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 Joy Christian » Sat Aug 07, 2021 5:42 pm

Justo wrote:
minkwe wrote:Justo,
Can you please demonstrate the violation of the CHSH inequality by QM? Please write it out in full mathematically so we can see. And then explain what that expression means in QM.

I can't write out for you a detailed calculation. It is a standard textbook calculation. It gives , assuming a and b are unit vectors. Normally, the calculation in papers discussing the Bell inequalities is not included since it is an elementary unpolemical result. Using the appropriate orientations for a_1, a_2, b_1, and b_2 after elementary trigonometry we find


I suppose Joy would agree with me on this.

Justo, the result you cite is indeed elementary, unpolemical, and standard. I agree with it. Such a standard, two-step derivation can be found, for example, in my 2007 paper:

https://arxiv.org/abs/quant-ph/0703179

But you have not understood minkwe's question. He is well aware of the above standard derivation. He is asking something different. I will let him explain to you what he is asking.
.
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Re: Institutionalized Denial of the Disproof of Bell's Theor

Postby minkwe » Sat Aug 07, 2021 10:01 pm

Justo wrote:
minkwe wrote:Justo,
Can you please demonstrate the violation of the CHSH inequality by QM? Please write it out in full mathematically so we can see. And then explain what that expression means in QM.

I can't write out for you a detailed calculation. It is a standard textbook calculation. It gives , assuming a and b are unit vectors. Normally, the calculation in papers discussing the Bell inequalities is not included since it is an elementary unpolemical result. Using the appropriate orientations for a_1, a_2, b_1, and b_2 after elementary trigonometry we find


I suppose Joy would agree with me on this.

This makes no sense to me. What are the subscripts in the second expression? Where did they come from all of a sudden? Please try again, no shut-cuts, write it out in full. Do you mean






When you are done, also explain what T is supposed to mean in QM.

Is that what you mean? If not what exactly do you mean.
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Re: Institutionalized Denial of the Disproof of Bell's Theor

Postby Justo » Sat Aug 07, 2021 11:07 pm

minkwe wrote:
Justo wrote:
minkwe wrote:Justo,
Can you please demonstrate the violation of the CHSH inequality by QM? Please write it out in full mathematically so we can see. And then explain what that expression means in QM.

I can't write out for you a detailed calculation. It is a standard textbook calculation. It gives , assuming a and b are unit vectors. Normally, the calculation in papers discussing the Bell inequalities is not included since it is an elementary unpolemical result. Using the appropriate orientations for a_1, a_2, b_1, and b_2 after elementary trigonometry we find


I suppose Joy would agree with me on this.

This makes no sense to me. What are the subscripts in the second expression? Where did they come from all of a sudden? Please try again, no shut-cuts, write it out in full. Do you mean






When you are done, also explain what T is supposed to mean in QM.

Is that what you mean? If not what exactly do you mean.


I am sorry, but Idon't see your point. It does not make sense to me.
Justo
 

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

Postby gill1109 » Sun Aug 08, 2021 1:13 am

Justo wrote:
minkwe wrote:Justo,
Can you please demonstrate the violation of the CHSH inequality by QM? Please write it out in full mathematically so we can see. And then explain what that expression means in QM.

I can't write out for you a detailed calculation. It is a standard textbook calculation. It gives , assuming a and b are unit vectors. Normally, the calculation in papers discussing the Bell inequalities is not included since it is an elementary unpolemical result. Using the appropriate orientations for a_1, a_2, b_1, and b_2 after elementary trigonometry we find


I suppose Joy would agree with me on this.

Justo, I suppose you mean

(Note the “\cdot”s). And of course this depends on the choice of the four vectors (two a’, two b’s) and the choice of state vector “psi”.

What it “means” in this context is obvious. It is the sum of three correlations minus a fourth, according to a certain mathematical model in quantum mechanics. Each of the correlations would be measured separately using measurements on pairs of particles. All the particle pairs would be created in the same way, but the four ways they are measured would be different.
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Re: Institutionalized Denial of the Disproof of Bell's Theor

Postby Justo » Sun Aug 08, 2021 2:27 am

gill1109 wrote:
Justo wrote:
minkwe wrote:Justo,
Can you please demonstrate the violation of the CHSH inequality by QM? Please write it out in full mathematically so we can see. And then explain what that expression means in QM.

I can't write out for you a detailed calculation. It is a standard textbook calculation. It gives , assuming a and b are unit vectors. Normally, the calculation in papers discussing the Bell inequalities is not included since it is an elementary unpolemical result. Using the appropriate orientations for a_1, a_2, b_1, and b_2 after elementary trigonometry we find


I suppose Joy would agree with me on this.

Justo, I suppose you mean

(Note the “\cdot”s). And of course this depends on the choice of the four vectors (two a’, two b’s) and the choice of state vector “psi”.

