Bell & CHSH type inequalities and experiments

[minkwe]

But I never said that the CHSH bound "applies" to an experiment in the sense that the experimental results will certainly be below that bound. I've kept saying that with large probability, they will be below a slightly larger bound.

Do you know what a bound means?

I am not stupid.

Sometimes I wonder.

[Joy Christian]

Here is the proof that you do not know the difference between what is a bi-vector and what is a multi-vector:

"...his standardized correlations are the bivectors - a . b - a x b"

This is a sentence from your abstract. Your paper has been online for several years now. Many people have noticed your lack of understanding of basic algebra. The above sentence from your abstract speaks for itself. Need I say more?

Question of notation. Do you want me to change my notation or terminology? At least my algebra is correct.

This is a further proof that you still don't see what the problem is. It is not an issue of notation or terminology. You simply don't understand the difference, and I am not going to explain it to you. I am all too happy that you think it is just a matter of notation or terminology. The world, however, can see exactly what the problem is.

[gill1109]

But I never said that the CHSH bound "applies" to an experiment in the sense that the experimental results will certainly be below that bound. I've kept saying that with large probability, they will be below a slightly larger bound.

Do you know what a bound means?

I am not stupid.

Sometimes I wonder.

Did you do my experiment yet? That might help settle the question.

[gill1109]

I am all too happy that you think it is just a matter of notation or terminology. The world, however, can see exactly what the problem is.

The world is keeping quite quiet about this.

But good that you are happy. That is a nice note to end the evening with. And as I said, we made great progress today, on many fronts!

[minkwe]

I am not stupid.

Sometimes I wonder.

The expression axb - axb' + a'xb + a'xb' has an *upper bound* of 2.

Please can you give me a single example of values (a,b,a',b') each +/-1 which violates this bound by 0.0000000000001 even? Can you give me a spreadsheet of values with 4 columns of a,b,a',b' for which averages of those paired products will exceed this bound by 0.0000000000000000000000000000000000001 even? Why do you keep deluding yourself that because of "statistical error" or other statistical tricks, you will have a "somewhat" larger bound?

The expression a1xb1 - a2xb2' + a3'xb3 + a4'xb4' where each of the values (a1, b1, a2, b2', a3', b3, a4', b4') are +/-1 has an upper bound of 4. Can you give me an example of a single set of 8 values which violates that bound by even 0.0000000000000000000000000000000001? Can you give me a spreadsheet of 8 columns of values for those variables for which the averages of the paired products exceed the bound of 4 by even 0.0000000000000000000000000000001? Then why do you keep deluding yourself that due to statistical error or some other statistical tricks, the upper bound can be revised-up?

Why are you still unable to see that just because you can write a silly piece of R-code to generate a value of the expression which is much less than 4, does not change the fact that THE UPPER BOUND OF THE EXPRESSION IS 4???????????????????? Duh! it is an upper bound, it means it can not be higher, it doesn't mean any Tom and Dick can not generate a value lower than it!

Why do you continue to claim that QM violates the upper bound of an expression when I've explained to you and you accept that the upper bound is 4 and the QM value is 2 root 2, nowhere close?

[Joy Christian]

David Hestenes, Lucien Hardy, Izhar Aqbal, Manfried Faber, and many, many others have agreed with it entirely. They are not bothered by a slip of the tongue or pen or a slightly unorthodox terminology.

This is total nonsense. They are all well aware of your silly errors and your lack of understanding of basic algebra. They are just too polite to tell you that on your face. They all agree with me that, in addition to your silly mistakes, you simply haven't understood what the hidden variable is in my model. It is entirely your loss.

[minkwe]

I told you, I have read these papers, and de Raedt's, I know all these people more or less, and they are all (or were, in Giulaume's case) equally confused as you are.

So according to you Hans de Raedt is your friend, and you agree with him on all substantial points:

De Raedt has known my work for a long time. We have discussed both of our works with one another. We fully agree on all substantial points.

But at the same time, you now say he is confused. Yet you have invited him to adjudicate on your bet with Joy.

ROTFLMAO.

