Institutionalized Denial of the Disproof of Bell's Theorem

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

Re: Institutionalized Denial of the Disproof of Bell's Theor

gill1109 wrote:
minkwe wrote:
gill1109 wrote:Of course not. However you fill that spreadsheet of mine, you won’t violate Bell-CHSH, as a matter of simple spreadsheet arithmetic.

But we are not talking about your spreadsheet. We are talking about scenarios 1 to 4 described above. QM has not violated any of the relevant inequalities that arose in Bell's work.

If you disagree, show me an inequality from Bell's work that has been violated by QM.

Bell derived an inequality under an assumption called nowadays "local realism", also called "local hidden variables". The four values which are involved in his proof exist mathematically under a class of mathematical models called "local realistic models". According to conventional interpretations of QM they don't exist at all in reality; or they only exist in parallel worlds ("many worlds interpretation"; don't ask me what that means). Bell's point is that local realism would imply that a certain inequality would hold involving four observable correlations, each one coming from different experimental settings. QM predicts that those four correlations would not satisfy that inequality. Experiments have produced results which do not satisfy the inequality. In the experiments, one essentially performs four sub-experiments, each with a different pair of settings, and calculated four empirical correlations. Whether or not you find this remarkable depends on whether or not you think that the physical world operates according to the picture called "local realism". Clearly, Einstein did. Gerard 't Hooft does. Tim Palmer does.

Please: How do you comprehensively define the "realism" that your nominees believe in?

Gordon
Gordon Watson

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Re: Institutionalized Denial of the Disproof of Bell's Theor

Gordon Watson wrote:
gill1109 wrote:
minkwe wrote:
gill1109 wrote:Of course not. However you fill that spreadsheet of mine, you won’t violate Bell-CHSH, as a matter of simple spreadsheet arithmetic.

But we are not talking about your spreadsheet. We are talking about scenarios 1 to 4 described above. QM has not violated any of the relevant inequalities that arose in Bell's work.

If you disagree, show me an inequality from Bell's work that has been violated by QM.

Bell derived an inequality under an assumption called nowadays "local realism", also called "local hidden variables". The four values which are involved in his proof exist mathematically under a class of mathematical models called "local realistic models". According to conventional interpretations of QM they don't exist at all in reality; or they only exist in parallel worlds ("many worlds interpretation"; don't ask me what that means). Bell's point is that local realism would imply that a certain inequality would hold involving four observable correlations, each one coming from different experimental settings. QM predicts that those four correlations would not satisfy that inequality. Experiments have produced results which do not satisfy the inequality. In the experiments, one essentially performs four sub-experiments, each with a different pair of settings, and calculated four empirical correlations. Whether or not you find this remarkable depends on whether or not you think that the physical world operates according to the picture called "local realism". Clearly, Einstein did. Gerard 't Hooft does. Tim Palmer does.

Please: How do you comprehensively define the "realism" that your nominees believe in?

Gordon

I think that Einstein, Bell, ’t Hooft, and Palmer really just mean ‘determinism’. Of course there may be apparent randomness caused by chaotic systems, perhaps at a very deep level.

I’m not a physicist and not a philosopher so it is not up to me to define (meta-)physical concepts. Bell was clear how it should be expressed mathematically in specific cases. I follow his mathematical characterisation and I do mathematics.
gill1109
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Re: Institutionalized Denial of the Disproof of Bell's Theor

minkwe wrote:But do you realize that Bell derived his inequalities using just 4 values, not 8? Please take a look at the original references (see links in my previous post), how Bell did the derivation in multiple papers. If you are not convinced we can go through it here step by step. CFD is irrelevant to the discussion so far. I have not relied on any CFD so far. All the spreadsheets we are talking about are actual data from realizable real experiments.

Let us agree on this: if Bell's result is based on 4 values instead of 8, the Bell inequality is silly nonsense.
It is also obvious that we can interpret Bell's derivation as nonsense, just read the abstract of this paper: https://doi.org/10.3389/fphy.2020.00273

My point is that when the Bell inequality is interpreted as based on 8 actually measured values, it is a meaningful prediction that can be compared with actual experiments and QM predictions.
I have also pointed out before that I published 4 papers explaining this point to people who misinterpret the Bell inequality as based on only 4 values or, even worse, based on 2 actually measured values and 6 imaginary and impossible experiments(CFD) finally containing only 4 values.
I will not explain that here but if you want to know why you can read any of my papers.

