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OK, I am going to throw my weight around, such as it is, as the symposium moderator. Besides that the current month is June, can we all agree about the following five matters?

1) Using a prepared singlet state, Quantum Mechanics (QM) predicts a strong correlation ? And that this has robust empirical support?

2) This correlation in #1 above is stronger that the linear correlation , with , at all except 0, 90 and 180 degrees, where they are equal?

3) At, say, , #1 is larger than #2 above by a factor of which is traceable to the outer bounds of the CSHS inequality for QM, versus just 2 for linear correlations?

4) One we agree about #1, #2 and #3, we really don't need to talk any further about the inequality, but can just talk about the correlations, because we can all figure out how that translates to the inequality?

5) The prevailing view is that QM is not a "local," "realistic," "hidden variable" theory, as those terms are generally defined? (I am not asking at the moment for a debate about these terms.)

Anybody have a disagreement with any of the above? Or, can we at least put this into the same basket as agreeing that it is June?

Jay

Re 5: To be precise, QM can't be *all* of those, but it can e.g. easily be replicated by a hidden variable model, which would then not be local.

Yablon wrote:OK, I am going to throw my weight around, such as it is, as the symposium moderator. Besides that the current month is June, can we all agree about the following five matters?

1) Using a prepared singlet state, Quantum Mechanics (QM) predicts a strong correlation ? And that this has robust empirical support?

2) This correlation in #1 above is stronger that the linear correlation , with , at all except 0, 90 and 180 degrees, where they are equal?

3) At, say, , #2 is larger than #1 above by a factor of which is traceable to the outer bounds of the CSHS inequality for QM, versus just 2 for linear correlations?

4) One we agree about #1, #2 and #3, we really don't need to talk any further about the inequality, but can just talk about the correlations, because we can all figure out how that translates to the inequality?

5) The prevailing view is that QM is not a "local," "realistic," "hidden variable" theory, as those terms are generally defined? (I am not asking at the moment for a debate about these terms.)

Anybody have a disagreement with any of the above? Or, can we at least put this into the same basket as agreeing that it is June?

Jay

What do you mean, in your item (2), by “stronger”?

[off topic comment moved to new thread here.]

Yablon wrote:OK, I am going to throw my weight around, such as it is, as the symposium moderator. Besides that the current month is June, can we all agree about the following five matters?

1) Using a prepared singlet state, Quantum Mechanics (QM) predicts a strong correlation ? And that this has robust empirical support?

2) This correlation in #1 above is stronger that the linear correlation , with , at all except 0, 90 and 180 degrees, where they are equal?

3) At, say, , #2 is larger than #1 above by a factor of which is traceable to the outer bounds of the CSHS inequality for QM, versus just 2 for linear correlations?

4) One we agree about #1, #2 and #3, we really don't need to talk any further about the inequality, but can just talk about the correlations, because we can all figure out how that translates to the inequality?

5) The prevailing view is that QM is not a "local," "realistic," "hidden variable" theory, as those terms are generally defined? (I am not asking at the moment for a debate about these terms.)

Anybody have a disagreement with any of the above? Or, can we at least put this into the same basket as agreeing that it is June?

Jay

At 135 degrees I get that #2 is 0.5 and #1 is 0.707 so not sure what happened there. Yes, I agree that we should just be talking about correlations only. And yes, the prevailing view is that QM is not a local realistic theory.

PS. Let's try to keep this thread on topic.
.

***
Those five points do not seem controversial.

Except, I find your unorthodox notation bothersome. In the Bell literature, big A and B usually denote measurement results and small a and b denote freely chosen parameters.

***

I have revised what I wrote to start this thread to incorporate comments, see below. Heinera I agree, made that change. Joy I went to lowercase. Richard, I have clarified " stronger" as "i.e., has a larger numeric magnitude." And you now have your own thread for discussion of the triangle wave paper. You can ask people to stay on topic on your thread; I will ask them to do so on mine.

