The simplest illustration of Bell's error

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

Re: The simplest illustration of Bell's error

Postby gill1109 » Sat Aug 28, 2021 9:44 pm

minkwe wrote:
Justo wrote:That you claim that his hidden variable theory does not imply the inequality he derived.That has nothing to with QM and bringing in QM into the discussion is unnessesary. It only distracts the main point.
In fact, if you want to shoot down Bell's theorem you only need a simulation that violates his inequality. It is not nessesary for your model to reproduce the QM predictions.

Are you serious? You don't care if Bell used the wrong QM prediction to claim violation of the inequality? The claim in the first post of this thread is that QM does not violate the inequality contrary to Bell's claims. Why don't you engage with that argument?

Justo and Heinera are completely right. Bell explained the error in Michel’s reasoning in half a page in his very short paper “Locality in Quantum Mechanics: Reply to Critics” (Chapter 8 in his book). I have tried to explain it many times. It’s the last objection dealt with in that paper.
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Re: The simplest illustration of Bell's error

Postby Mikko » Sun Aug 29, 2021 12:22 am

minkwe wrote:In his paper, Bell is dealing with correlations between pairs of particles formed in the singlet state and moving in opposite directions towards measurement stations and those correlations are specified as the average of the paired product of outcomes observed at those stations .


More precisely, Bell is considering what a theory of a particular kind may predict about such an experiment. The experiment will determine or or but it is not yet decided which. Therefore three predictions are needed, one of which may then be tested. Bell derives an inequality about the three predictions.
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Re: The simplest illustration of Bell's error

Postby gill1109 » Sun Aug 29, 2021 12:31 am

FrediFizzx wrote:Here is a link to that paper by Bell.

https://journals.aps.org/ppf/abstract/1 ... zika.1.195
.

And here’s the link to his “Reply to critics”. https://cds.cern.ch/record/980330/files/CM-P00061609.pdf

Mikko wrote:
minkwe wrote:In his paper, Bell is dealing with correlations between pairs of particles formed in the singlet state and moving in opposite directions towards measurement stations and those correlations are specified as the average of the paired product of outcomes observed at those stations .


More precisely, Bell is considering what a theory of a particular kind may predict about such an experiment. The experiment will determine or or but it is not yet decided which. Therefore three predictions are needed, one of which may then be tested. Bell derives an inequality about the three predictions.

Mikko is right.

There are two frameworks for predicting correlations observed between events occuring at distant locations. Quantum mechanics; and classical physics. Bell shows how the latter framework implies certain relationships between correlations observed in different experiments. Tsirelson showed how the first framework implies strictly weaker restrictions on the correlations. Experiments tell us which framework describes reality better.
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Re: The simplest illustration of Bell's error

Postby Justo » Sun Aug 29, 2021 1:02 am

Mikko wrote:
minkwe wrote:In his paper, Bell is dealing with correlations between pairs of particles formed in the singlet state and moving in opposite directions towards measurement stations and those correlations are specified as the average of the paired product of outcomes observed at those stations .


More precisely, Bell is considering what a theory of a particular kind may predict about such an experiment. The experiment will determine or or but it is not yet decided which. Therefore three predictions are needed, one of which may then be tested. Bell derives an inequality about the three predictions.

If the experiment only determines one of the three terms in the expresion, what's the use of making an experiment to test it?
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Re: The simplest illustration of Bell's error

Postby Justo » Sun Aug 29, 2021 1:28 am

P(a,b), P(a,c) and P(b,c) are results of three different experiments. In fact three different series of experimnts. That is what QM predicts and what real experiments can falsify.
If you claim that Bell did not derive that, then Bell derived a useless result. To reinterpret what QM predicts for Bell's wrong derivation is too wierd for me. What's the point of doing that? It is wrong period.
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Re: The simplest illustration of Bell's error

Postby gill1109 » Sun Aug 29, 2021 5:40 am

Justo wrote:P(a,b), P(a,c) and P(b,c) are results of three different experiments. In fact three different series of experimnts. That is what QM predicts and what real experiments can falsify.
If you claim that Bell did not derive that, then Bell derived a useless result. To reinterpret what QM predicts for Bell's wrong derivation is too wierd for me. What's the point of doing that? It is wrong period.