Allow me to tell a parable resembling the objection that Bell's result is based on only 4 values. Let us set the following experiment. Put 6 cards in a box each with a number from 1 to 6 written on it. A person is asked to randomly extract a card without replacement 6 times. Let a_i represent the value written on the card chosen in the i-th extraction. The result we are testing in this experiment is $S=a_1+a_2+a_3+a_4+a_5+a_6$.
That's when a physicist named John Bell steps in and says, I can predict the result of the experiment to falsify if the cards were numbered as was previously agreed without cheering. He performed the following calculation
$S=1 + 2 +3 +4 +5 + 6 = (1+6)*6/2=21$
He finds that in the experiments $S\neq 21$ and concludes that there was cheating.
But then a bunch of people rise and say, obviously what Bell assumed is incorrect because the cards were not extracted in the order he naively assumed.
That is exactly the same situation with the "only four values" issue. What Bell did in his derivation is to reorder the experimental data. Of course, one could question if that is indeed possible, for instance, that is what De Baere correctly observed back in 1984 but that's another story.

Summing up, I believe that we both made our points very clear and further discussion would be pointless.
Justo

Re: Institutionalized Denial of the Disproof of Bell's Theor

gill1109 wrote:Bell derived an inequality under an assumption called nowadays "local realism", also called "local hidden variables". The four values which are involved in his proof exist mathematically under a class of mathematical models called "local realistic models". According to conventional interpretations of QM they don't exist at all in reality; or they only exist in parallel worlds ("many worlds interpretation"; don't ask me what that means). Bell's point is that local realism would imply that a certain inequality would hold involving four observable correlations, each one coming from different experimental settings. QM predicts that those four correlations would not satisfy that inequality. Experiments have produced results which do not satisfy the inequality. In the experiments, one essentially performs four sub-experiments, each with a different pair of settings, and calculated four empirical correlations. Whether or not you find this remarkable depends on whether or not you think that the physical world operates according to the picture called "local realism". Clearly, Einstein did. Gerard 't Hooft does. Tim Palmer does.

This is all gish-gallop. Show me an inequality from Bell's work that QM violates.
minkwe

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Re: Institutionalized Denial of the Disproof of Bell's Theor

Justo wrote:Let us agree on this: if Bell's result is based on 4 values instead of 8, the Bell inequality is silly nonsense.
It is also obvious that we can interpret Bell's derivation as nonsense, just read the abstract of this paper: https://doi.org/10.3389/fphy.2020.00273

My point is that when the Bell inequality is interpreted as based on 8 actually measured values

Sorry, you can't do that. You can't change what Bell did and meant, as explicitly laid out in his own equations and papers.

, it is a meaningful prediction that can be compared with actual experiments and QM predictions.

By "re-interpreting" his inequality you are changing the meanings of the terms from their original intent and therefore the derivation is no longer valid for the new meaning. This is the point.

I have also pointed out before that I published 4 papers explaining this point to people who misinterpret the Bell inequality as based on only 4 values or, even worse, based on 2 actually measured values and 6 imaginary and impossible experiments(CFD) finally containing only 4 values.

First, Bell's inequality is based on only 4 columns of data. This is not a misinterpretation it is the original intent implicit in his papers and equations. If you want to re-interpret it, don't then claim that the original intent is a "misinterpretation".

CFD is a valid interpretation of Bell's original intent I'm going to show you exactly how. It is easy to see from Bell's original paper from equation 14 where he says:

https://cds.cern.ch/record/111654/files ... 00_001.pdf

It follows that $\overrightarrow{c}$ is another unit vector:

$P(\overrightarrow{a},\overrightarrow{b}) - P(\overrightarrow{a}, \overrightarrow{c}).$

Note for the 3-term version that Bell was deriving here, he is assuming the singlet state so we have a singlet state used to calculate $P(a,b)$ and a completely distinct singlet state use to calculate $P(a,c)$.