You may want to look carefully at Theorems 7.1, 7.2, 7.3 and 7.4 in Rosinger's paper. Where exactly is the confusion. Please point out the mathematical mistake you claim exists in the paper. Look carefully at the discussion in Section 7.5, where exactly is the confusion. Please point out the paragraph or line where you believe Rosinger has made an error.

I suspect you won't because you can not. You'd rather we run silly irrelevant pieces of R-code instead of you confronting the argument head on. I have presented very clear mathematical arguments here and you have agreed to them all. Rosinger does the same with even more rigor. You have no response.

[minkwe]

As concerns Adenier's paper, please Richard can you point to the line/paragraph where he has made any error?

Note that he proves that QM can not violate the CHSH. Here is his conclusion:
http://arxiv.org/pdf/quant-ph/0006014v3.pdf

It was shown that Bell’s Theorem cannot be derived, either within a strongly objective interpretation of the CHSH function, because Quantum Mechanics gives no strongly objective results for the CHSH function (see Section 4.2), or within a weakly objective interpretation, because the only derivable local realistic inequality is never violated, either by Quantum Mechanics or by experiments (see Section 5.2). It was demonstrated that the discrepancy in Bell’s Theorem is due only to a meaningless comparison between Sρstrong ≤ 2 and Sψweak = 2√2, where the former is relevant to a system with Nf degrees of freedom, whereas the latter to one with 4Nf (see Section 3). The only meaningful comparison is between the weakly objective local realistic inequality Sρweak ≤ 4 and the weakly objective quantum prediction Sψweak= 2√2, but these results are not incompatible. Bell’s Theorem, therefore, is refuted.

You say Adenier was confused. Richard, I challenge you that we go through his paper line by line and you show me the error in his mathematical arguments. You claim that Adenier has attempted to publish this several times without success, which suggests to me that maybe you were a reviewer of one of those Journals which allegedly rejected the paper. If you were, here is your opportunity to demonstrate that you are not part of the "Bell mafia" out to quench all dissent about Bell's theorem. Point out the error in the paper. Just one error. Since you like bets, I'm willing to bet on this one.

[gill1109]

Why do you continue to claim that QM violates the upper bound of an expression when I've explained to you and you accept that the upper bound is 4 and the QM value is 2 root 2, nowhere close?

My God, when the hell are you going to realize that I don't claim all the stupid things which you keep putting in my mouth?

I distinguish between theoretical mean values, and experimental sample averages. So if I say QM violates something, it is ought to be clear that I am talking about theory. If we want to verify violation in an experiment, we will have to move to a new level and take account of errors and chances of errors. A whole new ball-park. New issues, new concepts. If you don't even have a vocabulary for this new ball-park, we are not going to be able to communicate about it very well.

See A silly computer experiment ... or, the heart of the matter?
http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=40&p=1321#p1321

[gill1109]

You say Adenier was confused. Richard, I challenge you that we go through his paper line by line and you show me the error in his mathematical arguments. You claim that Adenier has attempted to publish this several times without success, which suggests to me that maybe you were a reviewer of one of those Journals which allegedly rejected the paper. If you were, here is your opportunity to demonstrate that you are not part of the "Bell mafia" out to quench all dissent about Bell's theorem. Point out the error in the paper. Just one error. Since you like bets, I'm willing to bet on this one.

Ill be more than happy to make you happy by doing exactly this, *after* you have made me happy by performing the experiment which I asked you to do, and reporting back what you saw. You seem to believe the experiment is pointless. Then it must also be harmless, right?

Do I have to rewrite my R code in Python first? Do you need any further instructions/explanations? I'll start a new thread, to keep everything carefully separated.


See A silly computer experiment ... or, the heart of the matter?
http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=40&p=1321#p1321

[gill1109]

I told you, I have read these papers, and de Raedt's, I know all these people more or less, and they are all (or were, in Giulaume's case) equally confused as you are.

So according to you Hans de Raedt is your friend, and you agree with him on all substantial points:

De Raedt has known my work for a long time. We have discussed both of our works with one another. We fully agree on all substantial points.