By the way, Bell (1964) also assumes that P(a, b) = -1 if a = b. Performing a real experiment with enough trials would quickly prove that that assumption is false! Bell understood that very well, and at the end of his paper he shows that it is enough that this should only hold approximately. But this means that he knows that at least four experiments have to be done, each consisting of many trials. Naturally, he adopted CHSH enthusiastically, as soon as it came along.
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Re: The simplest illustration of Bell's error

Postby Justo » Sun Aug 29, 2021 6:27 am

gill1109 wrote:By the way, Bell (1964) also assumes that P(a, b) = -1 if a = b. Performing a real experiment with enough trials would quickly prove that that assumption is false! Bell understood that very well, and at the end of his paper he shows that it is enough that this should only hold approximately. But this means that he knows that at least four experiments have to be done, each consisting of many trials. Naturally, he adopted CHSH enthusiastically, as soon as it came along.


From a logical standpoint, his mathematical derivation rests on the assumption that P(a,a)=-1. According to CHSH this assumption is problematic which is why they derived the CHSH inequality.
For me, menkwe's claim is an odd way to look at Bell's presumed errors. Why do you want to interpret what QM predicts for a wrong experiment? It is enough to know that is wrong. Then show that it is wrong.
The Bell inequality is about the prediction of a physical experiment. I thought we all agreed in what that experiment is. In the case of the original inequality, it involves three different series of experiments. In the case of the CHSH, it is 4 different series.
There are two different theories making predictions for the same experiment. One theory is HV, the other is QM.
menkwe's argument seems to be that Bell predicted another experiment, not the one he claimed he did. Then, what should be discussed is: why did he(Bell) derive the result of a different experiment? To bring in QM prediction for the alleged wrong experiment is absolutely superfluous.
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Re: The simplest illustration of Bell's error

Postby Mikko » Sun Aug 29, 2021 6:28 am

Justo wrote:
Mikko wrote:
minkwe wrote:In his paper, Bell is dealing with correlations between pairs of particles formed in the singlet state and moving in opposite directions towards measurement stations and those correlations are specified as the average of the paired product of outcomes observed at those stations .


More precisely, Bell is considering what a theory of a particular kind may predict about such an experiment. The experiment will determine or or but it is not yet decided which. Therefore three predictions are needed, one of which may then be tested. Bell derives an inequality about the three predictions.

If the experiment only determines one of the three terms in the expresion, what's the use of making an experiment to test it?


For the purposes of Bell's original article no experiment is needed. But one might want to know whether the quantum mechanical prediction is correct in the real world.
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Re: The simplest illustration of Bell's error

Postby Justo » Sun Aug 29, 2021 7:33 am

Mikko wrote:
Justo wrote:
Mikko wrote:
minkwe wrote:In his paper, Bell is dealing with correlations between pairs of particles formed in the singlet state and moving in opposite directions towards measurement stations and those correlations are specified as the average of the paired product of outcomes observed at those stations .


More precisely, Bell is considering what a theory of a particular kind may predict about such an experiment. The experiment will determine or or but it is not yet decided which. Therefore three predictions are needed, one of which may then be tested. Bell derives an inequality about the three predictions.

If the experiment only determines one of the three terms in the expresion, what's the use of making an experiment to test it?


For the purposes of Bell's original article no experiment is needed. But one might want to know whether the quantum mechanical prediction is correct in the real world.