Now you can follow the derivation through to equation 15 where all of a sudden through factorization, he has derived $P(b,c)$. This is the same as recombining columns as was done for my scenario 4 above. He took the column of data from one singlet state pair, and combined it with the column of data from an uncorrelated singlet state pair and from that he generated $P(b,c)$.

According to QM, the prediction for P(b,c) from what Bell was doing is 0, not $\sqrt{2}$.

Therefore the error is present in Bell's original paper. All discussion of locality or realism or other such nonsense is irrelevant for this mistake. Contrary to what Bell says, QM does not violate his equation 15 at all because he used the wrong QM prediction for P(b,c).

But what exactly is P(b,c) in Bell's inequality (equation 15)? P(b,c) is a counterfactual outcome because it is not a direct measurement of a singlet state at two stations. It is what would have been observed if the measurement had been performed at the same time at two stations. But as I showed in Scenario 4, the measurement can be performed and we can stitch together P(b,c) in exactly the way Bell did in his equations, just be re-using column b and column c.

Allow me to tell a parable resembling the objection that Bell's result is based on only 4 values. Let us set the following experiment. Put 6 cards in a box each with a number from 1 to 6 written on it. A person is asked to randomly extract a card without replacement 6 times. Let a_i represent the value written on the card chosen in the i-th extraction. The result we are testing in this experiment is $S=a_1+a_2+a_3+a_4+a_5+a_6$.
That's when a physicist named John Bell steps in and says, I can predict the result of the experiment to falsify if the cards were numbered as was previously agreed without cheering. He performed the following calculation
$S=1 + 2 +3 +4 +5 + 6 = (1+6)*6/2=21$
He finds that in the experiments $S\neq 21$ and concludes that there was cheating.
But then a bunch of people rise and say, obviously what Bell assumed is incorrect because the cards were not extracted in the order he naively assumed.
That is exactly the same situation with the "only four values" issue. What Bell did in his derivation is to reorder the experimental data. Of course, one could question if that is indeed possible, for instance, that is what De Baere correctly observed back in 1984 but that's another story.

I think that's a very bad analogy. But re-ordering the data is not very different from what I've discussed above. In fact, I have a whole thread discussing the re-ordering, in which I showed that it is impossible to re-order the data as required.
See viewtopic.php?f=6&t=181
minkwe

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Re: Institutionalized Denial of the Disproof of Bell's Theor

Justo wrote: What Bell did in his derivation is to reorder the experimental data.

One other thing to note is that the "hidden assumption" that the data can be re-arranged is essentially the same is the assumption that

< A B > + < A B' > + < A' B > - < A' B' > = < A B + A B' + A' B - A' B' >

Which is the point of Joy's paper. The thread I mentioned above is actually very relevant.
minkwe

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Re: Institutionalized Denial of the Disproof of Bell's Theor

Justo wrote:I will not explain that here but if you want to know why you can read any of my papers.

Okay, let take a look at one of your paper: https://arxiv.org/pdf/1911.00343.pdf. I've read it carefully. You present a derivation of the inequality by invoking CFD. You simply claim that CFD is not necessary but you don't provide another derivation that is free from CFD. In fact what you call "standard" derivation does not actually show any derivation it jumps all the steps and goes directly to the conclusion. There is a big gulf between equations 3 and 5!

You go on to claim that freedom is required to derive the inequality but you provide no mathematical evidence or arguments on precisely how freedom/independence comes into the derivation. So let me ask you this. What is the meaning of your equation 1.

$E(a_1,b_1) - E(a_1, b_2) + E(a_2, b_1) + E(a_2, b_2)$

Are all expectation values supposed to be the results of measurements on the same set particle pairs in the singlet state or do they each result from separate measurements from separate sets of particle pairs in the singlet state?

Secondly, in any Bell test, the settings used are a constant set So for all practical purposes $a_1, a_2, b_1, b_2$ are constants and don't (shouldn't) affect the derivation in any way. It is therefore obvious that "Freedom" is irrelevant and the discussion you have in section 3 about freedom is superfluous and meaningless.
minkwe

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Re: Institutionalized Denial of the Disproof of Bell's Theor

minkwe wrote:You go on to claim that freedom is required to derive the inequality but you provide no mathematical evidence or arguments on precisely how freedom/independence comes into the derivation. So let me ask you this. What is the meaning of your equation 1.

