What is wrong with Christian's proof of Tsireson's bound

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

What is wrong with Christian's proof of Tsireson's bound

Postby gill1109 » Mon Apr 07, 2014 11:47 pm

According to QM, in a CHSH type experiment the following bound holds:

E(a, b) - E(a, b') - E(a', b) - E(a', b') <= 2 sqrt 2 = 2.828...

A clear violation of this bound (i.e., taking account of experimental error) has almost never been reported, though many attempts were made.

On the other hand, simulation programs like those of Michel Fodje can easily violate this bound, getting results all the way up to 4.

The bound 2 sqrt 2 was first proven by Boris Tsirelson and later Joy Christian also gave a proof.

According to Michel Fodje and Fred Diether, the only bound one can assert is 4.

Is Joy Christian's work flawed, or are Michel and Fred missing something?

Should the Tsirelson bound follow the CHSH bound to the waste-bin?
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Re: What is wrong with Christian's proof of Tsireson's bound

Postby gill1109 » Mon Apr 07, 2014 11:53 pm

By the way, the bound "4" is called the no-signaling bound. It can be attained through the use of so-called Rohrlich-Popescu boxes. They have so far never been seen. They violate quantum theory, but they do not violate relativity.

Amazingly, it seems that Michel Fodje has already been able to simulate them in a local realist (LHV) way. Actually, Hans de Raedt already did this. Or rather: it is easy to tune parameters in his programs so that this happens, but he never published that finding. He says he only wants to reproduce actual, past, experiments. But if his simulation models are physically meaningful, he has stumbled upon an astounding discovery which totally changes the face of science. Dramatic, major, breakdown of quantum mechanics! Is he scared to announce this finding?

Michel is not scared. He already told us this in forum and email exchanges.

This could be a Nobel prize.
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Re: What is wrong with Christian's proof of Tsireson's bound

Postby Joy Christian » Tue Apr 08, 2014 12:10 am

gill1109 wrote:According to QM, in a CHSH type experiment the following bound holds:

E(a, b) - E(a, b') - E(a', b) - E(a', b') <= 2 sqrt 2 = 2.828...

A clear violation of this bound (i.e., taking account of experimental error) has almost never been reported, though many attempts were made.

On the other hand, simulation programs like those of Michel Fodje can easily violate this bound, getting results all the way up to 4.

The bound 2 sqrt 2 was first proven by Boris Tsirelson and later Joy Christian also gave a proof.

According to Michel Fodje and Fred Diether, the only bound one can assert is 4.

Is Joy Christian's work flawed, or are Michel and Fred missing something?

Should the Tsirelson bound follow the CHSH bound to the waste-bin?


There is nothing wrong with the Tsirelson's bound, or with my local-realistic proof of it: http://arxiv.org/pdf/1101.1958v1.pdf (see also this paper).

As shown in these papers, the bound of 2 sqrt 2 arises because of the torsion T in the physical space. It has nothing whatsoever to do with QM per se.

There is nothing wrong with what Michel and Fred are saying either. Their argument is purely logical argument. And as such quite correct. When one considers a bit of physics (as in the second paper I have linked above), or the full structure of the normed division algebras (as in the first paper I have linked above), then the story is quite different. Then the bound cannot exceed 2 sqrt 2. So, in sum, the logically possible bound is 4. The physically and algebraically possible bound is 2 sqrt 2. But if we ignore both the non-commutative structures of S^3 and S^7 and consider only S^0 and S^1 as the Bell-believers do, then the bound is the dumb bound, namely 2.

By the way, I have already discussed in detail how to generate correlations of any strength in Michel's simulation of my model on this thread: viewtopic.php?f=6&t=29
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Re: What is wrong with Christian's proof of Tsireson's bound

Postby gill1109 » Tue Apr 08, 2014 12:25 am

Good. Joy's bound is 2 sqrt 2, and it is correct. But it is of course theoretical.

Michel says that the only bound which applies to experiment is 4.

Does this mean that it is meaningless to do experiments?
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Re: What is wrong with Christian's proof of Tsireson's bound

Postby gill1109 » Tue Apr 08, 2014 12:27 am

Does this mean that Joy's experiment is meaningless? The bet is meaningless?

The only bound which applies to an experiment is 4.

Aspect, Weihs ... observed a result <= 4 so their experiment was a waste of time, since we knew this would be the case, in advance.

I hereby withdraw from the bet. I am convinced that the only meaningful experimental bound is 4 and no experiment can ever disprove that. Experiments cannot distinguish between theories since experiments can generate any results whatsoever allowed by logic.

