gill1109 wrote:This is the letter I am thinking of sending to the adjudicators:

Nice letter, but in the mean time a new argument has emerged that "b" may be fixed in my simulation. I would like to investigate that further before we proceed.

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gill1109 wrote:This is the letter I am thinking of sending to the adjudicators:

Nice letter, but in the mean time a new argument has emerged that "b" may be fixed in my simulation. I would like to investigate that further before we proceed.

- Joy Christian
- Research Physicist
**Posts:**2370**Joined:**Wed Feb 05, 2014 4:49 am**Location:**Oxford, United Kingdom

Joy Christian wrote:minkwe wrote:Heinera wrote:First the code loops on i (the alpha angles), and then on j (the beta angles).

But the assignment to the correlations corrs[i] within the j-loop only has one index i. So for each new value of j, the previous assignment to corrs[i] is simply forgotten and overwritten. So at the end of the loop, we end up with corrs[i] dependent only on angles[K-1] (the last assignment to beta). All other values of beta are irrelevant. Agree?

That is a fair criticism.

How is this equivalent to "b" being fixed? It seems to me that the last assignment of beta can take any value.

The criticism is that the value is overwritten by the next assignment. The outer loop runs K times, the inner loop runs K*K times, there are only K values of corrs. The only effective corrs value is then only the last one calculated.

- minkwe
**Posts:**1151**Joined:**Sat Feb 08, 2014 10:22 am

Joy Christian wrote:gill1109 wrote:This is the letter I am thinking of sending to the adjudicators:

Nice letter, but in the mean time a new argument has emerged that "b" may be fixed in my simulation. I would like to investigate that further before we proceed.

Sure. No hurry. I don't want to send them the letter if we are not pretty sure we are going to be going ahead, pretty soon.

The challenge is open. It stands. It's a Randi-type challenge. Everything is on record. I respect your wish to temporarily freeze and possibly withdraw your present submission. I did not do anything with it yet ... You may withdraw it or give it the go ahead, as you please, when you are ready. If after *withdrawal* of this submission you wish to make a new submission, you are always welcome (well - unless someone else in the meantime has been successful). But once you proceed you only have one chance to win the hearts and/or minds of the adjudicators.

The draft letter to the adjudicators is on record. We know who we have in mind to ask for this job. I'm rather pleased with the letter, myself! We made a very great deal of progress today.

- gill1109
- Mathematical Statistician
**Posts:**1943**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

minkwe wrote:1) Is Joy's simulation local-realistic or not? If not state precisely where in the code.

2) Does any of the correlations E(a,b) deviate from the QM prediction by more than 0.2 or not? (Simply look at the plot. or point out precisely why you believe the calculation of the plot is in error, the code is public).

Regarding the second question: A plot of one curve is not enough if we want to inspect four points on a surface. Four points which do not lie above a straight line in the x-y plane. The four points lie on the corners of a square in the x-y plane (a square aligned with the x and y axes).

It is not difficult to plot the correlation surface and then you immediately see massive failure of many of the correlations.

Regarding the first question: The present simulation is local-realistic, that is easy to see.

I suspect that that is why it fails to deliver! (At least, as far as I can see).

Before rushing in to tell me how mean and stupid I am, you ought at least to read the posting early on in this topic where the challenge (not a bet, really) is spelt out. The wording of the challenge was agreed, for 100%, by Christian and me. We drew it up together.

You can advise Christian to withdraw, if you think he was unwise to accept that wording.

The challenge makes perfectly clear what each of us has to do, in turn. So you don't have to tell me what I have to do. I receive a file from Christian, process it according to the challenge's instructions, deliver my verdict. If Joy disagrees with my verdict we refer to our adjudicators. They decide and either I pay or I don't. Pretty clear, don't you think?

Do you think the challenge is stupid because no one can win it? Well if so please try and explain that to our friend Christian. I tried, but did not succeed. This shows that it is not a stupid challenge. It has a pedagogical function. Nobody loses (except I might lose a lot of money), everyone can learn something. The challenge remains open till someone wins it, or I die or am legally declared insolvent or insane or equivalent.

- gill1109
- Mathematical Statistician
**Posts:**1943**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

Zen asked me to run and post an R script which draws Christian's correlation surface

http://rpubs.com/gill1109/ZenSurface

Red is JC, blue is QM

http://rpubs.com/gill1109/ZenSurface

Red is JC, blue is QM

- gill1109
- Mathematical Statistician
**Posts:**1943**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

[quote="gill1109"]Zen asked me to run and post an R script which draws Christian's correlation surface

http://rpubs.com/gill1109/ZenSurface

Nice!