But at the same time, you now say he is confused. Yet you have invited him to adjudicate on your bet with Joy.

ROTFLMAO.

You may want to look carefully at Theorems 7.1, 7.2, 7.3 and 7.4 in Rosinger's paper. Where exactly is the confusion. Please point out the mathematical mistake you claim exists in the paper. Look carefully at the discussion in Section 7.5, where exactly is the confusion. Please point out the paragraph or line where you believe Rosinger has made an error.

I suspect you won't because you can not. You'd rather we run silly irrelevant pieces of R-code instead of you confronting the argument head on. I have presented very clear mathematical arguments here and you have agreed to them all. Rosinger does the same with even more rigor. You have no response.

I agreed with your argument steps 1, 2 and 3 but I did not agree with the inference which you drew from them. Your concluding lines.

About confused people: I have a lot of confused friends! Just because someone is confused, doesn't mean they are a person without integrity or other positive qualities. I find confused people delightful. (As Niels Bohr said, now we have a contradiction. Wonderful. That means we can make progress).

The membership of the adjudication team was decided jointly by Joy and me in order to prove to the world that neither or us is rigging the bet by creating a board with a strong bias one way or another. The three persons we have chosen are persons of integrity and with independent minds and with very different opinions about quantum foundations and with different backgrounds (maths, theoretical physics, experimental physics).

About silly R code: I insist that you bear with me and do what I ask. After that I'll be delighted to present my analysis of Rosinger's, Adenaer's, or de Raedt's work. All of whom I consider as aquaintances with whom I am on the best of terms.

See A silly computer experiment ... or, the heart of the matter?
http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=40&p=1321#p1321

[minkwe]

About silly R code: I insist that you bear with me and do what I ask. After that I'll be delighted to present my analysis of Rosinger's, Adenaer's, or de Raedt's work. All of whom I consider as aquaintances with whom I am on the best of terms.

See A silly computer experiment ... or, the heart of the matter?
http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=40&p=1321#p1321

Person 1: For the toss of a single coin where outcome H = +1 and T = -1, and A is the result you obtain, and B is the other result you could have obtained, the UPPER BOUND of A + B is 1 ,ie A + B <= 1
Person 1: For the toss of two different coins where A is the result from the first and B is the result from the second, the UPPER BOUND of A + B is 2 ie, A + B <= 2
Person 1: Therefore it is inappropriate to apply the UPPER BOUND from the first scenario to an experiment of the second type.
Person 2: Here is some R code, simulating 2 coins of a specific type which shows that the AVERAGEs , <A> + <B> only exceeds 1 very rarely. Therefore it is okay to use the inequality from the first scenario in the second scenario. Oh and by the way, since QM and experiments of the second kind consistently produce values higher than 1, it proves that coins do not actually have two sides.

Just silly.

[gill1109]

About silly R code: I insist that you bear with me and do what I ask. After that I'll be delighted to present my analysis of Rosinger's, Adenaer's, or de Raedt's work. All of whom I consider as aquaintances with whom I am on the best of terms.

See A silly computer experiment ... or, the heart of the matter?
http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=40&p=1321#p1321

Person 1: For the toss of a single coin where outcome H = +1 and T = -1, and A is the result you obtain, and B is the other result you could have obtained the UPPER BOUND of A + B is 1 ,ie A + B <= 1
Person 1: For the toss of two different coins where A is the result from the first and B is the result from the second, the UPPER BOUND of A + B is 2 ie, A + B <= 2
Person 1: Therefore it is inappropriate to apply the UPPER BOUND from the first scenario to an experiment of the second type.
Person 2: Here is some R code, simulating 2 coins of a specific type which shows that the AVERAGEs , <A> + <B> only exceeds 1 very rarely. Therefore it is okay to use the inequality from the first scenario in the second scenario. Oh and by the way, since QM and experiments of the second kind consistently produce values higher than 1, it proves that coins do not actually have two sides.

Just silly.

