Another Response to Richard Gill's 10,000 Euros Challenge

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

Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby FrediFizzx » Mon Jun 09, 2014 11:07 pm

gill1109 wrote:
FrediFizzx wrote:The "bug" was fixed in the code I posted above. And Rick was online after I posted my question to him. I guess he can't now explain why he thinks it has nothing to do with 3-sphere geometry. I was hoping Rick would make an attempt at it.

Good morning, Fred! I think that what Rick was worried about, was not a bug which by now is fixed.

Well, the "bug" was removed so I am not sure what Rick was fretting about. Unless there was some kind of delay and he didn't see the code I posted. If he thinks what Joy is doing in the simulation is not related to 3-sphere geometry, I would certainly like to see his opinion of why not.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby Ben6993 » Mon Jun 09, 2014 11:59 pm

Hi Richard
If you have not found the draft letter yet,try this one:


Re: The (still) open one-sided bet.
Postby gill1109 » Sat May 03, 2014 12:15 pm

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

Dear ...

Recently I emailed you telling you that a certain bet I had made with Joy Christian was called off. At the time I was rather angry and pretty determined not to have anything to do with him again, but in the meantime my anger abaited somewhat and after some further contacts we came to a new agreement concerning the following challenge: ...

We would like to ask you if you would be prepared to adjudicate a submission to this challenge, just once. We moreover believe that very little work is required of you, and all that you will be required to produce is a yes/no answer to a simple question.

The procedure is: Christian submits a computer file to Gill who processes it to the best of his ability according to his interpretation of the rules set out in the challenge. (Gill and Christian have formulated these rules together, and both believe they are unambiguous).

He either accepts that Christian has succeeded, or he claims that Christian has failed.

In the latter case, and in the latter case only, and once only, you are asked to adjudicate.

Christian might submit some supporting material arguing why he disagrees with my conclusion. Up to you what you make of it.

Your decision is final and binding on all parties and no appeal is possible, no correspondence with the jury is allowed (on the subject of the challenge) either during their deliberations or after their conclusion is announced.

Christian and Gill expect to submit materials in a few days and would be delighted if the jury could come to a conclusion before the coming Vaxjo conference.

On Gill's side the only material expected would be the data file (which is not going to be very large at all) and an R script generating the numbers on the basis of which he comes to his initial decision. He has Python, Perl, and Excel versions available too (which have been tested on similar data sets to all give the same answer). These scripts are short and transparent. (It is a question of calculating four correlations). However, it must be emphasized that the jury is free to use whatever computer tools they like to get the answers. Their essential task is to independently calculate the four numbers described in the challenge.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby gill1109 » Tue Jun 10, 2014 12:35 am

Ben6993 wrote:Hi Richard
If you have not found the draft letter yet,try this one:


Re: The (still) open one-sided bet.
Postby gill1109 » Sat May 03, 2014 12:15 pm

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

Dear ...

Recently I emailed you telling you that a certain bet I had made with Joy Christian was called off. At the time I was rather angry and pretty determined not to have anything to do with him again, but in the meantime my anger abaited somewhat and after some further contacts we came to a new agreement concerning the following challenge: ...

We would like to ask you if you would be prepared to adjudicate a submission to this challenge, just once. We moreover believe that very little work is required of you, and all that you will be required to produce is a yes/no answer to a simple question.

The procedure is: Christian submits a computer file to Gill who processes it to the best of his ability according to his interpretation of the rules set out in the challenge. (Gill and Christian have formulated these rules together, and both believe they are unambiguous).

He either accepts that Christian has succeeded, or he claims that Christian has failed.

In the latter case, and in the latter case only, and once only, you are asked to adjudicate.

Christian might submit some supporting material arguing why he disagrees with my conclusion. Up to you what you make of it.

Your decision is final and binding on all parties and no appeal is possible, no correspondence with the jury is allowed (on the subject of the challenge) either during their deliberations or after their conclusion is announced.

Christian and Gill expect to submit materials in a few days and would be delighted if the jury could come to a conclusion before the coming Vaxjo conference.

On Gill's side the only material expected would be the data file (which is not going to be very large at all) and an R script generating the numbers on the basis of which he comes to his initial decision. He has Python, Perl, and Excel versions available too (which have been tested on similar data sets to all give the same answer). These scripts are short and transparent. (It is a question of calculating four correlations). However, it must be emphasized that the jury is free to use whatever computer tools they like to get the answers. Their essential task is to independently calculate the four numbers described in the challenge.

