## Simulation of local model for the GHZ correlations

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

### Simulation of local model for the GHZ correlations

Hi Folks,

We have implemented in GAViewer, Joy Christian's local-realistic S^7 model of the GHSZ 4-particle correlations using Euclidean primitives. It is based on his paper "Quantum Correlations are Weaved by the Spinors of the Euclidean Primitives". Here is the code for GAViewer.

Code: Select all
`//Adaptation of Albert Jan Wonnink's original code based on GAViewer for Joy Christian's S^7 Model of the 4-particle //GHSZ Correlations: http://challengingbell.blogspot.com/2015/03/numerical-validation-of-vanishing-of.htmlfunction getRandomLambda() {   if( rand()>0.5) {return 1;} else {return -1;}}function getRandomUnitVector() //uniform random unit vector:                                //http://mathworld.wolfram.com/SpherePointPicking.html{   v=randGaussStd()*e1+randGaussStd()*e2+ 0.00*e3;  //vectors are restricted to x-y plane (cf. GHSZ paper)   return normalize(v);}   batch test(){   set_window_title("Test of Joy Christian's Local-Realistic S^7 Model for the 4-particle GHSZ correlations");   default_model(p3ga);   N=200000;                               //number of iterations (trials)   I=e1^e2^e3;   s=0;   for(nn=0;nn<N;nn=nn+1)                  //perform the experiment N times   {          ar=getRandomUnitVector();          ad=ar.(e1*e2);                   //makes ad orthogonal to ar in the x-y plane          Da=normalize((I ar) + (ad e0));  //eq.(75) http://philsci-archive.pitt.edu/13019          br=getRandomUnitVector();          bd=br.(e1*e2);          Db=normalize((I br) + (bd e0));          cr=getRandomUnitVector();          cd=cr.(e1*e2);          Dc=normalize((I cr) + (cd e0));          dr=getRandomUnitVector();          dd=dr.(e1*e2);          Dd=normalize((I dr) + (dd e0));          lambda=getRandomLambda();        //lambda is a fair coin, giving the +1 or -1 choice           A=(-Da).(lambda*Da);             //eq.(188) of http://philsci-archive.pitt.edu/13019          B=(lambda*Db).(Db);              //eq.(189) of http://philsci-archive.pitt.edu/13019          LA=A/Da;          LB=B/Db;                         //implements the twist in the Hopf bundle of S^3          C=(-Dc).(lambda*Dc);             //eq.(190) of http://philsci-archive.pitt.edu/13019          D=(lambda*Dd).(Dd);              //eq.(191) of http://philsci-archive.pitt.edu/13019          LC=C/Dc;          LD=D/Dd;                         //implements the twist in the Hopf bundle of S^3          q=0;          if(lambda==1) {q=(LA LB LC LD);} else {q=(LD LC LB LA);}          s=s+q;          print(corrs=scalar(q), "f");     //Output the correlations          phi_a=atan2(scalar(-Da/(e2^e3)), scalar(Da/(e3^e1)))*180/pi;          phi_b=atan2(scalar(Db/(e2^e3)), scalar(Db/(e3^e1)))*180/pi;          phi_c=atan2(scalar(Dc/(e2^e3)), scalar(Dc/(e3^e1)))*180/pi;          phi_d=atan2(scalar(Dd/(e2^e3)), scalar(-Dd/(e3^e1)))*180/pi;          angle=abs(phi_a + phi_b - phi_c - phi_d);          print(angle);                    //Output the angles      }      mean=s/N;      print(mean, "f");      prompt();}`

And here is the result for 200,000 trials, Update Nov. 28: Please note that the code above was changed to better reflect the math in Joy's paper.
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FrediFizzx
Independent Physics Researcher

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### Re: Simulation of local model for the GHZ correlations

*** The proof I provided in response to Tim Maudlin's challenge can be found in this thread: viewtopic.php?f=6&t=275&start=40#p7905.

***
Joy Christian
Research Physicist

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### Re: Simulation of local model for the GHZ correlations

coool. it would be really *really* nice for all papers to be written that include actual source code that may be run on any computer, *actually* implementing the algorithms and equations listed. too many papers leave out huge yawning gaps (so as to be able to "fit publication") or assume some aspect or other which quotes everyone knows quotes. i had *absolutely no idea* for example until about six weeks ago that Maxwell's Equations EVERYONE KNOWS that the equations IMPLICITLY express TWO equations... including the complex conjugate +/- ! nobody told me that; i couldn't understand the equations enough to *tell* that... but if it had been *implemented in a computer program* i would have instantly been able to tell.

computer-implemented algorithms *have* to be completely unambiguous and leave absolutely nothing to chance. it should be a law of Publication Of Scientific Theories that the equations actually be implemented in an algorithm, in full lkcl

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### Re: Simulation of local model for the GHZ correlations

lkcl wrote:coool. it would be really *really* nice for all papers to be written that include actual source code that may be run on any computer, *actually* implementing the algorithms and equations listed. too many papers leave out huge yawning gaps (so as to be able to "fit publication") or assume some aspect or other which quotes everyone knows quotes. i had *absolutely no idea* for example until about six weeks ago that Maxwell's Equations EVERYONE KNOWS that the equations IMPLICITLY express TWO equations... including the complex conjugate +/- ! nobody told me that; i couldn't understand the equations enough to *tell* that... but if it had been *implemented in a computer program* i would have instantly been able to tell.

computer-implemented algorithms *have* to be completely unambiguous and leave absolutely nothing to chance. it should be a law of Publication Of Scientific Theories that the equations actually be implemented in an algorithm, in full I quite agree, Luke. Although I don't know much about programming, I am increasingly recognizing its value in theoretical physics. The credit for the above simulation, however, goes mostly to the dogged persistence and hard work of Fred Diether. And of course, we would not have gotten as far as we have without the original code of Albert Jan Wonnink. Michel Fodje also helps out occasionally. And I mustn't forget Chantal Roth, who was also quite helpful some years ago with a different simulation of my 3-sphere model, one based on a "complete state" formulation of S^3. I have been quite lucky that all these talented programmers have been willing to help me.

***
Joy Christian
Research Physicist

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Location: Oxford, United Kingdom

### Re: Simulation of local model for the GHZ correlations

Joy Christian wrote:I quite agree, Luke. Although I don't know much about programming, I am increasingly recognizing its value in theoretical physics. The credit for the above simulation, however, goes mostly to the dogged persistence and hard work of Fred Diether. And of course, we would not have gotten as far as we have without the original code of Albert Jan Wonnink. Michel Fodje also helps out occasionally. And I mustn't forget Chantal Roth, who was also quite helpful some years ago with a different simulation of my 3-sphere model, one based on a "complete state" formulation of S^3. I have been quite lucky that all these talented programmers have been willing to help me.

but... but... that's fantastic! that not only have you been able to preserve and pass on the knowledge in an absolutely unambiguous algorithmic fashion but that *you* were able to clearly and successfully pass on that knowledge to those programmers in the first place. the fact that it shuts up the detractors is actually a *subset* of the implications / achievements of this approach.

keep it up! if they lose interest or don't quite understand the significance do point them at this thread ok!

p.s. i have now managed to track down not one but _two_ mathematicians with programming skills, which is two more than i could ever have hoped or dreamed of as of last week lkcl

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Joined: Wed Sep 28, 2016 6:15 am 