What it “means” in this context is obvious. It is the sum of three correlations minus a fourth, according to a certain mathematical model in quantum mechanics. Each of the correlations would be measured separately using measurements on pairs of particles. All the particle pairs would be created in the same way, but the four ways they are measured would be different.

That's right. That is why I don't see the point to it. If we're discussing Bell theorem all this is well known and unpolemic
Justo
 

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

Postby minkwe » Sun Aug 08, 2021 8:44 am

Justo wrote:I am sorry, but Idon't see your point. It does not make sense to me.




I asked you to show how you calculate to demonstrate violation, and you glossed over a few very crucial details. I'm not trying to test your trigonometry skills.
Please, explain how you go from this

to

.

Which is the implication of your answer to my question. Whether it is polemic or not is irrelevant. Please don't skip any steps, and don't take anything for granted. Humour me for a second, I know that you don't see the point because of your response to Joy. You will soon, assuming you want to see the point.
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Re: Institutionalized Denial of the Disproof of Bell's Theor

Postby Justo » Sun Aug 08, 2021 12:54 pm

minkwe wrote:
Justo wrote:I am sorry, but Idon't see your point. It does not make sense to me.




I asked you to show how you calculate to demonstrate violation, and you glossed over a few very crucial details. I'm not trying to test your trigonometry skills.
Please, explain how you go from this

to

.

Which is the implication of your answer to my question. Whether it is polemic or not is irrelevant. Please don't skip any steps, and don't take anything for granted. Humour me for a second, I know that you don't see the point because of your response to Joy. You will soon, assuming you want to see the point.

Richard Gill already answered it for me. So I cannot add anything else. Also, Joy already told me what he thinks is wrong with my argument. If you want to tell me what is wrong with it just say it. I repeat once again, I can't add anything else.
Justo
 

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

Postby minkwe » Sun Aug 08, 2021 1:18 pm

Justo wrote:
minkwe wrote:
Justo wrote:I am sorry, but Idon't see your point. It does not make sense to me.




I asked you to show how you calculate to demonstrate violation, and you glossed over a few very crucial details. I'm not trying to test your trigonometry skills.
Please, explain how you go from this

to

.

Which is the implication of your answer to my question. Whether it is polemic or not is irrelevant. Please don't skip any steps, and don't take anything for granted. Humour me for a second, I know that you don't see the point because of your response to Joy. You will soon, assuming you want to see the point.

Richard Gill already answered it for me. So I cannot add anything else. Also, Joy already told me what he thinks is wrong with my argument. If you want to tell me what is wrong with it just say it. I repeat once again, I can't add anything else.

I guess you don't really want to know then? You can also quote the answer from Gill you believe answers the question. The best way to learn something is to find out yourself because when someone else tells you, it gets filtered through your existing misconceptions and biases but when your intuition tells you, you get it. I'm willing to help you see it but you have to be willing to go through the process with me.
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Re: Institutionalized Denial of the Disproof of Bell's Theor

Postby minkwe » Sun Aug 08, 2021 1:34 pm

gill1109 wrote:What it “means” in this context is obvious. It is the sum of three correlations minus a fourth, according to a certain mathematical model in quantum mechanics. Each of the correlations would be measured separately using measurements on pairs of particles. All the particle pairs would be created in the same way, but the four ways they are measured would be different.

Since you decided to answer for Justo, let's see if you continue the process for him (not holding my breath though). Please answer the following questions, without any gish galloping:

You say above that "All the particle pairs would be created in the same way". Why? is independent of any particles it only depends on the direction vectors of the instruments so why is it important to you that "All the particle pairs would be created in the same way"?

In other words, say we have 4 random researchers scattered around the world each measuring just one of the terms above in their lab. How similar will their particles have to be to each other before they can confirm the relationship , and for combined their results to produce:
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Re: Institutionalized Denial of the Disproof of Bell's Theor

Postby Justo » Sun Aug 08, 2021 2:49 pm

minkwe wrote:
gill1109 wrote:What it “means” in this context is obvious. It is the sum of three correlations minus a fourth, according to a certain mathematical model in quantum mechanics. Each of the correlations would be measured separately using measurements on pairs of particles. All the particle pairs would be created in the same way, but the four ways they are measured would be different.

Since you decided to answer for Justo, let's see if you continue the process for him (not holding my breath though). Please answer the following questions, without any gish galloping:

You say above that "All the particle pairs would be created in the same way". Why? is independent of any particles it only depends on the direction vectors of the instruments so why is it important to you that "All the particle pairs would be created in the same way"?