Then it would be useless all the same because QM does not make counterfactual predictions and under that interpretation the result can't be meaningfully compared with QM predictions.
I would be, at least, a very obscure prediction. It is the reason why Stapp's program of counterfactuals is not accepted by most physicists even those that are Bell-believers like Shymony.
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Re: The simplest illustration of Bell's error

Postby gill1109 » Sun Aug 29, 2021 10:06 am

Justo wrote:Then it would be useless all the same because QM does not make counterfactual predictions and under that interpretation the result can't be meaningfully compared with QM predictions. It would be, at least, a very obscure prediction. It is the reason why Stapp's program of counterfactuals is not accepted by most physicists even those that are Bell-believers like Shimony.

I just read some of Stapp’s papers on counterfactuals. Well … I tried to. To be honest, I found them incomprehensible. No wonder he gave counterfactuals a bad name in some quarters! I like Boris Tsirelson’s presentation https://en.citizendium.org/wiki/Entanglement_(physics)
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Re: The simplest illustration of Bell's error

Postby local » Sun Aug 29, 2021 10:16 am

gill1109 wrote:To be honest, I found them incomprehensible.

Thank you for being honest about your intellectual shortcomings. That's on you, not Stapp.
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Re: The simplest illustration of Bell's error

Postby minkwe » Sun Aug 29, 2021 10:39 am

I'm amazed that a whole bunch of learned people can't follow a simple argument. Richard, Justo, Mikko etc please answer one question. And don't go off on a tangent talking about CHSH and Bell's other papers. Please focus on just Bell's 1964 paper and answer this one question:

In Equation 14a, Bell has P(a,b) and P(a,c). There is no P(b,c) anywhere in that expression. Then all of a sudden, P(b,c) appears in equation 15.

Where did P(b,c) come from?

The answer is very easy. Just look at the arithmetic between eq 14 and eq 15. The only thing in doubt is whether any of you are intellectually honest enough to admit it.
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Re: The simplest illustration of Bell's error

Postby minkwe » Sun Aug 29, 2021 10:47 am

gill1109 wrote:And here’s the link to his “Reply to critics”. https://cds.cern.ch/record/980330/files/CM-P00061609.pdf

Then you don't understand it. Did you read the first post in this thread. The reply you point to is Bell's reply to Pena, Cetto and Brody which has nothing to do with this thread. There Bell simply states that his intention is to deal with actual experimental results. What has that got to this thread. Please read the first post again and answer the question I just asked.
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Re: The simplest illustration of Bell's error

Postby minkwe » Sun Aug 29, 2021 11:08 am

The claims I'm making in this thread are very simple.

Bell's original inequality (equation 15) as derived is:


Where is not the result of a separate measurement, but a "franken-correlation" re-assembled from the two other measurements. This is obvious from Bell's arithmetic in the derivation. He fails to recognize that according to QM and therefore by writing the final result as



He deceives himself into thinking the three terms correspond to three different experiments. He makes a hidden false assumption that . Therefore, he uses the QM predictions for three separate measurements to claim that QM violates an inequality that contains only two actual measurements plus a "franken-measurement". However, if he used the correct QM prediction, QM would not have violated the inequality.
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Re: The simplest illustration of Bell's error

Postby Justo » Sun Aug 29, 2021 12:20 pm

minkwe wrote:The claims I'm making in this thread are very simple.

Bell's original inequality (equation 15) as derived is:


Where is not the result of a separate measurement, but a "franken-correlation" re-assembled from the two other measurements. This is obvious from Bell's arithmetic in the derivation. He fails to recognize that according to QM and therefore by writing the final result as



He deceives himself into thinking the three terms correspond to three different experiments. He makes a hidden false assumption that . Therefore, he uses the QM predictions for three separate measurements to claim that QM violates an inequality that contains only two actual measurements plus a "franken-measurement". However, if he used the correct QM prediction, QM would not have violated the inequality.


The reasoning is the following:

STEP 1:
According to HV eq (14) is the mathematical expression for the mean result of a large number of experiments measured with settings a, and b, i.e., P(a,b).
Equation (14) is a generic expression meaning that settings (a,b) may be replaced with other symbols representing other experimental settings and the expression is supposed to be still valid.