Thanks Ben! That is the one I was thinking of.

I will email to Andrei, Hans and Gregor straight away. (In fact I am in a lecture room in Vaxjo at the moment and they are all within 20 meters of me, I believe...)

PS email has now been sent.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby gill1109 » Tue Jun 10, 2014 1:11 am

Joy Christian wrote:Now who has been adding ad hoc restrictions, Gill or me? He has been changing the rules of his challenge every time it has been defeated by me or others. If you make a challenge which says, "prove 2 = 3", then, sure, the challenge can't be won. But then it has also nothing to do with the real world. Physics is littered with high profile examples where intuitions of mathematicians have been proven totally wrong and misguided. I believe in the case of my work yours and Gill's mathematical intuitions are totally off the mark. EPR-Bohm experiments are about actual, laboratory physics, with physical systems, detectors, and so on, not about mathematics.

My challenge is of the following kind: "give me two positive integers p and q such that p^2 = 2 q^2 (ordinary arithmetic...), and if you can do that before June 11, I'll give you 10 000 Euro".

Anyone who knows a bit of mathematics knows Euclid's proof that square root of 2 is irrational. So they know that it can't be done.

Physics is littered with high profile examples where intuitions of physicists have been proven totally wrong and misguided. Christian's theory is a physicist's theory, and his experiment is about a physical experiment which in principle could be done today. Unfortunately, "the good outcome" to the experiment is a logical impossibility. This tells us something about the thinking of the physicist.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby gill1109 » Tue Jun 10, 2014 1:29 am

I posted my evaluation of Christian's submission of a few days ago as an R notebook

http://rpubs.com/gill1109/christian-test

The R script assumes you have downloaded the two files so that they are locally available in your R working directory. I'll put them up on internet and adapt the script so that it reads my current copy of the files from "my" cloud.

The "punchline" is

Code: Select all
 
E(0, 45)  E(0, 135)  E(90, 45) E(90, 135)
   -0.6262     0.6325    -0.3542    -0.3872

(though I keep seeing typos which need fixing, so this might change...)

PS. I fixed some typos, uploaded files to internet, gave them ".csv" extension name and gave the first column a name (which actually is just the row number). I updated my script so that it reads the files from internet, instead of locally.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby Joy Christian » Tue Jun 10, 2014 3:31 am

gill1109 wrote:I posted my evaluation of Christian's submission of a few days ago as an R notebook
http://rpubs.com/gill1109/christian-test.

Gill's R script has nothing whatsoever to do with his challenge, or my refutation of his contentions. The terms of his challenge are spelt out by him here and here. Evidently, his challlange is about my proposed experiment. My proposed experiment is about testing my local model for the EPRB correlation. My local model for the EPRB correlation is based on my hypothesis that we live in a parallelized 3-sphere, S^3, and our usual perception that we live in R^3 is just an illusion.

The idea behind the simulation of the experiment is thus to produce N spin vectors that are consistent with the geometry and topology of the 3-sphere. In my proposed experiment the experimenters are supposed to follow the procedure described on the page 4 of my paper. They are supposed to observe N spin directions, record them as N points of S^2, and calculate the correlations using eq. (16) of my paper. What they will find is what I have predicted, theoretically, in this simulation (modulo experimental errors): http://rpubs.com/jjc/19298. A much more detailed theoretical description of my local model can be found here.

The evidence presented in the above simulation is completely consistent with the terms of the Gill challenge. To reiterate: (1) a single set of spin directions u_k for Alice is used to calculate all four correlations, the negative of which, -u_k, being the spin directions used for Bob; (2) the same number of trials, N = 7070, is used in the calculations of all four correlations; and (3) the standard dot product, in the standard formula for the mean value, is used to calculate all four correlations. That is what Gill has been demanding. These calculations are not only fully consistent with the terms of the Gill challenge, but also with the eq. (16) of my paper.