Is everybody OK with they way it is worded below, before I move on to the next round? Please reply yes, or if not, why not. Jay


1) Using a prepared singlet state, Quantum Mechanics (QM) predicts a strong correlation ? And that this has robust empirical support?

2) This correlation in #1 above is stronger, i.e., has a larger numeric magnitude than the linear correlation , with , at all except 0, 90 and 180 degrees, where they are equal?

3) At, say, , #2 is larger than #1 above by a factor of which is traceable to the outer bounds of the CSHS inequality for QM, versus just 2 for linear correlations?

4) One we agree about #1, #2 and #3, we really don't need to talk any further about the inequality, but can just talk about the correlations, because we can all figure out how that translates to the inequality?

5) The prevailing view is that QM is not all of a "local" and "realistic" and "hidden variable" theory, as those terms are generally defined? (I am not asking at the moment for a debate about these terms.)

Yablon wrote:I have revised what I wrote to start this thread to incorporate comments, see below. Heinera I agree, made that change. Joy I went to lowercase. Richard, I have clarified " stronger" as "i.e., has a larger numeric magnitude." And you now have your own thread for discussion of the triangle wave paper. You can ask people to stay on topic on your thread; I will ask them to do so on mine.

Is everybody OK with they way it is worded below, before I move on to the next round? Please reply yes, or if not, why not. Jay


1) Using a prepared singlet state, Quantum Mechanics (QM) predicts a strong correlation ? And that this has robust empirical support?

2) This correlation in #1 above is stronger, i.e., has a larger numeric magnitude than the linear correlation , with , at all except 0, 90 and 180 degrees, where they are equal?

3) At, say, , #2 is larger than #1 above by a factor of which is traceable to the outer bounds of the CSHS inequality for QM, versus just 2 for linear correlations?

4) One we agree about #1, #2 and #3, we really don't need to talk any further about the inequality, but can just talk about the correlations, because we can all figure out how that translates to the inequality?

5) The prevailing view is that QM is not all of a "local" and "realistic" and "hidden variable" theory, as those terms are generally defined? (I am not asking at the moment for a debate about these terms.)

Well, there is something wrong with #3, because -1 + 2*135/180 = -1 + 1.5 = 0.5 and #1 at 135 degrees is 0.707. So #2 is smaller than #1 not larger.
Note to Fred from Jay: My typo, inverted #1 and #2, now fixed,

Yablon wrote:1) Using a prepared singlet state, Quantum Mechanics (QM) predicts a strong correlation ? And that this has robust empirical support?

2) This correlation in #1 above is stronger, i.e., has a larger numeric magnitude than the linear correlation , with , at all except 0, 90 and 180 degrees, where they are equal?

3) At, say, , #1 is larger than #2 above by a factor of which is traceable to the outer bounds of the CSHS inequality for QM, versus just 2 for linear correlations?

4) One we agree about #1, #2 and #3, we really don't need to talk any further about the inequality, but can just talk about the correlations, because we can all figure out how that translates to the inequality?

5) The prevailing view is that QM is not all of a "local" and "realistic" and "hidden variable" theory, as those terms are generally defined? (I am not asking at the moment for a debate about these terms.)

I am going to assume that everyone agrees on the above and will now go on to round 2. I am focusing on QM, not any other theory. Can we all agree on the following, and if not, why not? I will also cross reference equation numbers from https://jayryablon.files.wordpress.com/ ... -4.1-1.pdf. You may also wish to refer to https://en.wikipedia.org/wiki/Bell%27s_ ... equalities, and click "show" for "Details on calculation of Cq(a, b)".

1) Does everybody agree that the singlet state which is use to calculate the "strongest" i.e, largest-magnitude QM correlations is represented as follows?
(1.2a)
And that that left-side bra is related to the right side ket as its hermitian conjugate ?

2) Is everybody OK with these being the Pauli matrices?

(1.3)

3) Let's now take two vectors in three dimensional space, a and b. Does everybody agree that the following is a correct calculation?