Whatever the nature of physical reality, a CHSH experiment can in principle generate any outcome between -4 and 4.
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Re: What is wrong with Christian's proof of Tsireson's bound

Postby minkwe » Tue Apr 08, 2014 7:16 am

gill1109 wrote:According to QM, in a CHSH type experiment the following bound holds:

E(a, b) - E(a, b') - E(a', b) - E(a', b') <= 2 sqrt 2 = 2.828...

A clear violation of this bound (i.e., taking account of experimental error) has almost never been reported, though many attempts were made.

As already explained,
1. that is not a CHSH-type experiment. A CHSH-type experiment produces 4 columns of single-sided data which are recombined in pairs to calculate paired-correlations.
2. There is nothing wrong with 2.828 it is fully consistent with the upper bound of 4 for experiments of that type which produce 8 columns of data in 4 pairs.
3. An upper bound is never violated, never, not even by experimental error, never!!!

Anyone who disagrees, should use any spooky source of data and introduce as much experimental error as they like to:
a) produce a spreadsheet of ONLY 4 columns of +/- results of any length which violates the upper bound of 2.
b) produce a spreadsheet of 8 pairs of columns of data of any length which violates the upper bound of 4.

Hopefully, this falsehood will be put to rest once and for all. Upper bounds are NEVER NEVER NEVER violated.
Feel free to introduce as much experimental error as you like. I'm sure you can write an R script for that. All that I ask is that you maintain the degrees of freedom. 4 columns only for the bound of 2, and 4 pairs of columns ONLY for the upper bound of 4. And you only have to violate the bound by 0.0000001. You can even use QM or any non-local theory of your choosing, no limits there, I don't care where you get the data.

This is a simple challenge and the results should prove once and for all that all talk of upper bounds being violated are illusory.
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Re: What is wrong with Christian's proof of Tsireson's bound

Postby gill1109 » Tue Apr 08, 2014 8:12 am

Michel has not realized that I was deliberately confusing things in my initial posting, in order to imitate his way of arguing.
He argues that CHSH is meaningless.
I reproduced his argument, but replacing CHSH by Tsirelson.
So if Michel's argument is correct, Tsirelson is meaningless too.
Yet Joy Christian thinks that Tsirelson's bound is correct, the CHSH bound is incorrect.
This little conflict should have made Michel think. But no ...


My initial statement was deliberately false. A correct statement should be:

According to QM:

E(a, b) - E(a, b') - E(a', b) - E(a', b') <= 2 sqrt 2 = 2.828...

where E(a, b) etc are correlations predicted by quantum theory.

Therefore in a CHSH type experiment on quantum systems, the following bound will be true with large probability:

F(a, b) - F(a, b') - F(a', b) - F(a', b') <= 2 sqrt 2 plus a few standard deviations

where F(a, b) etc are empirically observed correlations (each based on a different, finite sample of pairs of particles).

minkwe wrote:
gill1109 wrote:According to QM, in a CHSH type experiment the following bound holds:

E(a, b) - E(a, b') - E(a', b) - E(a', b') <= 2 sqrt 2 = 2.828...

A clear violation of this bound (i.e., taking account of experimental error) has almost never been reported, though many attempts were made.

As already explained,
1. that is not a CHSH-type experiment. A CHSH-type experiment produces 4 columns of single-sided data which are recombined in pairs to calculate paired-correlations.
2. There is nothing wrong with 2.828 it is fully consistent with the upper bound of 4 for experiments of that type which produce 8 columns of data in 4 pairs.
3. An upper bound is never violated, never, not even by experimental error, never!!!


What should we learn from all this?

A CHSH experiment, and the CHSH inequality, are two very, very different things.

A CHSH-type experiment generates at the end of the day one data set of four columns, where the first column contains the setting being used by Alice (identified by names or labels, e.g. "1", "2"), the second column contains the setting being used by Bob (identified by names or labels, e.g. "1", "2"), the third column contains the outcome observed by Alice (+/-1), the fourth column contains the outcome observed by Bob (+/-1). Alice and Bob chose their settings by tossing fair coins, independently, again and again. The N rows of the data set correspond to N pairs of particles. Four empirical correlations are then computed or observed, by splitting the data set into four disjoint subsets, according to the pair of values of the settings. Each empirical correlation is just the average of the product of the outcomes within the relevant subset. Obviously an empirical correlation comes with a statistical error, an error bar, or a standard deviation. We get to see some numbers, e.g. 0.72 +/- 0.01, and we conclude that the true (population or ensemble) correlation is, with large probability, within 0.72 plus or minus a few multiples of 0.01. But we might have been very unlucky and our "best guess" might be far from the truth.