Now we are making progress. I see these images as both good news and bad news. Note that my LHV surface is a massive improvement over the traditional LHV surface (or Bell-CHSH surface). But the images also reveal that the surfaces do not match perfectly.

Good. So now I go back and work on the current model a little more. Note that, despite the confusion by Satori (who is a reincarnation of Zen) on the FQXi blog, the current model is for the very specific purpose of generating the 2 x N vectors involved in my experiment. The most accurate simulation of my analytical model is still this one: http://rpubs.com/jjc/13965.

http://rpubs.com/gill1109/ZenSurface

Nice!

Now we are making progress. I see these images as both good news and bad news. Note that my LHV surface is a massive improvement over the traditional LHV surface (or Bell-CHSH surface). But the images also reveal that the surfaces do not match perfectly.

Good. So now I go back and work on the current model a little more. Note that, despite the confusion by Satori (who is a reincarnation of Zen) on the FQXi blog, the current model is for the very specific purpose of generating the 2 x N vectors involved in my experiment. The most accurate simulation of my analytical model is still this one: http://rpubs.com/jjc/13965.

Last edited by Joy Christian on Sun May 04, 2014 12:35 am, edited 3 times in total.

- Joy Christian
- Research Physicist
**Posts:**2370**Joined:**Wed Feb 05, 2014 4:49 am**Location:**Oxford, United Kingdom

Chán is the Chinese form of the Japanese Zen, Sankskit Dhyāna, English closest equivalent: "enlightenment"

Satori is Japanese for Sanskrit Prajñā, English closest equivalent: "meditation"

Mr (or as far as I know, Ms) Chán Satori is an excellent programmer and a very sharp analyst.

I hope that soon that he'll have his own Rpubs site too ...

It would be fun to add the four crucial points to these two surfaces, so that we can better see where the maximal pain is being experienced. I love playing with R scripts myself but I really must break my addiction for a couple of days and do some other pressing work ... and after that go on vacation without my computer ...

Alongside of R, I highly recommend Buddhism and in particular Vipassana meditation. Though I am only a pre-novice myself. Programming is a form of meditation. It teaches one how to de-program, and to be aware of hidden programs. Some time I might write a book "Zen and the art of R programming" (if it hasn't already been done).

The Zen of R has been done: http://rpubs.com/gill1109/ZenOfR

Satori is Japanese for Sanskrit Prajñā, English closest equivalent: "meditation"

Mr (or as far as I know, Ms) Chán Satori is an excellent programmer and a very sharp analyst.

I hope that soon that he'll have his own Rpubs site too ...

It would be fun to add the four crucial points to these two surfaces, so that we can better see where the maximal pain is being experienced. I love playing with R scripts myself but I really must break my addiction for a couple of days and do some other pressing work ... and after that go on vacation without my computer ...

Alongside of R, I highly recommend Buddhism and in particular Vipassana meditation. Though I am only a pre-novice myself. Programming is a form of meditation. It teaches one how to de-program, and to be aware of hidden programs. Some time I might write a book "Zen and the art of R programming" (if it hasn't already been done).

The Zen of R has been done: http://rpubs.com/gill1109/ZenOfR

- gill1109
- Mathematical Statistician
**Posts:**1943**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

Joy Christian wrote:Nice!

Now we are making progress. I see these images as both good news and bad news. Note that my LHV surface is a massive improvement over the traditional LHV surface (or Bell-CHSH surface). But the images also reveal that the surfaces do not match perfectly.

Actually not. For some pints it is an improvement, for orher points it performs worse. If you take the average absolute difference between your surface and the QM surface, it persforms as bad as the picewice linear Bell surface.

- Heinera
**Posts:**767**Joined:**Thu Feb 06, 2014 1:50 am

Heinera wrote:Joy Christian wrote:Nice!

Now we are making progress. I see these images as both good news and bad news. Note that my LHV surface is a massive improvement over the traditional LHV surface (or Bell-CHSH surface). But the images also reveal that the surfaces do not match perfectly.

Actually not. For some pints it is an improvement, for orher points it performs worse. If you take the average absolute difference between your surface and the QM surface, it persforms as bad as the picewice linear Bell surface.

I disagree. I have run the R script for 10^6 and 10^7 trials, and the wrinkles in the LHV surface smooth out considerably for these larger number of trials. They do not go away, however, and so there are indeed specific points where my (current) LHV model does worse than the Bell-CHSH model.

- Joy Christian
- Research Physicist
**Posts:**2370**Joined:**Wed Feb 05, 2014 4:49 am**Location:**Oxford, United Kingdom

Joy Christian wrote:Heinera wrote:Joy Christian wrote:Nice!