(1.11)

4) Does everyone agree with that the expectation value of with normalized eigenkets , with denoting summation over both normalized eigenstates, is calculated to be the following?

(1.15)

5) Does everybody understand the different between calculating with sandwiched between and its bra in #3 above, versus sandwiched between between and its bra with state summation in #4 above? And why these need not be and are not the same, but in fact are related by a minus sign?

6) If you are clear with #5 above, then will anybody freak out if I use the common result to string together and equate all of the following?

(1.16)

7) Does anybody have any problem with connecting to a correlation as that term is defined in statistics, to arrive at:

(1.20)

Let's stop here for now.

Jay

I'm good with all of that. I ran what I could of it on my MathCad program and it all checks out. Especially eq. (1.11).

Yablon wrote:

Yablon wrote:1) Using a prepared singlet state, Quantum Mechanics (QM) predicts a strong correlation ? And that this has robust empirical support?

2) This correlation in #1 above is stronger, i.e., has a larger numeric magnitude than the linear correlation , with , at all except 0, 90 and 180 degrees, where they are equal?

3) At, say, , #1 is larger than #2 above by a factor of which is traceable to the outer bounds of the CSHS inequality for QM, versus just 2 for linear correlations?

4) One we agree about #1, #2 and #3, we really don't need to talk any further about the inequality, but can just talk about the correlations, because we can all figure out how that translates to the inequality?

5) The prevailing view is that QM is not all of a "local" and "realistic" and "hidden variable" theory, as those terms are generally defined? (I am not asking at the moment for a debate about these terms.)

I am going to assume that everyone agrees on the above and will now go on to round 2. I am focusing on QM, not any other theory. Can we all agree on the following, and if not, why not?

Sorry I wasn't finished with your first round. I agree with #1, #2 and #3; but I disagree with #4.

We don't want to talk *only* about the cosine wave and the triangle wave.

There are many, many more correlation curves allowed by QM and indeed engineered in the lab and used for Bell type experiments. In fact, the Vienna and Boulder experiments very deliberately used a not maximally entangled state. They used the only state which allows you to get away with only 75% detector efficiency. They had just slightly better...

There are many, many more correlation curves allowed by LR (or LHV or LRHV).

Bell's theorem, and Tsirelson's theorem, tell us about the *sets of all correlation curve*s allowed under each of the two theories (QM and LR respectively). One *set* is contained in the other. The famous 2 sqrt 2 comes from choosing a particular metric and then looking for the point in the QM set which is furthest from its own closest LR set. Those two curves - ie solutions of a minimax problem - are indeed the cosine and the triangle wave.

Yablon wrote:7) Does anybody have any problem with connecting to a correlation as that term is defined in statistics, to arrive at:

(1.20)

Jay: I need to know how you think that the term "correlation" is defined in "statistics" before I can make any comment on this statement.

I do have pretty firm ideas about what "statistics" is and how "correlation" is defined in statistics - I've been teaching statistics to mathematicians, economists, astronomers, and psychologists, and data-scientists, for 45 years.

*****************
OK, maybe I'm a bit old-fashioned. From here on, some old man's ramblings, connecting this all to the very important topic of old Dutch genever. Which I hope to enjoy with many of you when our Symposium and Workshop finally materialises. At which we will be able to admire, on a wall, the genuine and original signatures of Einstein, Lorentz and Ehrenfest.

I have been publicly called "a third-rate statistician" by academician (both US and Austrian) Karl Hess,but he much later told me that he is now deeply ashamed that he ever did this. Anyway, I love telling and re-telling the story! He's wrong about Bell, I think, but he's a decent guy really.

I recall at a meeting of the Royal Dutch Academy of Sciences, where I was giving a talk about lessons to be learnt from the case of the convicted killer nurse Lucia de Berk, that a very eminent but elderly surgeon suddenly burst in and told the surprised audience that my Dutch passport and my membership of the Academy should both be revoked and I should go back to England. Then he stormed out again (didn't stay for the nibbles and Dutch "old genever"). I guess he would also have approved of an even worse fate.