Traditionally, for an experiment on spin half particles, Alice's settings "1" and "2" might correspond to directions 0 degrees, 90 degrees; while Bob's settings "1" and "2" might correspond to directions 45 degrees, 135 degrees.

The CHSH inequality is an inequality constraining four theoretical correlations - i.e. population or ensemble averages - if the mathematical model from which those correlations are determined leads to a formula something like E(a, b) = integral A(a, lambda) B(b, lambda) rho(lambda) d lambda). (The formula indeed only makes sense within a LHV theory).

Notice that a CHSH experiment, and the CHSH inequality, are two very, very different things.

The four empirical correlations observed in a CHSH-type experiment can all be anything from -1 to +1, since there is no constraint at all connecting the numbers involved in one of the correlations with those in any of the others. Hence one of the four correlations minus the sum of the other three can be anything between -4 and +4.

Perhaps people who talk of bounds being violated should be a bit more careful in what they say. What do they mean, precisely?

For a very precise statement, see Theorem 1 in my paper http://arxiv.org/abs/1207.5103.
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Re: What is wrong with Christian's proof of Tsireson's bound

Postby minkwe » Tue Apr 08, 2014 10:19 am

minkwe wrote:3. An upper bound is never violated, never, not even by experimental error, never!!!

Anyone who disagrees, should use any spooky source of data and introduce as much experimental error as they like to:
a) produce a spreadsheet of ONLY 4 columns of +/- results of any length which violates the upper bound of 2.
b) produce a spreadsheet of 8 pairs of columns of data of any length which violates the upper bound of 4.

Hopefully, this falsehood will be put to rest once and for all. Upper bounds are NEVER NEVER NEVER violated.
Feel free to introduce as much experimental error as you like. I'm sure you can write an R script for that. All that I ask is that you maintain the degrees of freedom. 4 columns only for the bound of 2, and 4 pairs of columns ONLY for the upper bound of 4. And you only have to violate the bound by 0.0000001. You can even use QM or any non-local theory of your choosing, no limits there, I don't care where you get the data.

This is a simple challenge and the results should prove once and for all that all talk of upper bounds being violated are illusory.
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Re: What is wrong with Christian's proof of Tsireson's bound

Postby minkwe » Tue Apr 08, 2014 11:35 am

gill1109 wrote:Perhaps people who talk of bounds being violated should be a bit more careful in what they say. What do they mean, precisely?

Agreed!

Is Bell's inequality an upper bound or not?
Is the CHSH an upper bound or not?
How can you talk of "violation of an inequality" which is an upper bound, and at the same time not mean "violation of an upper bound"?

So who are those claiming violation of Bell-CHSH inequalities by QM?
http://arxiv.org/pdf/quant-ph/0110137v4.pdf
The violation of the Bell inequalities show that any deterministic, underlying, theory intending to explain the surface randomness of quantum physical predictions, has to be grossly non-local in character.

I wonder what the author meant when he talked of violation of Bell's inequalities by QM.

How can one describe the CHSH-like inequalities as "these inequalities are the bounding hyperplanes of a convex polytope everything allowed by local realism" and then claim that when they talk of violation of the CHSH they do not mean violation of a bound?
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Re: What is wrong with Christian's proof of Tsireson's bound

Postby gill1109 » Tue Apr 08, 2014 11:47 am

minkwe wrote:3. An upper bound is never violated, never, not even by experimental error, never!!!


Terminology.

Suppose that in some area of physics there occurs a quantity called mu. Suppose that according to a certain physical theory, |mu| <= 1.

In other words, mu is unknown, but according to a particular theory, there is a known upper bound to |mu|, namely +1.

Do you agree that the value +1 could be called an upper bound to |mu| ?

Suppose I do an experiment and because of experimental error, my measured value X = mu plus error, and measurement error = the realization of a Gaussian random variable with mean zero and standard deviation 0.1

So if the theory in question were true:

I could possibly observe X = 1.1
I might even observe X = 1.2
I would almost never observe X = 1.5

If I did observe X = 1.5 I would be inclined to reject the theory saying that |mu| <= 1.

Do you agree with this, Michel?

Someone who did the experiment and saw X = 1.5 would say "we experimentally confirmed violation of the ... bound." You seem to be saying that the word "bound" shouldn't be used here at all, since there is no bound to the value of X.

"Violating a bound" means something different when we are talking about theory, from what it means when we are talking about experiment.

My little example exactly parallels the two possible meanings, in connection with the three bounds set by local hidden variables (CHSH bound = 2), the bound set by QM (Tsirelson = 2 sqrt 2), the bound set by no-signalling (no-signalling bound = 4).