As usual, you are stupidly attributing notions to me which I do not have. You are so proud that you have logically defeated your straw-man representation of what I actually say or write, that you are not going to learn anything new. Rather sad. Just try the experiment, and then I'll explain why it was so important, even though you thought it was just silly.

[minkwe]

About silly R code: I insist that you bear with me and do what I ask. After that I'll be delighted to present my analysis of Rosinger's, Adenaer's, or de Raedt's work. All of whom I consider as aquaintances with whom I am on the best of terms.

See A silly computer experiment ... or, the heart of the matter?
http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=40&p=1321#p1321

Person 1: For the toss of a single coin where outcome H = +1 and T = -1, and A is the result you obtain, and B is the other result you could have obtained the UPPER BOUND of A + B is 1 ,ie A + B <= 1
Person 1: For the toss of two different coins where A is the result from the first and B is the result from the second, the UPPER BOUND of A + B is 2 ie, A + B <= 2
Person 1: Therefore it is inappropriate to apply the UPPER BOUND from the first scenario to an experiment of the second type.
Person 2: Here is some R code, simulating 2 coins of a specific type which shows that the AVERAGEs , <A> + <B> only exceeds 1 very rarely. Therefore it is okay to use the inequality from the first scenario in the second scenario. Oh and by the way, since QM and experiments of the second kind consistently produce values higher than 1, it proves that coins do not actually have two sides.

Just silly.

As usual, you are stupidly attributing notions to me which I do not have. You are so proud that you have logically defeated your straw-man representation of what I actually say or write, that you are not going to learn anything new. Rather sad. Just try the experiment, and then I'll explain why it was so important, even though you thought it was just silly.

You can present your argument without me trying any silly R-code, if I am confused as you say then why do you care that I try the silly R-code or not. Present your argument and convince your self and other "non-confused" on-lookers that you are right. I won't waste my time with your R-code, and you can interpret that anyway you like. If it pleases you, you can even conclude that I have nightmares about R, or that I believe R was responsible for slavery, etc, for all I care.

[gill1109]

Michel, I made you an offer. The offer stands. If you don't accept it, then that's just too bad. Everyone can judge for themselves who is being childish or silly.

I also kindly asked over on the new thread, if you (or anyone else) might care to write a Python version of my R scripts. That might be useful for other people. It would be useful for me, learning Python.

Java and Mathematica versions would also be nice.

A silly computer experiment ... or, the heart of the matter?
http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=40

For me, the present thread is closed for the time being. I await answers on the other. I wanted to explain to you why the answers you got to your three (well, five actually) questions, do not actually lead to the conclusion which you gave at the end of your initial posting in this thread. I think that you jumped to conclusions. I think you missed something important. Too bad for you, if you don't want to know what that might have been.

Right now I have some other important stuff to do.

Draft a protocol for Joy and my bet, cf.
Joy Christian's colourful exploding balls experiment
http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=31

Prepare several lectures.

Learn Python.

Do some statistics for a British "Lucia de B case" cf.
Statistical errors in court: Richard Gill at TEDxFlanders
https://www.youtube.com/watch?v=cbkdhD6BsoY

Write a lot of referee reports.

Enjoy the Spring.

[minkwe]

Person 1: For the toss of a single coin where outcome H = +1 and T = -1, and A is the result you obtain, and B is the other result you could have obtained, the UPPER BOUND of A + B is 1 ,ie A + B <= 1
Person 1: For the toss of two different coins where A is the result from the first and B is the result from the second, the UPPER BOUND of A + B is 2 ie, A + B <= 2
Person 1 conclusion: Therefore it is inappropriate to apply the UPPER BOUND from the first scenario to an experiment of the second type.
Person 2: Person 1 is absolutely right about the first two statements. But his conclusion is false, because statistics and probability, allows me to apply the "bound" from the first scenario to the second scenario. I never talk of "upper bound" I only talk of eh, eh, em ... bound, which is not a "certain" bound but can be violated sometimes, as the following R-code proves, which you must run before I explain to you how that eh, em ... bound was obtained.