$E(a_1,b_1) - E(a_1, b_2) + E(a_2, b_1) + E(a_2, b_2)$

Are all expectation values supposed to be the results of measurements on the same set particle pairs in the singlet state or do they each result from separate measurements from separate sets of particle pairs in the singlet state?

Secondly, in any Bell test, the settings used are a constant set So for all practical purposes $a_1, a_2, b_1, b_2$ are constants and don't (shouldn't) affect the derivation in any way. It is therefore obvious that "Freedom" is irrelevant and the discussion you have in section 3 about freedom is superfluous and meaningless.

$E(a_i,b_k)$ is the mean of a long series of joint measurements by Alice and Bob with setting a_i and b_k, each made on different entangled particles generated on the same event.
Freedom means that $\rho(\lambda|a,b)=\rho(\lambda)$, if you do not assume that, the derivation cannot go through. It should be very simple and obvious.
Justo

Re: Institutionalized Denial of the Disproof of Bell's Theor

Justo wrote:
minkwe wrote:You go on to claim that freedom is required to derive the inequality but you provide no mathematical evidence or arguments on precisely how freedom/independence comes into the derivation. So let me ask you this. What is the meaning of your equation 1.

$E(a_1,b_1) - E(a_1, b_2) + E(a_2, b_1) + E(a_2, b_2)$

Are all expectation values supposed to be the results of measurements on the same set particle pairs in the singlet state or do they each result from separate measurements from separate sets of particle pairs in the singlet state?

Secondly, in any Bell test, the settings used are a constant set So for all practical purposes $a_1, a_2, b_1, b_2$ are constants and don't (shouldn't) affect the derivation in any way. It is therefore obvious that "Freedom" is irrelevant and the discussion you have in section 3 about freedom is superfluous and meaningless.

$E(a_i,b_k)$ is the mean of a long series of joint measurements by Alice and Bob with setting a_i and b_k, each made on different entangled particles generated on the same event.
Freedom means that $\rho(\lambda|a,b)=\rho(\lambda)$, if you do not assume that, the derivation cannot go through. It should be very simple and obvious.

Justo, what do you mean by "generated on the same event"? I think you mean "generated in the same way" (i.e., with the detectors set to the same settings).
I agree with you. Michel asks "Are all expectation values supposed to be the results of measurements on the same set particle pairs?" The answer is *no*. The alternative: "they each result from separate measurements from separate sets of particle pairs in the singlet state" is correct.

It is necessary to distinguish between data collected from an experiment, and mathematical calculations in a model.
Quantum mechanics is one mathematical framework. Local realism is another mathematical framework. The "meaning of" the expression $E(a_1,b_1) - E(a_1, b_2) + E(a_2, b_1) + E(a_2, b_2)$ therefore depends on the context: result of analysis of data from an experiment? result of a computation of four "expectation values" using the theoretical framework called quantum mechanics and making certain hypotheses about state and measurements on single particle pairs? result of a computation of our "expectation values" using the theoretical framework called local realism with particular choices of probability measure rho and measurement functions A = A(a, lambda) and B = B(b, lambda)?
gill1109
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Re: Institutionalized Denial of the Disproof of Bell's Theor

gill1109 wrote:Justo, what do you mean by "generated on the same event"? I think you mean "generated in the same way" (i.e., with the detectors set to the same settings).

Generated in the same way, yes but it is not enough. Alices' and Bob's joint measurements must have originated in the same event, otherwise they would not correspond to an entangled pair.

gill1109 wrote:It is necessary to distinguish between data collected from an experiment, and mathematical calculations in a model.
Quantum mechanics is one mathematical framework. Local realism is another mathematical framework.