The straight forward calculations computed in my R script give the following results:

alpha <- 0 * pi/180
beta <- 45 * pi/180
a <- c(cos(alpha), sin(alpha))
b <- c(cos(beta), sin(beta))
ca <- colSums(u * a) ## Inner products of cols of 'u' with 'a'
cb <- colSums(u * b) ## Inner products of cols of 'u' with 'b'
(E_0_45 <- sum(sign(ca) * sign(-cb))/N)

## [1] -0.6993

(N)

## [1] 7070

alpha <- 0 * pi/180
beta <- 135 * pi/180
a <- c(cos(alpha), sin(alpha))
b <- c(cos(beta), sin(beta))
ca <- colSums(u * a) ## Inner products of cols of 'u' with 'a'
cb <- colSums(u * b) ## Inner products of cols of 'u' with 'b'
(E_0_135 <- sum(sign(ca) * sign(-cb))/N)

## [1] 0.703

(N)

## [1] 7070

alpha <- 90 * pi/180
beta <- 45 * pi/180
a <- c(cos(alpha), sin(alpha))
b <- c(cos(beta), sin(beta))
ca <- colSums(u * a) ## Inner products of cols of 'u' with 'a'
cb <- colSums(u * b) ## Inner products of cols of 'u' with 'b'
(E_90_45 <- sum(sign(ca) * sign(-cb))/N)

## [1] -0.699

(N)

## [1] 7070

alpha <- 90 * pi/180
beta <- 135 * pi/180
a <- c(cos(alpha), sin(alpha))
b <- c(cos(beta), sin(beta))
ca <- colSums(u * a) ## Inner products of cols of 'u' with 'a'
cb <- colSums(u * b) ## Inner products of cols of 'u' with 'b'
(E_90_135 <- sum(sign(ca) * sign(-cb))/N)

## [1] -0.7276

(N)

## [1] 7070

## The Bell-CHSH inequality is violated:

abs(E_0_45 - E_0_135 + E_90_45 + E_90_135)

## [1] 2.829

Please note that the terms of the Gill challenge are duly satisfied. Only a single set of 7,070 u-vectors is used, in the standard calculations of the correlations.

The reason why Gill is getting wrong results is because he has departed from my model and constructed his own unphysical model , which gives him the wrong results.
Last edited by Joy Christian on Tue Jun 10, 2014 5:10 am, edited 9 times in total.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby gill1109 » Tue Jun 10, 2014 3:49 am

It's not so difficult to arrange that the value of N is the same in each correlation. Unfortunately the list of N directions u is different, for each of the four calculations which Christian presents here.

And apparently Christian has now created a different pair of data sets. A few days ago the number of lines in the files AliceDirections.txt and BobDirections.txt was 6912

Those are the files I have sent to our hoped-for adjudicators
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby Joy Christian » Tue Jun 10, 2014 3:55 am

gill1109 wrote:It's not so difficult to arrange that the value of N is the same in each correlation. Unfortunately the list of N directions u is different, for each of the four calculations which Christian presents here.

And apparently Christian has now created a different pair of data sets. A few days ago the number of lines in the files AliceDirections.txt and BobDirections.txt was 6912

Those are the files I have sent to our hoped-for adjudicators


I have not changed anything apart from inserting "(N)" after each calculation to exhibit the number N = 7,070. This was your suggestion, and it is a good suggestion.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby gill1109 » Tue Jun 10, 2014 7:59 am

Joy, will you please check that the two files

http://www.math.leidenuniv.nl/~gill/AliceDirections.csv

http://www.math.leidenuniv.nl/~gill/BobDirections.csv

are the two files which you submitted?

They each have (apart from the header) 6912 lines, each line containing a sequence number, an x coordinate, and a y coordinate.

You should be able to open them in any decent spreadsheet software.

These are the files which I sent to the adjudicators. I don't want to cause them extra work by having to tell them to replace those files by others. This is urgent.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby Joy Christian » Tue Jun 10, 2014 8:48 am

gill1109 wrote:Joy, will you please check that the two files

http://www.math.leidenuniv.nl/~gill/AliceDirections.csv

http://www.math.leidenuniv.nl/~gill/BobDirections.csv

are the two files which you submitted?

They each have (apart from the header) 6912 lines, each line containing a sequence number, an x coordinate, and a y coordinate.

You should be able to open them in any decent spreadsheet software.

These are the files which I sent to the adjudicators. I don't want to cause them extra work by having to tell them to replace those files by others. This is urgent.


I am not sure why the number N in your files is different from how it appears in my simulation: http://rpubs.com/jjc/19298.