Allegedly, "genever" was invented by my departed colleague Sylvius, after whom the building is named where I have my office.

I guess my reply to Jay is that it's not clear to me where this is going, and whether it will be worth the time to keep following the development.

My issue here is that we need to stick with the definition of a "hidden variable" in the sense of Bell. I could write down the letter on a piece of paper, bury it in my garden and claim I had a hidden variable, but it would not be what Bell had in mind. The main takeaway from Bell's theorem is that no tweaking of classical theory that retains realism and locality can replicate QM theory. So QM is in some sense fundamentally different. Introducing an extra (and probably superfluous) variable into QM, and calling it "hidden", won't change that fact.

gill1109 wrote:OK, maybe I'm a bit old-fashioned. From here on, some old man's ramblings, connecting this all to the very important topic of old Dutch genever. Which I hope to enjoy with many of you when our Symposium and Workshop finally materialises. At which we will be able to admire, on a wall, the genuine and original signatures of Einstein, Lorentz and Ehrenfest.

I too look forward to all that. Let's keep trucking on to the symposium!

Two comments came in overnight, this one from Richard, and another from Heinera. I will reply to Richard here, then hopefully this evening after a busy day with my little grandson, to Heinera.

gill1109 wrote:

Yablon wrote:7) Does anybody have any problem with connecting to a correlation as that term is defined in statistics, to arrive at:

(1.20)

Jay: I need to know how you think that the term "correlation" is defined in "statistics" before I can make any comment on this statement.

I do have pretty firm ideas about what "statistics" is and how "correlation" is defined in statistics - I've been teaching statistics to mathematicians, economists, astronomers, and psychologists, and data-scientists, for 45 years.

Richard, I am glad you asked that question. And you are the ideal person to be asking that question given your first rate background in this area. Probably nobody except my own high school chums know or remember this, but in high school, I was allowed by the faculty to teach a course in probability and statistics which was attended by fellow students and even a few teachers. Indeed, my first mathematics love was probability and statistics. Done with this old man's ramblings and on to business.

It is my impression that many discussions of QM correlations focus on the from QM reviewed in my most recent points 1-6 , but not sufficiently on why we can call this a correlation, the point 7 your cited. Is this some unique type of correlation developed for QM? Of course it is not. It is a correlation precisely as that term is used in statistics, and I felt it important, at least in anything I write, to not omit that point.

So, my detailed explanation is in (1.17) through (1.20) of https://jayryablon.files.wordpress.com/ ... -4.1-1.pdf. Here, let me just review the main points:

We start with the standard statistics definition where , and the standard deviations are and . In sum, the correlation is a normalized covariance.

Because , point 4, equation (1.15), we want to first calculate the correlation between and , by plugging these right into the statistical definitions.

This leads to:

(1.17a)

with the standard deviations:


(1.17b)

I know that you, Richard, raised the point to me privately whether you can actually plug the Hermitan matrices and into the statistical formulas because they are matrices not random variables. But, if you look at (1.17), the only real question is whether each expression inside (1.17) has definite mathematical meaning for these matrices. And if you inspect closely you will see that they do. I discuss this in more detail in the paper draft.

So when we do the calculations and include a minus sign in front of , we end up with:

(1.19)

Finally, we make the definition:

(1.20)

recognizing that the minus sign is attributable not to the orientation of the Alice and Bob detectors, but to the oppositely-oriented angular momenta emerging in the two particles which split off out of each singlet prepared state.

Jay

OK. We keep on truckin!

There are mathematical definitions, which belong inside “abstract” mathematical structures.

There are the algorithms that data scientists, accountants, shopkeepers, and ordinary folk use, when given a spreadsheet with a heap of numbers.

