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

Postby minkwe » Mon Aug 09, 2021 6:00 pm

Justo wrote:
minkwe wrote:
Justo wrote:
minkwe wrote:

If you disagree explain why. If you agree then we can proceed.

I disagree. Under the conditions you described, all we know is that



There are no reasons that justify the upper bound should be equal to 2.

Perhaps you did not understand it. For the first case which you agree to, we have 4 experiments each with no restrictions whatsoever, each measuring pairs of results and each calculating E(a,b) for their set of settings. For that experiment, you already agreed that their results will never exceed 4, which is the correct answer.

Now we move to a different scenario in which we again have 4 experimenters again with no restrictions except each is measuring just a single stream of N particles at one setting. From their results which we can place on an Nx4 spreadsheet, we can calculate E(a,b) for each of the setting pairs above. And for this scenario, their results will never exceed 2. Do you disagree with this? If you still disagree, I can show you the proof but I'm hoping it's so obvious that we don't have to waste time doing it.

Note when I say "will never exceed", I mean not even by experimental error. So Heinera's complaint is not only irrelevant it is unfounded. The results are mathematically bounded above by that value, not statistically. So it is impossible to exceed it under any circumstances. That is the meaning of upper bound.

Still I desagree that QM predics a bound of 2 under those conditions. I would agree that the hidden variables prediction is bounded by 2.


I'm not asking you about QM specifically and reference to hidden variables is actually irrelevant. Remember I said already that there are no restrictions on types of particles or how the data are generated. I'm asking generally about what the results of such an experiment can show. And I'm claiming that NOTHING (QM or not) can produce a result that exceeds 2 in that scenario. It is mathematically impossible.

If you disagree, can you give me a single row of a such a spreadsheet that exceeds 2. In other words give me 4 values corresponding to the settings that will produce a result above 2? You can use whatever method you like to obtain the 4 values, even QM. No restrictions there.
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Re: Institutionalized Denial of the Disproof of Bell's Theor

Postby Justo » Mon Aug 09, 2021 6:58 pm

minkwe wrote: I'm not asking you about QM specifically and reference to hidden variables is actually irrelevant. Remember I said already that there are no restrictions on types of particles or how the data are generated. I'm asking generally about what the results of such an experiment can show. And I'm claiming that NOTHING (QM or not) can produce a result that exceeds 2 in that scenario. It is mathematically impossible.

If you disagree, can you give me a single row of a such a spreadsheet that exceeds 2. In other words give me 4 values corresponding to the settings that will produce a result above 2? You can use whatever method you like to obtain the 4 values, even QM. No restrictions there.


I completly agree with what you say about the rows of the spreadsheet. But what does that has to do with the values actually measured in the experiment or with the Bell inequality?
Justo
 

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

Postby minkwe » Mon Aug 09, 2021 7:55 pm

Justo wrote:I completly agree with what you say about the rows of the spreadsheet. But what does that has to do with the values actually measured in the experiment or with the Bell inequality?

The results from any Bell-type experiment can be thought of as a spreadsheet with columns of numbers . So it pays to understand what relationships those numbers can obey irrespective of what process is producing the numbers. Too often we miss very important points by glossing over this part. Therefore have some patience, we are building an argument step by step, don't worry about the endpoint, just follow the argument and make sure you are understanding every step.

We started with

1. 4 Random experimenters, each measuring particle pairs with the ONLY restriction being that they generate their particle pairs in the singlet state. I asked you for the QM prediction and you said it was :

Note that for such an experiment, each researcher produces a 2xN spreadsheet from which they estimate their assigned E(a,b) term. The QM prediction for such an experiment is above.

2. Then we removed the requirement of a singlet state and asked you in general what the upper bound for such an experiment would be and you agreed that it would be

confirming that the introduction of the singlet state did not cause any violation since the upper bound is much higher than to begin with. Note like in scenario 1, each researcher also has a 2xN spreadsheet from which they estimate their assigned E(a,b) term.

3. Then we removed the requirement for each experimenter to measure pairs of particles, only requiring them to measure one stream of particles, without any restriction on how the particles are generated. In this case, each researcher produces a spreadsheet with just one column which we assemble into a single 4xN spreadsheet with columns From these columns we can select pairs to calculate the corresponding E(a,b) terms. In this case, the following expression holds and the upper bound of 2 can never be exceeded.