I have made only two harmless changes in the R script since my initial submission:

(1) I have fixed the "bug" Rick pointed out, which did not change any numbers, especially N = 7,070 (because the "bug" was completely harmless), and

(2) I have inserted "(N)" after each calculation to exhibit the number N = 7,070, following your suggestion (which, as I said above, was a good suggestion).

I will ask Fred if he can figure out what is going on, because he created the .csv files for me (but, as you know, my R script itself can be used for the evaluation).
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby gill1109 » Tue Jun 10, 2014 9:01 am

Please create new files, then ... it is nearly June 11 in Växjö. In fact, you have less than 6 hours left. Otherwise we use the old files.

You could alternatively try adding two "write.csv" commands to your script, so that anyone can make the files myself, but then the script needs to be posted to internet before midnight on mainland Europe.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby Joy Christian » Tue Jun 10, 2014 9:10 am

gill1109 wrote:Please create new files, then ... it is nearly June 11 in Växjö. In fact, you have less than 6 hours left. Otherwise we use the old files.

You could alternatively try adding two "write.csv" commands to your script, so that anyone can make the files myself, but then the script needs to be posted to internet before midnight on mainland Europe.


I can easily add the "write.csv" command in my R script and repost it if you can please let me know the exact command.

That would be best, because Fred is 8 hours behind us, and he has to work during the day time.

Thanks.

PS: Actually, the two "write.csv" commands already exist in my R script. So you already have everything you need here: http://rpubs.com/jjc/19298.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby gill1109 » Tue Jun 10, 2014 9:24 am

Joy Christian wrote:
gill1109 wrote:Please create new files, then ... it is nearly June 11 in Växjö. In fact, you have less than 6 hours left. Otherwise we use the old files.

You could alternatively try adding two "write.csv" commands to your script, so that anyone can make the files myself, but then the script needs to be posted to internet before midnight on mainland Europe.


I can easily add the "write.csv" command in my R script and repost it if you can please let me know the exact command.

That would be best, because Fred is 8 hours behind us, and he has to work during the day time.

Thanks.

PS: Actually, the two "write.csv" commands already exist in my R script. So you already have everything you need here: http://rpubs.com/jjc/19298.

OK I just created two files. They each have 7070 rows and three columns (and a header row). The first column is unnamed, the next two are named "t" and "w". Do they stand for what used to be called "x" and "y"?

PS I changed the names of the variables in the header, uploaded them to my cloud, and updated my R script
http://rpubs.com/gill1109/christian-test

Please verify that these are indeed your submitted files and that columns 2 and 3 indeed stand for x and y coordinates.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby Joy Christian » Tue Jun 10, 2014 9:33 am

gill1109 wrote:OK I just created two files. They each have 7070 rows and three columns (and a header row). The first column is unnamed, the next two are named "t" and "w". Do they stand for what used to be called "x" and "y"?

PS I changed the names of the variables in the header, uploaded them to my cloud, and updated my R script
http://rpubs.com/gill1109/christian-test

Please verify that these are indeed your submitted files and that columns 2 and 3 indeed stand for x and y coordinates.


I quote myself from my initial post, which should answer your questions:

Joy Christian wrote:For technical reasons of producing the text files from the R script, Fred and I have had to separate out the x and y components of the u matrix and bind them again in the matrix e = cbind(t,w), as defined in the R script. But I have also left the directions tables from the u matrix in the script, just in case someone has difficulty using the x and y components generated from the e matrix. Note also that Fred has checked the e-lists against the u output and the "good" truth table, and they match.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby Rick Lockyer » Tue Jun 10, 2014 10:09 am

Sorry but no, the bug was not fixed. I really could not care less if you write a program with the exceptionally bad practice of later using variable values assigned within the body of loops. The bug was the colSums were over 10000 values, yet the E_'s were calculated by dividing by 7070 and NOT 10000, artificially inflating their absolute values. That was the "bug" and it remains in Joy's latest RPub. What does the u array have to do with the cherry picked 7070 element e that goes into the .csv files for submission anyway? I see no justification coming out of the use of the full u anyway, and when properly scaled they come out around +/- 0.5 as one would (should) expect. The cherry picked e looks ad hoc and not something 3-sphere geometry demands. Not my job to demonstrate it is not, which is a significantly more difficult task than showing mathematically how it is required by the geometry. There has been a progression of different algorithms to do this cherry picking, each with its own element of ad hocness. I think if the geometry demanded it, there would be one and only one, and it could be rigorously derived mathematically, which has not been done by Joy to date. The triangle inequality hand waving includes an ad hoc expression inserted without stated justification. Show me the rigorous math for the current one, I am sure I will understand it.