Now we are making progress. I see these images as both good news and bad news. Note that my LHV surface is a massive improvement over the traditional LHV surface (or Bell-CHSH surface). But the images also reveal that the surfaces do not match perfectly.

Actually not. For some pints it is an improvement, for orher points it performs worse. If you take the average absolute difference between your surface and the QM surface, it persforms as bad as the picewice linear Bell surface.

I disagree. I have run the R script for 10^6 and 10^7 trials, and the wrinkles in the LHV surface smooth out considerably for these larger number of trials. They do not go away, however, and so there are indeed specific points where my (current) LHV model does worse than the Bell-CHSH model.

I have published an R script where average performance is computed:

http://rpubs.com/heinera/16559

- Heinera
**Posts:**767**Joined:**Thu Feb 06, 2014 1:50 am

Heinera wrote:I have published an R script where average performance is computed:

http://rpubs.com/heinera/16559

Wonderful pictures guys! Could you add onto the surfaces four little balls marking the four CHSH correlations? Just so that we can see what they look like, and where they are?

QM has three of them as low as possible while at the same time just one of them is as high as possible. One of many equivalent ways to say that is that if you want to maximise the sum of - rho(a1, b1) + rho(a1, b2) - rho(a2, b1) - rho(a2, b2) under QM, then your best choice is a1 = 0, a2 = 90, b1 = 45, b2 = 135. Tsirelson's theorem shows that this is not only optimal *given* the singlet state and just optimizing over von Neumann measurements, but also optimal over all possible joint states, of whatever dimension Hilbert spaces you like, and over generalised as well as von Neumann measurements; in other words, over the largest possible class of states and measurements allowed within conventional QM. That's quite some theorem...

The Tsirelson choice makes directions a1 and b2 as "opposite as possible" while a1 and b1, and b1 and a2, and a2 and b2 are all as "close together" as possible. There are deep connections with inequalities of Grothendieck and really difficult stuff in geometry and functional analysis ...

Under the Bell model, your best choice is at the same directions but does not do so well as QM. All LHV models are contained within the class of all quantum models, so Tsirelson already says that Bell can't do as well as this particular QM model.

- gill1109
- Mathematical Statistician
**Posts:**1943**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

gill1109 wrote:Tsirelson's theorem shows that this is not only optimal *given* the singlet state and just optimizing over von Neumann measurements, but also optimal over all possible joint states, of whatever dimension Hilbert spaces you like, and over generalised as well as von Neumann measurements; in other words, over the largest possible class of states and measurements allowed within conventional QM. That's quite some theorem...

Tsirelson's theorem is easy to understand. It is a consequence of the topological structure of S^7, which is of course deeply connected to the four possible division algebras: http://arxiv.org/abs/1101.1958. See especially the concluding section of this paper for the physical significance of the theorem.

- Joy Christian
- Research Physicist
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Joy Christian wrote:gill1109 wrote:Tsirelson's theorem shows that this is not only optimal *given* the singlet state and just optimizing over von Neumann measurements, but also optimal over all possible joint states, of whatever dimension Hilbert spaces you like, and over generalised as well as von Neumann measurements; in other words, over the largest possible class of states and measurements allowed within conventional QM. That's quite some theorem...

Tsirelson's theorem is easy to understand. It is a consequence of the topological structure of S^7, which is of course deeply connected to the four possible division algebras: http://arxiv.org/abs/1101.1958. See especially the concluding section of this paper for the physical significance of the theorem.

You mean Christian's theorem. Surely, there are no Hilbert spaces in Christian's http://arxiv.org/abs/1101.1958 ? Tsirelson's theorem is a mathematical theorem (a tautology) about Hilbert space geometry. Christian's theorem is (I presume) a mathematical theorem (a tautology) about division algebras.

Are you saying that all of conventional quantum theory, including all the Hilbert spaces, the POVM's, etc etc can be *derived* from a mathematical structure grounded on division algebras? If that were true, it would be a very exciting theorem.

I think you claim that Tsirelson's bound,the number 2 sqrt 2, also turns up in an analogous investigation of parallelizable manifolds where you have introduced your own novel concept of correlation.

"The corresponding parallelizing torsion T then naturally provides a measure of this strength, and the maximum of all possible parallelizing torsions within all possible parallelizable manifolds imposes an absolute upper bound—i.e., the Tsirel’son bound—on the strength of all causally possible correlations."