STEP 2:
Forget real experiments an let us do a little math. He writes mathematical expression for |P(a,b)-P(a,c)| and after elementary and valid mathematical operations he finds that

Observation:He did not "literally" materialized a third actual experiment from only two. He did that with a mathematical expression that finally can be interpreted as representing three actual experiments if the assumption in STEP 1 is correct.

STEP 3:
Applying STEP 1 he predicts the result of three different series of experiments performed with three different settings (a,b),(a,c), and (b,c) must be constrained by the inequality (15)

CONCLUSION
If you do not agree with equation (15) and what it represents you must reject either the interpretation given in STEP 1 or mathematics elementary laws.
Which one do you reject?
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Re: The simplest illustration of Bell's error

Postby minkwe » Sun Aug 29, 2021 12:34 pm

Justo wrote:The reasoning is the following:

STEP 1:
According to HV eq (14) is the mathematical expression for the mean result of a large number of experiments measured with settings a, and b, i.e., P(a,b).
Equation (14) is a generic expression meaning that settings (a,b) may be replaced with other symbols representing other experimental settings and the expression is supposed to be still valid.

STEP 2:
Forget real experiments an let us do a little math. He writes mathematical expression for |P(a,b)-P(a,c)| and after elementary and valid mathematical operations he finds that

Please, you refuse to answer a simple question. Did Bell or did he not generate P(b,c) through what you call "elementary and valid mathematical operations " on ?? Did those mathematical operations generate P(b,c) from P(a,b)-P(a,c) or not?

Until you answer this question, the rest of what you write is unimportant.

justo wrote:

Observation:He did not "literally" materialized a third actual experiment from only two. He did that with a mathematical expression that finally can be interpreted as representing three actual experiments if the assumption in STEP 1 is correct.

STEP 3:
Applying STEP 1 he predicts the result of three different series of experiments performed with three different settings (a,b),(a,c), and (b,c) must be constrained by the inequality (15)

CONCLUSION
If you do not agree with equation (15) and what it represents you must reject either the interpretation given in STEP 1 or mathematics elementary laws.
Which one do you reject?
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Re: The simplest illustration of Bell's error

Postby FrediFizzx » Sun Aug 29, 2021 12:37 pm

@Justo Yep, eq. (14) is bogus as I previously pointed out. It is only valid for half of the events, +- and -+.
.
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Re: The simplest illustration of Bell's error

Postby Justo » Sun Aug 29, 2021 12:45 pm

FrediFizzx wrote:@Justo Yep, eq. (14) is bogus as I previously pointed out. It is only valid for half of the events, +- and -+.
.

Excellent! Then at least we agree on what we disagree. That is progress.
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Re: The simplest illustration of Bell's error

Postby Justo » Sun Aug 29, 2021 12:54 pm

minkwe wrote:Please, you refuse to answer a simple question. Did Bell or did he not generate P(b,c) through what you call "elementary and valid mathematical operations " on ?? Did those mathematical operations generate P(b,c) from P(a,b)-P(a,c) or not?

Until you answer this question, the rest of what you write is unimportant.


I did not refuse to answer it. Of course, he does. That is what STEP 2 says.
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Re: The simplest illustration of Bell's error

Postby minkwe » Sun Aug 29, 2021 1:19 pm

Justo wrote:
minkwe wrote:Please, you refuse to answer a simple question. Did Bell or did he not generate P(b,c) through what you call "elementary and valid mathematical operations " on ?? Did those mathematical operations generate P(b,c) from P(a,b)-P(a,c) or not?

Until you answer this question, the rest of what you write is unimportant.


I did not refuse to answer it. Of course, he does. That is what STEP 2 says.


So you agree that according to STEP 2, P(b,c) is constructed from part of P(a,b) and Part of P(a,c)?

Then what makes you think P(b,c) represents a singlet state at all?
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