If the intelligent writer is talking about theoretical correlations, he or she means "bound" and "violation of bound" in the strict mathematical sense, and the intelligent reader (who understands something about theoretical science) understands that perfectly well.

If the intelligent writer is talking about real world experiments, then by "violation of the bound" he or she means statistically highly significant exceedance of the value set in the theoretical bound, by a decent statistical estimate of the quantity in question; and the intelligent reader (who understands something about experimental science) understands that perfectly well, too.

Think of the CERN physicists, who said they had found the Higgs boson. Actually, the data which they saw was logically consistent with no Higgs. But with no HIggs, it would have been very unlikely to see such a large number (value of some signal, some statistical estimate). If there were a Higgs, then it would be rather likely to see such a large number, as they had seen. Are you saying that they should have kept their mouths shut? And that we never should have built the large Hadron collider, because you can't prove anything with it?

Do you think that experiments are unnecessary, because they can never prove anything? Is that why you won't do my experiment? Because you know that one cannot learn from experiments?
Last edited by gill1109 on Tue Apr 08, 2014 12:06 pm, edited 5 times in total.
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Re: What is wrong with Christian's proof of Tsireson's bound

Postby gill1109 » Tue Apr 08, 2014 11:50 am

minkwe wrote:I wonder what the author meant when he talked of violation of Bell's inequalities by QM.

I have told you many, many times. See Theorem 1 of my paper. What does it say?

When are you going to do my little experiment? I need your help translating that silly bit of R code into Python, because it is part of the code in the evaluation of the outcome of Joy and my bet.
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Re: What is wrong with Christian's proof of Tsireson's bound

Postby minkwe » Tue Apr 08, 2014 1:03 pm

gill1109 wrote:When are you going to do my little experiment? I need your help translating that silly bit of R code into Python, because it is part of the code in the evaluation of the outcome of Joy and my bet.

Your bet with Joy should not depend on what I do or don't do. If you've changed your mind about the bet due to the arguments I've been presenting then that is wise.

But it will be silly if you cancel your bet with Joy just because somebody you call "confused" said something you don't like, and refused to run your R-code or translate it into python.
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Re: What is wrong with Christian's proof of Tsireson's bound

Postby gill1109 » Tue Apr 08, 2014 10:09 pm

Why this obsesion with bounds?

The question is, is E(45) = -0.707 and is E(135) = +0.707 ?

Or is E(45) = -0.5 and is E(135) = +0.5 ?

In an experiment there is always experimental error. N is large but finite so there's always statistical error.

When people say "we observed a violation of CHSH" they just mean that they observed correlations much closer to +/- 0.7 than +/- 0.5, and that the statistical error is much smaller than 0.1, so that one can have confidence that this was not just due to chance.

Why this refusal to help out in the preparations for the great experiment? To translate 20 lines of R into Python? What can you be scared of? Incomprehensible.
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Re: What is wrong with Christian's proof of Tsireson's bound

Postby minkwe » Wed Apr 09, 2014 9:05 am

gill1109 wrote:Why this refusal to help out in the preparations for the great experiment? To translate 20 lines of R into Python? What can you be scared of? Incomprehensible.

Richard, since you asked so nicely, I will translate your R-code into python if Joy agrees that it is needed for the bet. Convince Joy that your R-code is necessary for the bet, and I will translate it for you into Python, C++, JavaScript, and even Ruby.
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Re: What is wrong with Christian's proof of Tsireson's bound

Postby gill1109 » Wed Apr 09, 2014 10:32 am

minkwe wrote:
gill1109 wrote:Why this refusal to help out in the preparations for the great experiment? To translate 20 lines of R into Python? What can you be scared of? Incomprehensible.

Richard, since you asked so nicely, I will translate your R-code into python if Joy agrees that it is needed for the bet. Convince Joy that your R-code is necessary for the bet, and I will translate it for you into Python, C++, JavaScript, and even Ruby.


*My* R-code is not needed. What is needed is an agreed algorithm or protocol. It doesn't matter how it is implemented. The adjudicators can use whichever implementation they prefer. But it's not their job to write computer programs.

I wrote down a precise algorithm in R because R is my native language for this kind of job. But Joy should not trust my R-code. He should not trust my interpretation of the English sentences which we wrote to one another.

I'll ask him it he would appreciate your help in making sure my code is a correct implementation of our agreed algorithm, by generating some translations into more languages, so that more people can all independently see it is OK.

This is a great opportunity for me to learn some more of those great programming languages which you mentioned, by studying your code and testing both implementations.
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