Fred, just because someone has not logged out, it does not mean they are paying attention, or care to take the time for an immediate reply. Beyond that, I have routinely left discussions after someone else's rebuttal of my position, even if I was not convinced by their arguments, even if they were blatantly out of touch with reality. A certain quacking duck comes to mind.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby Joy Christian » Tue Jun 10, 2014 10:30 am

Rick Lockyer wrote:Sorry but no, the bug was not fixed. I really could not care less if you write a program with the exceptionally bad practice of later using variable values assigned within the body of loops. The bug was the colSums were over 10000 values, yet the E_'s were calculated by dividing by 7070 and NOT 10000, artificially inflating their absolute values. That was the "bug" and it remains in Joy's latest RPub. What does the u array have to do with the cherry picked 7070 element e that goes into the .csv files for submission anyway? I see no justification coming out of the use of the full u anyway, and when properly scaled they come out around +/- 0.5 as one would (should) expect. The cherry picked e looks ad hoc and not something 3-sphere geometry demands. Not my job to demonstrate it is not, which is a significantly more difficult task than showing mathematically how it is required by the geometry. There has been a progression of different algorithms to do this cherry picking, each with its own element of ad hocness. I think if the geometry demanded it, there would be one and only one, and it could be rigorously derived mathematically, which has not been done by Joy to date. The triangle inequality hand waving includes an ad hoc expression inserted without stated justification. Show me the rigorous math for the current one, I am sure I will understand it.

Fred, just because someone has not logged out, it does not mean they are paying attention, or care to take the time for an immediate reply. Beyond that, I have routinely left discussions after someone else's rebuttal of my position, even if I was not convinced by their arguments, even if they were blatantly out of touch with reality. A certain quacking duck comes to mind.


Rick,

I do not agree with your comments. The "bug" you pointed out was completely harmless. I would be impressed by your comments if you knew what the "initial" or "complete" state means in Bell's local-realistic framework. Since you evidently do not know what it means, I see no reason to engage with your comments. For those of you who do know what it means, you will understand my lack of enthusiasm for engaging with Rick's comments by reading this paper: http://arxiv.org/abs/1405.2355.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby FrediFizzx » Tue Jun 10, 2014 4:39 pm

Rick Lockyer wrote:Sorry but no, the bug was not fixed. I really could not care less if you write a program with the exceptionally bad practice of later using variable values assigned within the body of loops. The bug was the colSums were over 10000 values, yet the E_'s were calculated by dividing by 7070 and NOT 10000, artificially inflating their absolute values. That was the "bug" and it remains in Joy's latest RPub. What does the u array have to do with the cherry picked 7070 element e that goes into the .csv files for submission anyway? I see no justification coming out of the use of the full u anyway, and when properly scaled they come out around +/- 0.5 as one would (should) expect. The cherry picked e looks ad hoc and not something 3-sphere geometry demands. Not my job to demonstrate it is not, which is a significantly more difficult task than showing mathematically how it is required by the geometry. There has been a progression of different algorithms to do this cherry picking, each with its own element of ad hocness. I think if the geometry demanded it, there would be one and only one, and it could be rigorously derived mathematically, which has not been done by Joy to date. The triangle inequality hand waving includes an ad hoc expression inserted without stated justification. Show me the rigorous math for the current one, I am sure I will understand it.

You can say it is ad hoc all you want but what you say doesn't mean anything unless you care to show more specifically why and how it can't be related to 3-sphere geometry. I think Joy has given a good mathematical argument in the paper linked above. The ball is in your court. Thanks.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby gill1109 » Tue Jun 10, 2014 8:07 pm

Joy Christian wrote:
gill1109 wrote:OK I just created two files. They each have 7070 rows and three columns (and a header row). The first column is unnamed, the next two are named "t" and "w". Do they stand for what used to be called "x" and "y"?

PS I changed the names of the variables in the header, uploaded them to my cloud, and updated my R script
http://rpubs.com/gill1109/christian-test

Please verify that these are indeed your submitted files and that columns 2 and 3 indeed stand for x and y coordinates.