Do you agree?
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Re: Institutionalized Denial of the Disproof of Bell's Theor

Postby Justo » Mon Aug 09, 2021 8:35 pm

I do not understand what you are doing in case 3. Each experimenter measures a stream of N results. Then you put the values of each experimenter in a row filling the 4 colums with the values of each experimenter. Why that should give you an upper bound of 2? May be I do not understand you.
Justo
 

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

Postby minkwe » Mon Aug 09, 2021 8:39 pm

Justo wrote:I do not understand what you are doing in case 3. Each experimenter measures a stream of N results. Then you put the values of each experimenter in a row filling the 4 colums with the values of each experimenter. Why that should give you an upper bound of 2? May be I do not understand you.

No, the results of each experimenter goes in a column not a row. Do you still not understand why it must be less than two?

Given four numbers the consider the expression



since they terms can only take values , it follows that when is 0, then necessarily, and vice versa. Therefore, at extrema, one of the terms will be zero and the other will either be +2 or -2. Therefore


Here we just demonstrated at a given row on this 4xN spreadsheet can never violate 2. Considering averages it follows that:




Therefore



This upper bound applies to for any length of the spreadsheet but you can see easily that as , we have



This is exactly what we have for scenario 3. Now do you see why the upper bound is 2?
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Re: Institutionalized Denial of the Disproof of Bell's Theor

Postby Justo » Mon Aug 09, 2021 11:10 pm

minkwe wrote:
Justo wrote:I do not understand what you are doing in case 3. Each experimenter measures a stream of N results. Then you put the values of each experimenter in a row filling the 4 colums with the values of each experimenter. Why that should give you an upper bound of 2? May be I do not understand you.

No, the results of each experimenter goes in a column not a row. Do you still not understand why it must be less than two?

Given four numbers the consider the expression



since they terms can only take values , it follows that when is 0, then necessarily, and vice versa. Therefore, at extrema, one of the terms will be zero and the other will either be +2 or -2. Therefore


Here we just demonstrated at a given row on this 4xN spreadsheet can never violate 2. Considering averages it follows that:




Therefore



This upper bound applies to for any length of the spreadsheet but you can see easily that as , we have



This is exactly what we have for scenario 3. Now do you see why the upper bound is 2?

The expresion wx-wz+yx+yz is supposed to be originated from 4 different experiments and should contain 8 different numbers, not yust four.
I have published 4 papers explainig why your dervation is incorrec.
Justo
 

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

Postby Heinera » Tue Aug 10, 2021 2:02 am

I guess minkwe means that while in the original case, the analyzer receives eight datasets in order to compute the CHSH value (four experimenters, two sides for each), he now only receives four datasets, and will have to use each twice.

Needless to say this restriction makes a huge difference of what results he can achieve.
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Re: Institutionalized Denial of the Disproof of Bell's Theor

Postby Justo » Tue Aug 10, 2021 4:17 am

Heinera wrote:I guess minkwe means that while in the original case, the analyzer receives eight datasets in order to compute the CHSH value (four experimenters, two sides for each), he now only receives four datasets, and will have to use each twice.

Needless to say this restriction makes a huge difference of what results he can achieve.


Yes, the problem is that the spreadsheet minkwe is considering has only four columns. As far as I know that spreadsheet was introduced by Richard Gill in his paper "Statistics, Causality and Bell’s Theorem". The correct derivation in that paper is probabilistic and uses only two columns representing actually measured values. The columns in Gill's paper show the possible values of the functions for a given . The hidden variable lambda is the row number since each row lists the possible values considered in the row ( in Gill's paper this is implicit because he does not use hidden variables explicitly).
Unfortunately, the paper also contains a meaningless derivation that is based con counterfactual definiteness which is what minkwee is using.
Justo
 

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

Postby minkwe » Tue Aug 10, 2021 5:55 am

Justo wrote:
Heinera wrote:I guess minkwe means that while in the original case, the analyzer receives eight datasets in order to compute the CHSH value (four experimenters, two sides for each), he now only receives four datasets, and will have to use each twice.

Needless to say this restriction makes a huge difference of what results he can achieve.


Yes, the problem is that the spreadsheet minkwe is considering has only four columns. As far as I know that spreadsheet was introduced by Richard Gill in his paper "Statistics, Causality and Bell’s Theorem". The correct derivation in that paper is probabilistic and uses only two columns representing actually measured values. The columns in Gill's paper show the possible values of the functions for a given . The hidden variable lambda is the row number since each row lists the possible values considered in the row ( in Gill's paper this is implicit because he does not use hidden variables explicitly).
Unfortunately, the paper also contains a meaningless derivation that is based con counterfactual definiteness which is what minkwee is using.