Not quite so, if your mathematical framework does not describe what is happening in the experiment, then it is meaningless to compare your theoretical prediction with what you find in the experiment.
Both, quantum mechanics and hidden variables describe the same experiment.

minkwe and others are right to say that the Bell inequality is meaningless because they interpret it as disconnected to what is actually done in the experiments. In that I sense, I agree with them, however, I disagree with them when they say that Bell's derivation does not describe the real experiments.
Justo

Re: Institutionalized Denial of the Disproof of Bell's Theor

Justo wrote:
gill1109 wrote:Justo, what do you mean by "generated on the same event"? I think you mean "generated in the same way" (i.e., with the detectors set to the same settings).

Generated in the same way, yes but it is not enough. Alices' and Bob's joint measurements must have originated in the same event, otherwise they would not correspond to an entangled pair.

gill1109 wrote:It is necessary to distinguish between data collected from an experiment, and mathematical calculations in a model.
Quantum mechanics is one mathematical framework. Local realism is another mathematical framework.

Not quite so, if your mathematical framework does not describe what is happening in the experiment, then it is meaningless to compare your theoretical prediction with what you find in the experiment.
Both, quantum mechanics and hidden variables describe the same experiment.

minkwe and others are right to say that the Bell inequality is meaningless because they interpret it as disconnected to what is actually done in the experiments. In that I sense, I agree with them, however, I disagree with them when they say that Bell's derivation does not describe the real experiments.

Ah, when I say "generated in the same way" I mean the whole process including what goes on earlier at the source, which obviously is designed to create correlations between what is observed by Alice and what is observed at Bob.

If we put some monkeys behind typewriters they will eventually write all of Bell's works including reproducing some of his proofs of his inequalities. "The meaning of the inequality" depends on the intention of the agent who writes it down. And that depends on the context that they have in mind.

Quantum mechanics and local hidden variables can both be used in an attempt to describe a Bell-CHSH type experiment. If the experiment is done rigorously as has only been possible for the last couple of years, then quantum mechanics has been shown to describe such experiments rather well, while local realism has been shown to fail badly. On the other hand, quantum mechanics does not *explain* in a *mechanical* way what actually happened, trial by trial. It only yields statistical predictions. Local realism is an attempt to describe, trial by trial, a mechanism which could generate those same statistical results. Moreover, the mechanism should not require the instantaneous transmission of information from one place to another. Bohmian mechanics does explain trial by trial what actually happened but it requires action at a distance.

See: Very strong evidence in favor of quantum mechanics and against local hidden variables from a Bayesian analysis
Yanwu Gu, Weijun Li, Michael Evans, and Berthold-Georg Englert
Phys. Rev. A 99, 022112 – Published 13 February 2019
https://arxiv.org/abs/1808.06863

The phrase "local hidden variables" is terribly misleading. The hidden variables need not be local at all. It's just the settings which should have only local impact.
gill1109
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Re: Institutionalized Denial of the Disproof of Bell's Theor

Justo wrote:Generated in the same way, yes but it is not enough. Alices' and Bob's joint measurements must have originated in the same event, otherwise, they would not correspond to an entangled pair.

Exactly!

Justo wrote:
gill1109 wrote:It is necessary to distinguish between data collected from an experiment and mathematical calculations in a model.

Not quite so, if your mathematical framework does not describe what is happening in the experiment, then it is meaningless to compare your theoretical prediction with what you find in the experiment.Both, quantum mechanics and hidden variables describe the same experiment.

Exactly! The question I'm addressing in scenarios 1 to 4 is the question of whether the inequalities describe the same experiment.
Justo wrote:minkwe and others are right to say that the Bell inequality is meaningless because they interpret it as disconnected from what is actually done in the experiments. In that I sense, I agree with them, however, I disagree with them when they say that Bell's derivation does not describe the real experiments.

It's more subtle than that. The way the inequality is derived puts limits on how you can interpret its result. If you say the terms in the inequality are strongly objective (from the same set of particle pairs), then it is divorced from the real experiments & QM prediction and can't ever be tested. If you say the terms in the inequality are weakly objective (from different particle pairs), then you can't complete the derivation without making other hidden assumptions that are also false (eg. that the data can be rearranged).

gill1109 wrote:Ah, when I say "generated in the same way" I mean the whole process including what goes on earlier at the source, which obviously is designed to create correlations between what is observed by Alice and what is observed at Bob.