Since he answered instead of me before, I answer this one: the result is not independent of the particles. It also depends on their state. They are supposed to be in the singlet state; otherwise, the prediction is not valid.

minkwe wrote:In other words, say we have 4 random researchers scattered around the world each measuring just one of the terms above in their lab. How similar will their particles have to be to each other before they can confirm the relationship , and for combined their results to produce:

Tthe same answer as before. All particles should be prepared in the singlet state.
Justo
 

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

Postby minkwe » Sun Aug 08, 2021 9:20 pm

Justo wrote:Since he answered instead of me before, I answer this one: the result is not independent of the particles. It also depends on their state. They are supposed to be in the singlet state; otherwise, the prediction is not valid.

Are you sure that Is that all? Gill already knew that we were talking about particles in the singlet state when he made the statement, and Bell's theorem is dealing with particles in the singlet state. So perhaps he has something else in mind when he says "All the particle pairs would be created in the same way". Please be absolutely sure that is the only thing that is meant because it would be a pity if you have to backtrack to amend this point later.
Justo wrote:
minkwe wrote:In other words, say we have 4 random researchers scattered around the world each measuring just one of the terms above in their lab. How similar will their particles have to be to each other before they can confirm the relationship , and for combined their results to produce:

Tthe same answer as before. All particles should be prepared in the singlet state.

So let us be clear then, if the 4 random researchers scattered around the world each prepare their sets of particles in the singlet state, you would expect their results to obey the relationship:


Again you believe "All the particle pairs would be created in the same way" means ONLY that the particles are they are prepared in the singlet state.

Now let us generalize a little bit. Let us keep everything just agreed above for the singlet state and instead let us relax the singlet state requirement and say all that the researchers have to do is prepare their particles anyway they like. They can use the singlet state if they like, but they can also use any other type of state. In fact, we don't even restrict the type of particle they are to use. All they have to do is perform a similar experiment with any set of pairs of particles (no restrictions) and record the correlations. Once they bring their results together, the maximum value they can observe for the following expression is 4.


Note that experimentally, Were is the outcome for measurement and is the outcome of measurement
If you disagree explain why. If you agree then we can proceed. Note, the only thing I've removed is Gill's condition that "all the particles be prepared in exactly the same way", or as you say I've removed the condition that the particles are prepared in a singlet state.
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Re: Institutionalized Denial of the Disproof of Bell's Theor

Postby Justo » Mon Aug 09, 2021 5:07 am

minkwe wrote:
Justo wrote:Since he answered instead of me before, I answer this one: the result is not independent of the particles. It also depends on their state. They are supposed to be in the singlet state; otherwise, the prediction is not valid.

Are you sure that Is that all? Gill already knew that we were talking about particles in the singlet state when he made the statement, and Bell's theorem is dealing with particles in the singlet state. So perhaps he has something else in mind when he says "All the particle pairs would be created in the same way". Please be absolutely sure that is the only thing that is meant because it would be a pity if you have to backtrack to amend this point later.


Is this the only thing that I meant. I can't talk for Gill.

minkwe wrote:
Justo wrote:
minkwe wrote:In other words, say we have 4 random researchers scattered around the world each measuring just one of the terms above in their lab. How similar will their particles have to be to each other before they can confirm the relationship , and for combined their results to produce:

Tthe same answer as before. All particles should be prepared in the singlet state.

So let us be clear then, if the 4 random researchers scattered around the world each prepare their sets of particles in the singlet state, you would expect their results to obey the relationship:


Again you believe "All the particle pairs would be created in the same way" means ONLY that the particles are they are prepared in the singlet state.

Now let us generalize a little bit. Let us keep everything just agreed above for the singlet state and instead let us relax the singlet state requirement and say all that the researchers have to do is prepare their particles anyway they like. They can use the singlet state if they like, but they can also use any other type of state. In fact, we don't even restrict the type of particle they are to use. All they have to do is perform a similar experiment with any set of pairs of particles (no restrictions) and record the correlations. Once they bring their results together, the maximum value they can observe for the following expression is 4.


Note that experimentally, Were is the outcome for measurement and is the outcome of measurement
If you disagree explain why. If you agree then we can proceed. Note, the only thing I've removed is Gill's condition that "all the particles be prepared in exactly the same way", or as you say I've removed the condition that the particles are prepared in a singlet state.

I agree.
Justo
 

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

Postby minkwe » Mon Aug 09, 2021 7:02 am

Justo wrote:
minkwe wrote:Now let us generalize a little bit. Let us keep everything just agreed above for the singlet state and instead let us relax the singlet state requirement and say all that the researchers have to do is prepare their particles anyway they like. They can use the singlet state if they like, but they can also use any other type of state. In fact, we don't even restrict the type of particle they are to use. All they have to do is perform a similar experiment with any set of pairs of particles (no restrictions) and record the correlations. Once they bring their results together, the maximum value they can observe for the following expression is 4.


Note that experimentally, Were is the outcome for measurement and is the outcome of measurement
If you disagree explain why. If you agree then we can proceed. Note, the only thing I've removed is Gill's condition that "all the particles be prepared in exactly the same way", or as you say I've removed the condition that the particles are prepared in a single state.