Please you guys are confusing issues by bringing up irrelevant papers. Can we stick to following the argument in this thread without assuming what I mean? Just read what I mean because I must have explained this like 5 times aleady.

Justo wrote:The expresion wx-wz+yx+yz is supposed to be originated from 4 different experiments and should contain 8 different numbers, not yust four.
I have published 4 papers explainig why your dervation is incorrec.

I never said anything about w, x, y, z being an experiment. All I said was that w, x, y, z are four numbers with values . In the proof, we considered just 4 of such numbers corresponding to a row in a 4xN spreadsheet and then we considered averages from the spreadsheet. I'm astounded that you consider the obvious result I present controversial.

BTW Richard Gill did not invent 4xN spreadsheets of numbers
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Re: Institutionalized Denial of the Disproof of Bell's Theor

Postby Justo » Tue Aug 10, 2021 6:47 am

minkwe wrote: I never said anything about w, x, y, z being an experiment. All I said was that w, x, y, z are four numbers with values . In the proof, we considered just 4 of such numbers corresponding to a row in a 4xN spreadsheet and then we considered averages from the spreadsheet. I'm astounded that you consider the obvious result I present controversial.


You did not understand me. I do not consider your result controversial. I consider it an obvious triviality.

minkwe wrote:
BTW Richard Gill did not invent 4xN spreadsheets of number


Good to know, thank you.
Justo
 

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

Postby minkwe » Tue Aug 10, 2021 6:52 am

Justo wrote:
minkwe wrote: I never said anything about w, x, y, z being an experiment. All I said was that w, x, y, z are four numbers with values . In the proof, we considered just 4 of such numbers corresponding to a row in a 4xN spreadsheet and then we considered averages from the spreadsheet. I'm astounded that you consider the obvious result I present controversial.


You did not understand me. I do not consider your result controversial. I consider it an obvious triviality.

minkwe wrote:
BTW Richard Gill did not invent 4xN spreadsheets of number


Good to know, thank you.

So why did you disagree with point 3 then? In fact, you argued that you have papers proving that my proof is incorrect. I still don't have a clear answer that you agree with scenario 3 in my presentation?
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Re: Institutionalized Denial of the Disproof of Bell's Theor

Postby JUsto » Tue Aug 10, 2021 7:19 am

minkwe wrote:So why did you disagree with point 3 then? In fact, you argued that you have papers proving that my proof is incorrect. I still don't have a clear answer that you agree with scenario 3 in my presentation?


Because point 3 reads

minkwe wrote:3. Then we removed the requirement for each experimenter to measure pairs of particles, only requiring them to measure one stream of particles, without any restriction on how the particles are generated. In this case, each researcher produces a spreadsheet with just one column which we assemble into a single 4xN spreadsheet with columns From these columns we can select pairs to calculate the corresponding E(a,b) terms. In this case, the following expression holds and the upper bound of 2 can never be exceeded.


Do you agree?


It is not clear how you choose those values. For instance, If you pick randomly two columns(in the same row) from four rows you do not necessarily end up with an expression like wx-wz+yx+yz containing only four different values.

What I explain in my papers is that the derivation you did to obtain the bound 2 has nothing to do with the Bell inequality.
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Re: Institutionalized Denial of the Disproof of Bell's Theor

Postby minkwe » Tue Aug 10, 2021 7:39 am

JUsto wrote:
minkwe wrote:So why did you disagree with point 3 then? In fact, you argued that you have papers proving that my proof is incorrect. I still don't have a clear answer that you agree with scenario 3 in my presentation?


Because point 3 reads

minkwe wrote:3. Then we removed the requirement for each experimenter to measure pairs of particles, only requiring them to measure one stream of particles, without any restriction on how the particles are generated. In this case, each researcher produces a spreadsheet with just one column which we assemble into a single 4xN spreadsheet with columns From these columns we can select pairs to calculate the corresponding E(a,b) terms. In this case, the following expression holds and the upper bound of 2 can never be exceeded.


Do you agree?


It is not clear how you choose those values. For instance, If you pick randomly two columns(in the same row) from four rows you do not necessarily end up with an expression like wx-wz+yx+yz containing only four different values.