I think we agreed already that "generated in the same way" meant, particles in the singlet state. There is no way for 8 sets of particle pairs to all be in the singlet state with every other pair after recombination. Therefore the only meaning that is consistent with QM is the weakly objective one.

gill1109 wrote:If we put some monkeys behind typewriters they will eventually write all of Bell's works including reproducing some of his proofs of his inequalities.

They very very likely will never do that. There are more plausible events that will never happen. This is why the interpretation of probability as long-running averages is problematic.

gill1109 wrote: "The meaning of the inequality" depends on the intention of the agent who writes it down. And that depends on the context that they have in mind.

Nope. Sometimes agents make mistakes and they think their equations mean one thing when it means something completely different. Therefore, the meaning is what the equations say unambiguously, not what the agent says.

Quantum mechanics and local hidden variables can both be used in an attempt to describe a Bell-CHSH type experiment. If the experiment is done rigorously as has only been possible for the last couple of years, then quantum mechanics has been shown to describe such experiments rather well, while local realism has been shown to fail badly.

Not true. Local realism has been shown to describe these experiments very well. The problem is those who judge these things are part of an institution that stands to benefit from the allure of mysticism. Therefore the judgements have been unfair. Every time local realism describes the experiment, it is recast as "a loophole". But since nobody understands QM and how QM "explains" these experiments, nobody is able to characterize the QM predictions as "exploiting loopholes".

But as I explained above in scenarios 1 to 4, just a little bit of effort thinking about the actual QM prediction for the different scenarios shows that QM does not actually violate anything. The experiments don't actually violate anything. All that is happening is that we are doing a bait-and-switch tactic. Derive the inequalities for one scenario, and then calculate QM predictions for a completely different scenario.

On the other hand, quantum mechanics does not *explain* in a *mechanical* way what actually happened, trial by trial. It only yields statistical predictions.

Exactly. That's why it is difficult to tell if QM actually exploits so-called "loopholes".

Local realism is an attempt to describe, trial by trial, a mechanism which could generate those same statistical results. Moreover, the mechanism should not require the instantaneous transmission of information from one place to another. Bohmian mechanics does explain trial by trial what actually happened but it requires action at a distance.

Yes, and there are plenty of local realistic models that accomplish it without transmitting any information. I have a couple. But then as I already said, you will claim "loophole" when you see that.
minkwe

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Re: Institutionalized Denial of the Disproof of Bell's Theor

minkwe wrote:Yes, and there are plenty of local realistic models that accomplish it without transmitting any information. I have a couple. But then as I already said, you will claim "loophole" when you see that.

I don’t recall seeing your or anyone else’s local realist explanations of the four 2015 experiments and several more done after that. Your own published simulations certainly don’t do that.
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Re: Institutionalized Denial of the Disproof of Bell's Theor

minkwe wrote: All that is happening is that we are doing a bait-and-switch tactic. Derive the inequalities for one scenario, and then calculate QM predictions for a completely different scenario.

Let's go back to your scenario 1. Do you agree that with eight experimental datasets generated by a CHSH urn experiment¹, the CHSH bound is 2 in the limit as N goes to infinity?

¹) The CHSH urn model is an urn with slips of paper, each containing four numbers -1/+1. Alice randomly (coin toss) pics one of two settings a1 or a2, and Bob randomly picks one of two settings b1 or b2. A slip is then drawn from the urn, and Alice records one of the first two numbers according to her setting a1 or a2, while Bob does the same with the last two numbers according to his setting b1 or b2. The slip is then put back into the urn. We also assume there is nothing spooky going on, so everything behaves according to the standard rules of chance.
Heinera

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Re: Institutionalized Denial of the Disproof of Bell's Theor

Heinera wrote:Let's go back to your scenario 1. Do you agree that with eight experimental datasets generated by a CHSH urn experiment¹, the CHSH bound is 2 in the limit as N goes to infinity?