There has to be some kind of bridge. You could call it meta-physics, or philosophy. The ancient hindus have a story in the Mahabharata about how a prince lost his Kingdom and his wife by gambling. He wandered destitute into the forest where he met a God disguised, I think, as a snake. The God showed him how to count the leaves on a tree by just picking a branch at random, counting the leaves on the branch, and counting the number of branches. The prince (who obviously had already been taught long multiplication) went back and won back his kingdom and his girl by cleverly gambling. He went on to become a famous wise king who no doubt had the necessary skills to raise taxes and raise Armies, and use them wisely, for which some “merely” statistical skills can come in handy, as well as the Insight that randomness can be an asset as well as a horror and an abomination. We humans hate randomness, and we tend to hate maths too. Silly!

The point of this rambling old trucker’s story is that we do have to venture into the foundations of probability, into areas where people are still vehemently fighting one another (Bayesians versus frequentists) much more viciously than in the relatively recent and quiet Bell wars.

Heinera wrote:I guess my reply to Jay is that it's not clear to me where this is going, and whether it will be worth the time to keep following the development.

My issue here is that we need to stick with the definition of a "hidden variable" in the sense of Bell. I could write down the letter on a piece of paper, bury it in my garden and claim I had a hidden variable, but it would not be what Bell had in mind. The main takeaway from Bell's theorem is that no tweaking of classical theory that retains realism and locality can replicate QM theory. So QM is in some sense fundamentally different. Introducing an extra (and probably superfluous) variable into QM, and calling it "hidden", won't change that fact.

Perhaps let's not say "replicate QM theory" but a classical local realistic theory that gives the same predictions as QM. Yes, the hidden variable should be defined in the sense of Bell. Of course, Joy has already accomplished that task. Jay's task here is to get a hidden variable to work directly in QM.
.

FrediFizzx wrote:Perhaps let's not say "replicate QM theory" but a classical local realistic theory that gives the same predictions as QM.
.

Yes, with "replicate" I mean the predictions.

And furthermore, can someone please refrain from this endless plugging of Joy Christian's theory? It's like Cato, who reputedly ended all his speeches in the Roman senate with "Ceterum autem censeo Carthaginem esse delendamt" (Furthermore, I consider that Carthage must be destroyed.)

Heinera wrote:And furthermore, can someone please refrain from this endless plugging of Joy Christian's theory? It's like Cato, who reputedly ended all his speeches in the Roman senate with "Ceterum autem censeo Carthaginem esse delendamt" (Furthermore, I consider that Carthage must be destroyed.)

Can someone please refrain from this endless plugging of the nonsensical "theorem" of Bell? It's like Cato, who reputedly ended all his speeches in the Roman senate with "Ceterum autem censeo Carthaginem esse delendamt" (Furthermore, I consider that Carthage must be destroyed.): (1) https://arxiv.org/abs/1704.02876, (2) https://arxiv.org/abs/1103.1879.

***

Guys, let's try to stay on topic here. My fault for mentioning that.

Jay, I think everyone agrees with what you have presented so far except for #4. But I think you only want to talk about QM correlations here so please proceed.

gill1109 wrote:

Yablon wrote:

Yablon wrote:1) Using a prepared singlet state, Quantum Mechanics (QM) predicts a strong correlation ? And that this has robust empirical support?

2) This correlation in #1 above is stronger, i.e., has a larger numeric magnitude than the linear correlation , with , at all except 0, 90 and 180 degrees, where they are equal?

3) At, say, , #1 is larger than #2 above by a factor of which is traceable to the outer bounds of the CSHS inequality for QM, versus just 2 for linear correlations?

4) One we agree about #1, #2 and #3, we really don't need to talk any further about the inequality, but can just talk about the correlations, because we can all figure out how that translates to the inequality?

5) The prevailing view is that QM is not all of a "local" and "realistic" and "hidden variable" theory, as those terms are generally defined? (I am not asking at the moment for a debate about these terms.)

I am going to assume that everyone agrees on the above and will now go on to round 2. I am focusing on QM, not any other theory. Can we all agree on the following, and if not, why not?

Sorry I wasn't finished with your first round. I agree with #1, #2 and #3; but I disagree with #4.