What I explain in my papers is that the derivation you did to obtain the bound 2 has nothing to do with the Bell inequality.

We have 4 columns labelled and we select pairs of columns to calculate the corresponding E(a,b) terms. I don't see what is unclear about it You calculate from the and columns, from the and columns, etc. Also, I never said anything about selecting columns randomly. I think you are not reading what I'm writing because you seem to be responding to some other preconceived notion rather than what I'm actually saying. This is not the first time you do this.

Now that you understand what I meant about scenario 3, do you agree with it?
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Re: Institutionalized Denial of the Disproof of Bell's Theor

Postby Justo » Tue Aug 10, 2021 7:59 am

minkwe wrote:We have 4 columns labelled and we select pairs of columns to calculate the corresponding E(a,b) terms. I don't see what is unclear about it You calculate from the and columns, from the and columns, etc. Also, I never said anything about selecting columns randomly. I think you are not reading what I'm writing because you seem to be responding to some other preconceived notion rather than what I'm actually saying. This is not the first time you do this.

Now that you understand what I meant about scenario 3, do you agree with it?


I do not understand what you are doing. However, whatever it is that you're doing it is obvious that it has nothing to do with the Bell inequality.
The Bell inequality predicts the result of a physical experiment where two experimenters measure the spin of entangled particles. The experiment is repeated many times to obtain enough data that allows the calculations of the expressions E(a,b) for four different combinations of settings.

Based on a previous experience, I think that it is pointless pursuing this discussion any further, so I consider it closed.
Justo
 

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

Postby minkwe » Tue Aug 10, 2021 2:47 pm

Justo wrote:
minkwe wrote:We have 4 columns labelled and we select pairs of columns to calculate the corresponding E(a,b) terms. I don't see what is unclear about it You calculate from the and columns, from the and columns, etc. Also, I never said anything about selecting columns randomly. I think you are not reading what I'm writing because you seem to be responding to some other preconceived notion rather than what I'm actually saying. This is not the first time you do this.

Now that you understand what I meant about scenario 3, do you agree with it?


I do not understand what you are doing. However, whatever it is that you're doing it is obvious that it has nothing to do with the Bell inequality.
The Bell inequality predicts the result of a physical experiment where two experimenters measure the spin of entangled particles. The experiment is repeated many times to obtain enough data that allows the calculations of the expressions E(a,b) for four different combinations of settings.

Based on a previous experience, I think that it is pointless pursuing this discussion any further, so I consider it closed.

This is a very interesting turn of events. For some strange reason, despite the fact that I presented mathematical proof of the point, you can't bring yourself to agree that scenario 3 of my argument is absolutely correct. Anyone else reading this should start asking themselves why that is (https://arxiv.org/pdf/1911.00343.pdf, https://arxiv.org/pdf/2012.10238.pdf). Now you are not even interested in hearing about scenario 4, and the rest of the argument.

You claim that what I'm doing does not have anything to do with Bell's inequality. But you aren't even interested in hearing what I'm doing so you can't possibly know that. Secondly, anyone with elementary arithmetic skills can look at the proof I presented in scenario 3 and confirm that it is essentially the proof of the CHSH inequality.
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Re: Institutionalized Denial of the Disproof of Bell's Theor

Postby Justo » Tue Aug 10, 2021 3:21 pm

minkwe wrote:This is a very interesting turn of events. For some strange reason, despite the fact that I presented mathematical proof of the point, you can't bring yourself to agree that scenario 3 of my argument is absolutely correct. Anyone else reading this should start asking themselves why that is (https://arxiv.org/pdf/1911.00343.pdf, https://arxiv.org/pdf/2012.10238.pdf). Now you are not even interested in hearing about scenario 4, and the rest of the argument.

You claim that what I'm doing does not have anything to do with Bell's inequality. But you aren't even interested in hearing what I'm doing so you can't possibly know that. Secondly, anyone with elementary arithmetic skills can look at the proof I presented in scenario 3 and confirm that it is essentially the proof of the CHSH inequality.