¹) The CHSH urn model is an urn with slips of paper, each containing four numbers -1/+1. Alice randomly (coin toss) pics one of two settings a1 or a2, and Bob randomly picks one of two settings b1 or b2. A slip is then drawn from the urn, and Alice records one of the first two numbers according to her setting a1 or a2, while Bob does the same with the last two numbers according to his setting b1 or b2. The slip is then put back into the urn. We also assume there is nothing spooky going on, so everything behaves according to the standard rules of chance.

Heinera
Scenario 1 is what real experiments do and is what QM predicts. It also should be what the Bell inequality predicts if is going to have any meaning. My claim is that when Bell's-like derivations are interpreted correctly, that is the scenario the Bell inequality predicts. What is your answer to your own question?
Justo

Re: Institutionalized Denial of the Disproof of Bell's Theor

The upper bound is 2, and the proof is trivial and can be done by brute force since there are only a finite (16) number of possibilities for different paper slips. But I would like to hear minkwe's answer.
Heinera

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Re: Institutionalized Denial of the Disproof of Bell's Theor

Heinera wrote:

The upper bound is 2, and the proof is trivial and can be done by brute force since there are only a finite (16) number of possibilities for different paper slips. But I would like to hear minkwe's answer.

I agree with you. Although the finiteness issue was ignored by Bell, it is a way to rigorously justify his result, but I suspect is not the only way to produce a rigorous result.
The claim that the Bell inequality only contains four different values is true if you look at the expression containing four terms with the same hidden variable. But that expression is obtained as a consequence of the existence of those variables and their finiteness. Bell did not assume that expression as minkwe and others claim. That would have been a very silly assumption and Bell was a very clear-minded thinker. He never mentioned things like CFD or incompatible experiments and similar blunders to justify his derivation.
Justo

Re: Institutionalized Denial of the Disproof of Bell's Theor

Justo wrote:
Heinera wrote:

The upper bound is 2, and the proof is trivial and can be done by brute force since there are only a finite (16) number of possibilities for different paper slips. But I would like to hear minkwe's answer.

I agree with you. Although the finiteness issue was ignored by Bell, it is a way to rigorously justify his result, but I suspect is not the only way to produce a rigorous result.
The claim that the Bell inequality only contains four different values is true if you look at the expression containing four terms with the same hidden variable. But that expression is obtained as a consequence of the existence of those variables and their finiteness. Bell did not assume that expression as minkwe and others claim. That would have been a very silly assumption and Bell was a very clear-minded thinker. He never mentioned things like CFD or incompatible experiments and similar blunders to justify his derivation.

I do not agree with this conclusion. To be sure, the bound on the CHSH correlator is trivially 2, as George Boole pointed out one hundred and eleven years before Bell's paper. But that bound has absolutely nothing to do with physics. It is purely a mathematically trivial fiction. Bell simply blundered very badly. He made the same blunder he ridiculed von Neumann for making.
.
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Re: Institutionalized Denial of the Disproof of Bell's Theor

Joy Christian wrote:I do not agree with this conclusion. To be sure, the bound on the CHSH correlator is trivially 2, as George Boole pointed out one hundred and eleven years before Bell's paper. But that bound has absolutely nothing to do with physics. It is purely a mathematically trivial fiction. Bell simply blundered very badly. He made the same blunder he ridiculed von Neumann for making.
.

Yadayada. Here we have the simplest physical situation possible, an urn with some paper slips in it. Before I go on I just want to know if @minkwe agrees that in this experiment the upper bound is 2.
Heinera

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Re: Institutionalized Denial of the Disproof of Bell's Theor

Heinera wrote:
Joy Christian wrote:I do not agree with this conclusion. To be sure, the bound on the CHSH correlator is trivially 2, as George Boole pointed out one hundred and eleven years before Bell's paper. But that bound has absolutely nothing to do with physics. It is purely a mathematically trivial fiction. Bell simply blundered very badly. He made the same blunder he ridiculed von Neumann for making.
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Yadayada. Here we have the simplest physical situation possible, an urn with some paper slips in it. Before I go on I just want to know if @minkwe agrees that in this experiment the upper bound is 2.

You can keep on making stupid comments. That does not change the fact that the urn model is pure fiction. It has nothing to do with how the experiments are done. Bell blundered. Period.
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Joy Christian
Research Physicist

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