We don't want to talk *only* about the cosine wave and the triangle wave.



There are many, many more correlation curves allowed by QM and indeed engineered in the lab and used for Bell type experiments. In fact, the Vienna and Boulder experiments very deliberately used a not maximally entangled state. They used the only state which allows you to get away with only 75% detector efficiency. They had just slightly better...

There are many, many more correlation curves allowed by LR (or LHV or LRHV).

Bell's theorem, and Tsirelson's theorem, tell us about the *sets of all correlation curve*s allowed under each of the two theories (QM and LR respectively). One *set* is contained in the other. The famous 2 sqrt 2 comes from choosing a particular metric and then looking for the point in the QM set which is furthest from its own closest LR set. Those two curves - ie solutions of a minimax problem - are indeed the cosine and the triangle wave.

Richard, I agree with what you said about the many correlation curves. Perhaps I should restate my number 4 like this:

On pretty much all else, I was looking for agreement about objective points of science and / or mathematics. In #4 I am really asking for a pedagogical agreement for the discussions we are having, that we all agree to stick with the strongest correlation from the singlet state because that is all we really need as a "laboratory" for discussing the LRHV properties (or not) of QM. Whatever LRHV attributes QM has or does not have for the singlet correlation, it will likewise have or not have for the other correlations. So I would for us to arrive at a pedagogical agreement that we all stay focused on the singlet state:

(1.1)

I am not in any way suggesting that these other states are irrelevant or uninteresting. Rather I am suggesting that once we resolve the major issues of principle for the singlet, those issues will fall the same way for other prepared states which are not as correlated as the singlet.

In fact, in an earlier draft of https://jayryablon.files.wordpress.com/ ... -4.1-1.pdf I also calculated correlations for the spin 1 triplet prepared states:

also(1.1)

But I decided to pull that out because I felt it would be a distraction from getting to the main issues as directly as possible. I am really trying to stay efficient and not get distracted by anything not directly relevant to the core questions of the LRHV or not properties of QM, or that will merely give answers of principle which are redundant to what we find for the singlet.

Jay

PS: I had a good but long day. After my grandson saw me dive into the pool he got all excited and had me get out and me repeat multiple, multiple times. So I am exhausted. I do want to pick up on Heinera's question regarding hidden variables, but will need to do so when I am fresh in the morning.

Heinera wrote:I guess my reply to Jay is that it's not clear to me where this is going, and whether it will be worth the time to keep following the development.

My issue here is that we need to stick with the definition of a "hidden variable" in the sense of Bell. I could write down the letter on a piece of paper, bury it in my garden and claim I had a hidden variable, but it would not be what Bell had in mind. The main takeaway from Bell's theorem is that no tweaking of classical theory that retains realism and locality can replicate QM theory. So QM is in some sense fundamentally different. Introducing an extra (and probably superfluous) variable into QM, and calling it "hidden", won't change that fact.

OK, Heinera, let's go the Bell, which you can find online at https://cds.cern.ch/record/111654/files ... 00_001.pdf. From the bottom of page 1 into page 2:

"Let this more complete specification be effected by means of parameters . It is a matter of indifference in the following whether denotes a single variable or a set, or even a set of functions, and whether
the variables are discrete or continuous. However, we write as if were a single continuous parameter. The result A of measuring is then determined by and , and the result B of measuring in the same instance is determined by and , and

(1)

The vital assumption . . . is that the result B for particle 2 does not depend on the setting of the magnet for particle 1, nor A on ."

This is actually a fairly broad definition. I am perfectly content to regard this "vital assumption" as a minimal necessary requirement for a "hidden variable" used in connection with QM correlations between A and B. Also I would even consider more restrictive requirements which tighten this definition, i.e., to entertain the possibility that this definition is insufficiently restrictive, as to how something acquires status as a "hidden variable" to begin with.

Does everyone agree this this as a "statement in principle" of how we define "hidden variables"?

Jay