I am sorry minkwe, is nothing personal. It is only that we seem to be talking different languages. You can tell me about scenario 4, I am interested in knowing it.
But don't ask me to agree with you in point 3 because I do not understand it.
Justo
 

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

Postby minkwe » Tue Aug 10, 2021 8:43 pm

Justo wrote:
minkwe wrote:This is a very interesting turn of events. For some strange reason, despite the fact that I presented mathematical proof of the point, you can't bring yourself to agree that scenario 3 of my argument is absolutely correct. Anyone else reading this should start asking themselves why that is (https://arxiv.org/pdf/1911.00343.pdf, https://arxiv.org/pdf/2012.10238.pdf). Now you are not even interested in hearing about scenario 4, and the rest of the argument.

You claim that what I'm doing does not have anything to do with Bell's inequality. But you aren't even interested in hearing what I'm doing so you can't possibly know that. Secondly, anyone with elementary arithmetic skills can look at the proof I presented in scenario 3 and confirm that it is essentially the proof of the CHSH inequality.


I am sorry minkwe, is nothing personal. It is only that we seem to be talking different languages. You can tell me about scenario 4, I am interested in knowing it.
But don't ask me to agree with you in point 3 because I do not understand it.

If you don't understand point 3 then you won't understand anything else, unfortunately. If you want to follow the argument, you have to take the time to read it and ask clarifying questions about what is not clear to you.
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Re: Institutionalized Denial of the Disproof of Bell's Theor

Postby gill1109 » Tue Aug 10, 2021 9:06 pm

minkwe wrote:
Justo wrote:
minkwe wrote:This is a very interesting turn of events. For some strange reason, despite the fact that I presented mathematical proof of the point, you can't bring yourself to agree that scenario 3 of my argument is absolutely correct. Anyone else reading this should start asking themselves why that is (https://arxiv.org/pdf/1911.00343.pdf, https://arxiv.org/pdf/2012.10238.pdf). Now you are not even interested in hearing about scenario 4, and the rest of the argument.

You claim that what I'm doing does not have anything to do with Bell's inequality. But you aren't even interested in hearing what I'm doing so you can't possibly know that. Secondly, anyone with elementary arithmetic skills can look at the proof I presented in scenario 3 and confirm that it is essentially the proof of the CHSH inequality.


I am sorry minkwe, is nothing personal. It is only that we seem to be talking different languages. You can tell me about scenario 4, I am interested in knowing it.
But don't ask me to agree with you in point 3 because I do not understand it.

If you don't understand point 3 then you won't understand anything else, unfortunately. If you want to follow the argument, you have to take the time to read it and ask clarifying questions about what is not clear to you.

In Michel’s Scenario 3, my Nx4 spreadsheet (the one which I invented) is filled with the numbers +/-1. It doesn’t matter who puts in those numbers, or how they do it. The CHSH inequality will hold when you compute four correlations from it in the way described above. Now we imagine that two of the columns represent the outcomes Alice would have seen under each of her two measurement options, the other two represent the outcomes Bob’s would have seen. Under a local hidden variables model of the experiment, such values exist (mathematically, in the model). “Counterfactual definiteness” is a philosophical position, which says that they exist, actually. I guess that depends on what you mean by “exist”. If I believed in local hidden variables then I would believe they exist, I think. That’s a counterfactual statement since I don’t *believe* in local hidden variables. As a mathematician I keep an open mind.

The interesting thing I did with my spreadsheet was imagining that each row of the spreadsheet is assigned to just one of the four experimental conditions, completely at random. Then four correlations are computed each on a different subset of rows, each using a different pair of the columns. I showed that CHSH would hold with probability exponentially close to 1, if N is large.
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Re: Institutionalized Denial of the Disproof of Bell's Theor

Postby Justo » Wed Aug 11, 2021 12:52 am

minkwe wrote:If you don't understand point 3 then you won't understand anything else, unfortunately. If you want to follow the argument, you have to take the time to read it and ask clarifying questions about what is not clear to you.

Ok, I read again your description and you choose from each row four values to obtain wx-wz+yx+yz. If that is what you do, then I understand it.
Justo
 

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

Postby Justo » Wed Aug 11, 2021 1:26 am

gill1109 wrote:The interesting thing I did with my spreadsheet was imagining that each row of the spreadsheet is assigned to just one of the four experimental conditions, completely at random. Then four correlations are computed each on a different subset of rows, each using a different pair of the columns. I showed that CHSH would hold with probability exponentially close to 1, if N is large.

Certainly it is interesting, you presented another derivation of the Bell inequqlity. It would be good if you can write another paper generalizing it for arbitrary probability of chosing two columns. In that way your derivation would be completely ganeral.
Justo
 

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