New GHZ 4 particle 2D simulation

[FrediFizzx]

I finally got Geometric Algebra to work in Mathematica using a Clifford package. Yay! This is Joy's 7-sphere model from his RSOS paper. 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.





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

EPRsims/joyGA_7-sphere5.nb
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[FrediFizzx]

Here is Joy's 2 particle model with 3D vectors. 50 thousand trials for the event by event product calculation.




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

Here is the notebook file.

EPRsims/joyGA_7-sphere2P2.nb
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[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.

...
...
...

Here is the Mathematica program with Geometric Algebra.





Here are the PDF and notebook files.

EPRsims/joyGA_7-sphere6abcd2.pdf
EPRsims/joyGA_7-sphere6abcd.nb

Anyways, Bell loses 6 times here.
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[gill1109]

Here is Joy's 2 particle model with 3D vectors. 50 thousand trials for the event by event product calculation.

...

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

Here is the notebook file.

EPRsims/joyGA_7-sphere2P2.nb

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.

[Joy Christian]

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

...
...
...

Here is the Mathematica program with Geometric Algebra.





Here are the PDF and notebook files.

EPRsims/joyGA_7-sphere6abcd2.pdf
EPRsims/joyGA_7-sphere6abcd.nb

Anyways, Bell loses 6 times here.

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 my RSOS paper:



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!
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[FrediFizzx]

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 my RSOS paper:



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!
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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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[FrediFizzx]

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


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..
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Here are the PDF and notebook files.

EPRsims/joyGA_7-sphere4Pabcd.pdf
EPRsims/joyGA_7-sphere4Pabcd.nb

Bell loses 7 times in this one!
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[FrediFizzx]

I found out that Joy's model also predicts the GHZ 4-particle correlation with 2D vectors.





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

EPRsims/joyGA_3-sphereGHZ1.nb

Bell loses yet again!
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[FrediFizzx]

Here is the quaternion version of the post above. 5 million trials. Joy's model also predicts the 4-particle GHZ 2D correlation using quaternions!





Here is the notebook file,

EPRsims/joyGA_3-sphereGHZ1quat2.nb

Bell loses two ways so take your pick; quaternions or Geometric Algebra!
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