gill and his followers that "lambda can be anything".

[FrediFizzx]

It is quite mind boggling how these Bell fanatics get stuck on really stupid stuff. If they think Bell was right then they should be able to prove that Jay's eq. (6) is true. But they can't because they already proved it has to be bounded by |2|.

[Heinera]

It is quite mind boggling how these Bell fanatics get stuck on really stupid stuff. If they think Bell was right then they should be able to prove that Jay's eq. (6) is true. But they can't because they already proved it has to be bounded by |2|.

It is quite mind boggling how these anit-Bell fanatics get stuck on really stupid stuff. If they think Bell was wrong then they should be able to provide 16 frequencies for the urn model so that the model produces a value for the CHSH-expression outside the bounds -2, +2. Only 16 numbers between 0 and 1; any idiot should be able to find those if they exist. Then we can compute the correlations by brute force.

[FrediFizzx]

It is quite mind boggling how these Bell fanatics get stuck on really stupid stuff. If they think Bell was right then they should be able to prove that Jay's eq. (6) is true. But they can't because they already proved it has to be bounded by |2|.

It is quite mind boggling how these anit-Bell fanatics get stuck on really stupid stuff. If they think Bell was wrong then they should be able to provide 16 frequencies for the urn model so that the model produces a value for the CHSH-expression outside the bounds -2, +2. Only 16 numbers between 0 and 1; any idiot should be able to find those if they exist. Then we can compute the correlations by brute force.

Prove that Jay's eq. (6) here could possibly be true. But you can't since it has already been mathematically proven to be bounded by |2|. Pretty silly if you want to continue to believe that Bell was right. Bell's junk theory has absolutely nothing to do with local-realism.

[thray]

It is quite mind boggling how these Bell fanatics get stuck on really stupid stuff. If they think Bell was right then they should be able to prove that Jay's eq. (6) is true. But they can't because they already proved it has to be bounded by |2|.

It is quite mind boggling how these anit-Bell fanatics get stuck on really stupid stuff. If they think Bell was wrong then they should be able to provide 16 frequencies for the urn model so that the model produces a value for the CHSH-expression outside the bounds -2, +2. Only 16 numbers between 0 and 1; any idiot should be able to find those if they exist. Then we can compute the correlations by brute force.

And you don't think this model is static? Funny what you think 'really stupid stuff' is. Could it just be stuff thought up by really stupid people?