So you found the same bound in a framework in which there are some analogous mathematical structures; you did not derive the theorem. To derive the theorem you would need a representation theory, embedding *all of conventional QM mathematical structures* within your theory. But you do not do this. Your whole program is to do *without* the conventional QM mathematical structures. They are abolished, replaced by what you define as LHV structures.

Last edited by gill1109 on Sun May 04, 2014 5:38 am, edited 1 time in total.

- gill1109
- Mathematical Statistician
**Posts:**1943**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

gill1109 wrote:Are you saying that all of conventional quantum theory, including all the Hilbert spaces, the POVM's, etc etc can be *derived* from a mathematical structure grounded on division algebras? If that were true, it would be a very exciting theorem.

See the "exciting" theorem on the page 12 of this paper: http://arxiv.org/abs/1201.0775 (the proof goes all the way up to page 16).

- Joy Christian
- Research Physicist
**Posts:**2370**Joined:**Wed Feb 05, 2014 4:49 am**Location:**Oxford, United Kingdom

Joy Christian wrote:gill1109 wrote:Are you saying that all of conventional quantum theory, including all the Hilbert spaces, the POVM's, etc etc can be *derived* from a mathematical structure grounded on division algebras? If that were true, it would be a very exciting theorem.

See the "exciting" theorem on the page 12 of this paper: http://arxiv.org/abs/1201.0775.

A "Theorema Egregium" is a remarkable theorem. It would certainly be a remarkable theorem if it were true. You did not give us a reference to the proof of the theorem. I did not yet see Atiyah, Penrose and so on getting wildly excited about it. Nor anyone citing it. Sorry, I am moving in the direction of "snide remarks" and I honestly want to avoid them. Which means not talking at all about certain subjects.

We have indeed gone wildy off topic here.

- gill1109
- Mathematical Statistician
**Posts:**1943**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

gill1109 wrote:I did not yet see Atiyah, Penrose and so on getting wildly excited about it.

That is thanks to you and your friends. You have been spooking them all (and indeed the whole community) out about anything I have to say.

- Joy Christian
- Research Physicist
**Posts:**2370**Joined:**Wed Feb 05, 2014 4:49 am**Location:**Oxford, United Kingdom

Joy Christian wrote:gill1109 wrote:I did not yet see Atiyah, Penrose and so on getting wildly excited about it.

That is thanks to you and your friends. You have been spooking them all (and indeed the whole community) out about anything I have to say.

I don't know Atiyah and I only rarely bump into Sir Roger Penrose. I certainly haven't said anything to them about your work. As far as I know, the "heavy duty" guys at the interface between pure mathematics and mathematical physics, ie algebraic topology <-> string theory, don't know anything about your work, never talk about it. I know some of them and never ever was your work raised in conversation. ie neither by me, neither by them. Those pure math guys don't take any notice what the people in quantum information are doing. Many are even more computer scientists than mathematicians, hardly any know what is a topos or a category even, for that matter.

I don't think "me and my friends" have anything whatsoever to do with the lack of interest shown in your work in the one place where one might have hoped that it would have been noticed. Worlds apart. Non-communicating vessels.

I won't tell you my opinion either of string theory or of algebraic topology.

I do communicate occasionally with Klaas Landsman. He always thought I was crazy to have any interest whatsoever in your work. So we never discussed in further, together.

So apparently he had noticed it about the same time I had, drawn his own conclusions, and forgotten about it again.

- gill1109
- Mathematical Statistician
**Posts:**1943**Joined:**Tue Feb 04, 2014 10:39 pm**Location:**Leiden

gill1109 wrote:I do communicate occasionally with Klaas Landsman. He always thought I was crazy to have any interest whatsoever in your work. So we never discussed in further, together.

So apparently he had noticed it about the same time I had, drawn his own conclusions, and forgotten about it again.

Well, I know Klaas very well. If what you are reporting about his reaction is true, then it tells more about the deep-seated prejudices in the community than about my work. I don't think you can know anything about anyone's work unless you spend considerable amount of time studying it, even if you were Klaas Landsman.

- Joy Christian
- Research Physicist
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I have published a 2D surface simulation of my 3-sphere model for the EPR-Bohm correlation: http://rpubs.com/jjc/16567.

- Joy Christian
- Research Physicist
**Posts:**2370**Joined:**Wed Feb 05, 2014 4:49 am**Location:**Oxford, United Kingdom

Joy Christian wrote:I have published a 2D surface simulation of my 3-sphere model for the EPR-Bohm correlation: http://rpubs.com/jjc/16567.

Sigh. Back to Pearle's model then. This looks more and more like an infinite loop.

- Heinera
**Posts:**767**Joined:**Thu Feb 06, 2014 1:50 am

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