Person 3: If the expectation value of A for a single coin does not change when you go from one coin to two of the same kinds of coins, then why should the expression <A> + <B> <= 1, which was derived from a single coin, not also apply to the two separate coins?

Person 2: Person 3, you are home.

[gill1109]

Person 1: For the toss of a single coin where outcome H = +1 and T = -1, and A is the result you obtain, and B is the other result you could have obtained, the UPPER BOUND of A + B is 1 ,ie A + B <= 1
Person 1: For the toss of two different coins where A is the result from the first and B is the result from the second, the UPPER BOUND of A + B is 2 ie, A + B <= 2
Person 1 conclusion: Therefore it is inappropriate to apply the UPPER BOUND from the first scenario to an experiment of the second type.
Person 2: Person 1 is absolutely right about the first two statements. But his conclusion is false, because statistics and probability, allows me to apply the "bound" from the first scenario to the second scenario. I never talk of "upper bound" I only talk of eh, eh, em ... bound, which is not a "certain" bound but can be violated sometimes, as the following R-code proves, which you must run before I explain to you how that eh, em ... bound was obtained.

Persons 1 and 2 are two stupid but fortunately purely imaginary persons who only seem to exist in the mind of Michel Fodje.

One can imagine other persons. For instance:

Person 0: It is completely silly to even imagine that anyone could possibly expect that the upper bound from the first scenario would be an upper bound for the second. But who ever said so? Sensible people said something rather more subtle. They said: after doing some more work, which Michel so far has refused to become aquainted with, one can show that if N is large, then with large probability the experiment will give a result less than the upper bound from the first scenario up to a given small margin of error; e.g., 0.1 (Of course: they are assuming that LHV is true, settings are chosen at random, etc, etc. Just like in real state of the art experiments).

These clever people even know how to figure out how large N must be, so that they can safely bet 5000 Euro's on the outcome: CHSH is less than 2.4 (knowing that the experiment was an experiment on a physical system which had LHV's, and the usual experimental loopholes have been ruled out by a strict experimental protocol).

Michel, I made you an offer. The offer stands. I'm asking for half an hour of your time. In return I'll give you half a day.

If you don't accept the offer, then that's just too bad. Everyone can judge for themselves who is being childish or silly.

[minkwe]

Here is the argument which has been demonstrated in this thread:

1. The CHSH inequality is a statement about the upper bound of a relationship between 4 mutually dependent expectation values.
2. It does not apply to independent terms.
3. The inequality relating mutually independent expectation values has an upper bound of 4 and has never been violated by QM or Aspect-type experiment, nor will it ever be.

Not only have I provided mathematical justification for these points, I've also cited several articles by various other authors, discussing similar arguments at depth.

I have presented a classical analogy using an obviously local realistic case to prove my point: Specifically, coins are clearly local realistic, yet the upper bound for the sum of counterfactual outcomes from a single coin toss is different from the upper bound for the sum of real outcomes from two different coins. No matter how many pairs of coins you throw, you can not change the upper bound, which is determined by the number of degrees of freedom. Presenting one example of a particular type of coin which has an average less than the upper bound does not constitute proof that the upper bound must be the same as in the single coin case. Upper bounds and inequalities especially the CHSH are derived by examining edge cases, not by examining mean values.

Nobody has presented a single mathematical argument against these points. Discussions about R-code belong in another thread.

[FrediFizzx]

Agreed!

[gill1109]

So Joy Christian's proof of the bound 2 sqrt 2 is wrong? (The Tsirelson bound). Are you telling Joy his work is totally wrong?

An upper bound in theory does not imply an upper bound to experiment. Michel is absolutely right but what he says is totally irrelevant. A list of banal trivialities which no one contests.

Experiments give results which have statistical error. Experimenters report error bars. Experimenters report a violation of CHSH of so many standard deviations.

Please take a look at the new thread I have started to learn about this exciting side of real science. I ask you to do an experiment, repeat it a few times, think about the results. It will take half an hour. What is there to lose?

Michel, please write me a Python version of my experiment. I want to learn. John Reed is doing it in Mathematica. I'll ask Chantal for a Java version.