SciPhysicsForums.com

[b]Here is the quaternion version of the post above. 5 million trials. Joy's [tex]S^3[/tex] model also predicts the 4-particle GHZ 2D correlation using quaternions![/b]

[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ2Dqt1.jpg[/img]
[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ2Dqt2.jpg[/img]
[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ2Dqt3.jpg[/img]

[b]Here is the notebook file,

http://www.sciphysicsforums.com/spfbb1/EPRsims/joyGA_3-sphereGHZ1quat2.nb

Bell loses two ways so take your pick; quaternions or Geometric Algebra![/b] :mrgreen:
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[b]I found out that Joy's [tex]S^3[/tex] model also predicts the GHZ 4-particle correlation with 2D vectors.[/b]

[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ2D8.jpg[/img]
[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ2D10.jpg[/img]
[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ2D9.jpg[/img]

Here is the notebook file for those that might be interested.

http://www.sciphysicsforums.com/spfbb1/EPRsims/joyGA_3-sphereGHZ1.nb

[b]Bell loses yet again![/b] :mrgreen: :mrgreen: :mrgreen: :mrgreen: :mrgreen:
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Yeah, the 2D vectors work better because I can run the ABCD correlation at the same time. I haven't figured it out yet for the 3D vectors. This is for 50,000 trials

[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ2D1.jpg[/img]
[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ2D2.jpg[/img]..[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ2D3.jpg[/img]
[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ2D4.jpg[/img]..[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ2D5.jpg[/img]
[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ2D6.jpg[/img]..[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ2D7.jpg[/img]

Here are the PDF and notebook files.

http://www.sciphysicsforums.com/spfbb1/EPRsims/joyGA_7-sphere4Pabcd.pdf
http://www.sciphysicsforums.com/spfbb1/EPRsims/joyGA_7-sphere4Pabcd.nb

Bell loses 7 times in this one! :mrgreen: :mrgreen: :mrgreen:
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[quote="Joy Christian"]
Thanks, Fred. I thought about these results. All six of them are the exact local-realistic predictions of the 7-sphere model for the correlations predicted for the GHZ state. Let me quote the predictions from [url=https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.180526]my RSOS paper[/url]:

[img]http://einstein-physics.org/wp-content/uploads/2021/05/GHZ-Local.png[/img]

In your simulation, all four polar angles, theta_a, theta_b, theta_c, and theta_d, have been set to 90 degrees. And for each of the four cross-correlations, two of the four azimuthal angles, phi_a, phi_b, phi_c, and phi_d, have been set to zero. Thus all six of your plots are exact predictions of the 7-sphere model. So, yes, once again Bell loses 6 times. But we knew that! :D
.[/quote]
You're welcome. Oh yeah, that is how it works basically. But it is actually a little bit different with the 3D vectors. The model with 2D vectors actually works better and is exactly like you are saying. I'm working on that now.
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[quote="FrediFizzx"]Here is something I possibly discovered about the 4 particle GHZ state. A, B, C and D are cross-correlated in 6 different pairs.

[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ3D1.jpg[/img]...[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ3D2.jpg[/img]
[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ3D3.jpg[/img]...[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ3D4.jpg[/img]
[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ3D5.jpg[/img]...[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ3D6.jpg[/img]

Here is the Mathematica program with Geometric Algebra.

[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ3D7.jpg[/img]
[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ3D8.jpg[/img]
[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ3D9.jpg[/img]

Here are the PDF and notebook files.

http://www.sciphysicsforums.com/spfbb1/EPRsims/joyGA_7-sphere6abcd2.pdf
http://www.sciphysicsforums.com/spfbb1/EPRsims/joyGA_7-sphere6abcd.nb

Anyways, Bell loses 6 times here. :mrgreen:
[/quote]
Thanks, Fred. I thought about these results. All six of them are the exact local-realistic predictions of the 7-sphere model for the correlations predicted for the GHZ state. Let me quote the predictions from [url=https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.180526]my RSOS paper[/url]:

[img]http://einstein-physics.org/wp-content/uploads/2021/05/GHZ-Local.png[/img]

In your simulation, all four polar angles, theta_a, theta_b, theta_c, and theta_d, have been set to 90 degrees. And for each of the four cross-correlations, two of the four azimuthal angles, phi_a, phi_b, phi_c, and phi_d, have been set to zero. Thus all six of your plots are exact predictions of the 7-sphere model. So, yes, once again Bell loses 6 times. But we knew that! :D
.

[quote="FrediFizzx"]Here is Joy's [tex]S^7[/tex] 2 particle model with [b]3D vectors[/b]. 50 thousand trials for the event by event product calculation.

...

Exact match again! And..., Bell loses again! :mrgreen:

Here is the notebook file.

http://www.sciphysicsforums.com/spfbb1/EPRsims/joyGA_7-sphere2P2.nb
[/quote]
Bell wins. It is an event by event simulation. But it is not a simulation of a local realistic model. You do not implement functions A, B taking values +/-1, standard computation of correlation, no post-selection, .... You could not use the model to do a loophole-free experiment (with source and detectors replaced by networked computers implementing the various ingredients of the model).

It is a nice illustration of the validity of Bell’s theorem. :P

Here is something I possibly discovered about the 4 particle GHZ state. A, B, C and D are cross-correlated in 6 different pairs.

[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ3D1.jpg[/img]...[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ3D2.jpg[/img]
[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ3D3.jpg[/img]...[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ3D4.jpg[/img]
[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ3D5.jpg[/img]...[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ3D6.jpg[/img]

Here is the Mathematica program with Geometric Algebra.

[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ3D7.jpg[/img]
[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ3D8.jpg[/img]
[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ3D9.jpg[/img]

Here are the PDF and notebook files.

http://www.sciphysicsforums.com/spfbb1/EPRsims/joyGA_7-sphere6abcd2.pdf
http://www.sciphysicsforums.com/spfbb1/EPRsims/joyGA_7-sphere6abcd.nb

Anyways, Bell loses 6 times here. :mrgreen:
.

Here is Joy's [tex]S^7[/tex] 2 particle model with [b]3D vectors[/b]. 50 thousand trials for the event by event product calculation.

[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy2PS750k2.jpg[/img]
[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy2PS750k.jpg[/img]

Exact match again! And..., Bell loses again! :mrgreen:

Here is the notebook file.

http://www.sciphysicsforums.com/spfbb1/EPRsims/joyGA_7-sphere2P2.nb
.

I finally got Geometric Algebra to work in Mathematica using a Clifford package. Yay! This is Joy's 7-sphere model from his [url=https://royalsocietypublishing.org/doi/10.1098/rsos.180526]RSOS paper[/url]. The symbols C, D and I are protected symbols in Mathematica so I had to use C1, D1 and I1. 2 million trials for the event by event product calculation.

[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ2m3.jpg[/img]
[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ2m4.jpg[/img]
[img]http://www.sciphysicsforums.com/spfbb1/EPRsims/joy4PGHZ2m.jpg[/img]

The match is exact! Bell is shot down again. Here is the notebook file for those interested.

http://www.sciphysicsforums.com/spfbb1/EPRsims/joyGA_7-sphere5.nb
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