I agree.

Good. In this scenario, our researchers have the highest amount of freedom with no restrictions whatsoever. Therefore in general the QM result for the singlet state does not violate anything so far.

But let's modify our experiment a little. We still have 4 random researchers scattered around the world. They have the exact same amount of freedom as the first 4, no restrictions on the types of particles they can use. The only difference is that now each person only generates one particle at a time, not pairs, and measures them at just one station, with the chosen setting. The 4 researchers are each given just one setting instead of a pair, ie respectively. Obviously in this scenario, each researcher can't calculate . It has to be done after the experiment and since each researcher may measure a different number of particles in their stream, we have may have to truncate their results in order to calculate the expectations but they are totally free to do whatever they want. We could instead just tell them to give us a stream of N results, and they do whatever they want to give us a list of N outcomes (I won't consider this an additional restriction because the previous group of researchers could have been given the same instruction without any change in outcome). From their results, we perform a similar calculation for the expectation , and for this scenario, the maximum value we can ever observe for the following expression is 2:



If you disagree explain why. If you agree then we can proceed.
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Re: Institutionalized Denial of the Disproof of Bell's Theor

Postby Justo » Mon Aug 09, 2021 7:51 am

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.
Justo
 

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

Postby Heinera » Mon Aug 09, 2021 8:05 am

minkwe wrote:Now let us generalize a little bit. Let us keep everything just agreed above for the singlet state and instead let us relax the singlet state requirement and say all that the researchers have to do is prepare their particles anyway they like. They can use the singlet state if they like, but they can also use any other type of state. In fact, we don't even restrict the type of particle they are to use. All they have to do is perform a similar experiment with any set of pairs of particles (no restrictions) and record the correlations. Once they bring their results together, the maximum value they can observe for the following expression is 4.



No, if the world behaves according to QM, the upper bound is no matter what state the particles are prepared in or what kind of particles they are (Tsirelson's bound).

And you are also confusing "expectation" with "observed averages" for a potentially small number of trials. The "expectation" is a theoretical limit when the number of trials goes to infinity.
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Re: Institutionalized Denial of the Disproof of Bell's Theor

Postby Heinera » Mon Aug 09, 2021 8:12 am

minkwe wrote: We still have 4 random researchers scattered around the world. They have the exact same amount of freedom as the first 4, no restrictions on the types of particles they can use. The only difference is that now each person only generates one particle at a time, not pairs, and measures them at just one station, with the chosen setting. The 4 researchers are each given just one setting instead of a pair, ie respectively. Obviously in this scenario, each researcher can't calculate . It has to be done after the experiment and since each researcher may measure a different number of particles in their stream, we have may have to truncate their results in order to calculate the expectations but they are totally free to do whatever they want. We could instead just tell them to give us a stream of N results, and they do whatever they want to give us a list of N outcomes (I won't consider this an additional restriction because the previous group of researchers could have been given the same instruction without any change in outcome). From their results, we perform a similar calculation for the expectation , and for this scenario, the maximum value we can ever observe for the following expression is 2:



You now start out with completely different states. According to QM, the bound in this situation is actually 0.
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Re: Institutionalized Denial of the Disproof of Bell's Theor

Postby Justo » Mon Aug 09, 2021 2:09 pm

Heinera wrote:
minkwe wrote:Now let us generalize a little bit. Let us keep everything just agreed above for the singlet state and instead let us relax the singlet state requirement and say all that the researchers have to do is prepare their particles anyway they like. They can use the singlet state if they like, but they can also use any other type of state. In fact, we don't even restrict the type of particle they are to use. All they have to do is perform a similar experiment with any set of pairs of particles (no restrictions) and record the correlations. Once they bring their results together, the maximum value they can observe for the following expression is 4.



No, if the world behaves according to QM, the upper bound is no matter what state the particles are prepared in or what kind of particles they are (Tsirelson's bound).

For Tirelson's bound to be valid, it is necessary the four experimenters use the same state. That condition is not clear from what minkwe required.

Heinera wrote:And you are also confusing "expectation" with "observed averages" for a potentially small number of trials. The "expectation" is a theoretical limit when the number of trials goes to infinity.

The distinction is not relevant for the discussion. We can assume that "observed averages" are equal to the theoretical value.
Justo
 

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

Postby Heinera » Mon Aug 09, 2021 3:40 pm

Justo wrote:For Tirelson's bound to be valid, it is necessary the four experimenters use the same state. That condition is not clear from what minkwe required.

After reading his post again I agree.
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Re: Institutionalized Denial of the Disproof of Bell's Theor

Postby minkwe » Mon Aug 09, 2021 5:12 pm

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

Postby Justo » Mon Aug 09, 2021 5:39 pm

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.
Justo
 

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