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Steven Parrott wrote: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.

Stephen Parrott wrote: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). )

Joy Christian wrote:
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.

Joy Christian wrote:***

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

Joy Christian wrote:
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.

***

thray wrote: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.

Parrott wrote: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.

Parrott wrote: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.

Parrott wrote: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).

Parrott wrote: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.

Graft posting more nonsense wrote:

Joy Christian wrote: 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.

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

Graft posting more nonsense wrote:

Joy Christian wrote: 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 wrote:
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.

minkwe wrote:
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.

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

Joy Christian wrote:
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.

more nonsense Parrott wrote:

Joy Christian wrote: 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.

Parrott wrote: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.

Parrott wrote: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.

Joy Christian wrote:
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.

more nonsense on RW that Parrott wrote:

HR wrote: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 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.

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”.

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.

nonsense Parrot wrote: 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.

then Jay wrote: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

then we have more nonsense Parrott wrote: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.

Stephen Parrott wrote:
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.

Joy Christian wrote:
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.

FrediFizzx wrote: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 wrote:

FrediFizzx wrote: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.

Heinera wrote:

FrediFizzx wrote: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.