I quote myself from my initial post, which should answer your questions:

Joy Christian wrote:For technical reasons of producing the text files from the R script, Fred and I have had to separate out the x and y components of the u matrix and bind them again in the matrix e = cbind(t,w), as defined in the R script. But I have also left the directions tables from the u matrix in the script, just in case someone has difficulty using the x and y components generated from the e matrix. Note also that Fred has checked the e-lists against the u output and the "good" truth table, and they match.

I take this answer to mean "yes". The two files contain a sequence number and the x and y coordinates of 7070 directions. I changed the headers to the two files accordingly. Yesterday at around 18:00 pm I uploaded them to the cloud, and my calculations are at http://rpubs.com/gill1109/christian-test.
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby FrediFizzx » Tue Jun 10, 2014 8:17 pm

gill1109 wrote:I take this answer to mean "yes". The two files contain a sequence number and the x and y coordinates of 7070 directions. I changed the headers to the two files accordingly. Yesterday at around 18:00 pm I uploaded them to the cloud, and my calculations are at http://rpubs.com/gill1109/christian-test.

Those are NOT the right files. I posted the correct direction files here on June 7th. Below is the result of reading those correct direction files back into Joy's latest simulation script. BAM!

Code: Select all
> ## Richard Gill has offered 10,000 Euroes to anyone who can simulate the N
> ## directions of angular momentum vectors appearing in equation (16) of my
> ## experimental proposal: http://arxiv.org/abs/0806.3078. In this simulation
> ## I provide such N directions. They are given by the vectors 'u' in this
> ## simulation. He has also offered further 5,000 Euros to me if my proposed
> ## experiment is realized successfully. I am hopeful that that will happen
> ## some day. The details of these challanges by Richard Gill can be found
> ## here: http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=52#p1898.
> ## While this is by no means the most perfect simulation of my model, it does
> ## meet all of the conditions set out by Richard Gill for his challenge.
>
> ## The theoretical description of the model can be found in this paper:
> ## http://arxiv.org/abs/1405.2355 (see also http://lccn.loc.gov/2013040705).
>
> ## Since after the explosion the angular momentum vectors 'u' moving along
> ## the z direction will be confined to the x-y plane, a 2D simulation is good
> ## enough for my proposed experiment.
>
> set.seed(9875)
>
> M <- 10^4  ## Sample size. Next, try 10^5, or even 10^6
>
> angles <- seq(from = 0, to = 360, by = 10) * pi/180
>
> K <- length(angles)
> Ns <- numeric(K)  ## Container for number of states
> corrs <- matrix(nrow = K, ncol = K, data = 0)  ## Container for correlations
>
> r <- runif(M, 0, 2 * pi)
> s <- runif(M, 0, pi)
>
> # x <- cos(r)
> # y <- sin(r)
>
> # u <- rbind(x, y)
> ad <- read.csv("AliceDirectionsu.txt")      # alice directions file
> u <- rbind(ad$x, ad$y)           # just the x and y coordinates as a 2xN matrix
> rownames(u) <- c("x", "y")
> bd <- read.csv("BobDirectionsv.txt")   # alice directions file
> v <- rbind(bd$x, bd$y)           # just the x and y coordinates as a 2xN matrix
> rownames(v) <- c("x", "y")
>
> ## 'u' and 'v' are 2xM matrix. The M columns of 'u' represent the x and y
> ## coordinates of points on a unit circle in the equatorial plane.
>
> p <- 1.21 * (-1 + (2/(sqrt(1 + (3 * s/pi)))))
>
> for (i in 1:K) {
+     alpha <- angles[i]
+     a <- c(cos(alpha), sin(alpha))
+     for (j in 1:K) {
+         beta <- angles[j]
+         b <- c(cos(beta), sin(beta))
+         ca <- colSums(u * a)  ## Inner products of cols of 'u' with 'a'
+         cb <- colSums(v * b)  ## Inner products of cols of 'v' with 'b'
+         good <- abs(ca) > p & abs(cb) > p  ## Sets the topology to that of S^3
+         N <- sum(good)
+         corrs[i, j] <- sum(sign(ca[good]) * sign(cb[good]))/N
+         Ns[i] <- N
+     }
+ }
> (N)
[1] 7070
> par(mar = c(0, 0, 2, 0))
> persp(x = angles, y = angles, z = corrs, zlim = c(-1, 1), col = "pink", theta = 135,
+     phi = 30, scale = FALSE, xlab = "alpha", ylab = "beta")
>

> alpha <- 0 * pi/180
> beta <- 45 * pi/180
> a <- c(cos(alpha), sin(alpha))
> b <- c(cos(beta), sin(beta))
> ca <- colSums(u * a)  ## Inner products of cols of 'u' with 'a'
> cb <- colSums(v * b)  ## Inner products of cols of 'v' with 'b'
> (E_0_45 <- sum(sign(ca) * sign(cb))/N)
[1] -0.6992928
> ## [1] -0.6993
>
> alpha <- 0 * pi/180
> beta <- 135 * pi/180
> a <- c(cos(alpha), sin(alpha))
> b <- c(cos(beta), sin(beta))
> ca <- colSums(u * a)  ## Inner products of cols of 'u' with 'a'
> cb <- colSums(v * b)  ## Inner products of cols of 'v' with 'b'
> (E_0_135 <- sum(sign(ca) * sign(cb))/N)
[1] 0.7029703
> ## [1] 0.703
>
> alpha <- 90 * pi/180
> beta <- 45 * pi/180
> a <- c(cos(alpha), sin(alpha))
> b <- c(cos(beta), sin(beta))
> ca <- colSums(u * a)  ## Inner products of cols of 'u' with 'a'
> cb <- colSums(v * b)  ## Inner products of cols of 'v' with 'b'
> (E_90_45 <- sum(sign(ca) * sign(cb))/N)
[1] -0.6990099
> ## [1] -0.699
>
> alpha <- 90 * pi/180
> beta <- 135 * pi/180
> a <- c(cos(alpha), sin(alpha))
> b <- c(cos(beta), sin(beta))
> ca <- colSums(u * a)  ## Inner products of cols of 'u' with 'a'
> cb <- colSums(v * b)  ## Inner products of cols of 'v' with 'b'
> (E_90_135 <- sum(sign(ca) * sign(cb))/N)
[1] -0.7275813
> ## [1] -0.7276
>
> ## The Bell-CHSH inequality is violated:
>
> abs(E_0_45 - E_0_135 + E_90_45 + E_90_135)
[1] 2.828854
> ## [1] 2.829
>
FrediFizzx
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Re: Another Response to Richard Gill's 10,000 Euros Challeng

Postby gill1109 » Tue Jun 10, 2014 8:24 pm

Rick Lockyer wrote:The cherry picked e looks ad hoc and not something 3-sphere geometry demands. Not my job to demonstrate it is not, which is a significantly more difficult task than showing mathematically how it is required by the geometry. There has been a progression of different algorithms to do this cherry picking, each with its own element of ad hocness. I think if the geometry demanded it, there would be one and only one, and it could be rigorously derived mathematically, which has not been done by Joy to date. The triangle inequality hand waving includes an ad hoc expression inserted without stated justification. Show me the rigorous math for the current one, I am sure I will understand it.

The cherry picking is not completely ad hoc. The idea is to disguise Pearle's 1970 detection loophole model as Christian's 3-sphere model but it doesn't work. I am reminded of the ugly sisters trying to fit on Cinderella's slippers. The idea of my challenge (which was carefully crafted to as to be impossible to win) is to make this ugly fact as painfully obvious as possible. Long after Christian wrote out his model and his experimental paper, he adopted Michel Fodje's detection loophole model as his own. I showed that this model did not reproduce the singlet correlations. I did a lot of work (it took me week to decode Pearle's calculus and non-standard notational conventions) to convert Pearle's model into a simple simulation algorithm and I even wrote the core R code which Christian has now adopted.

Anyway, our hoped-for adjudicators have the files now and I hope they will be prepared to independently verify the calculation I did at http://rpubs.com/gill1109/christian-test

Meanwhile at Växjo Hans de Raedt gave a splendid talk on deriving quantum mechanics from informational principles including Fisher information; his wife Kristel Michielsen gave a nice talk about event-based simulation. She is betting strongly on a loophole-free Bell experiment never ever getting done. However the experimentalists seem to be betting strongly on it coming fairly soon. Excellent talk by Anton Zeilinger, and many more.
gill1109
Mathematical Statistician
 
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