Dr Bertlmann's socks and the 3-sphere model of EPR-Bohm

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

Re: Dr Bertlmann's socks and the 3-sphere model of EPR-Bohm

Postby local » Tue Nov 26, 2019 7:16 pm

Cool! Thank you for the link and info. Will read both tomorrow with great interest.
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Re: Dr Bertlmann's socks and the 3-sphere model of EPR-Bohm

Postby FrediFizzx » Tue Nov 26, 2019 7:54 pm

Here is some typical output of the GAViewer code that is in the paper.

Code: Select all
neg_adotb = 0.574949
theta = 234.903931
correlation = 0.574949
neg_adotb = 0.386546
theta = 247.260223
correlation = 0.386546
neg_adotb = 0.006321
theta = 90.362167
correlation = 0.006321
neg_adotb = -0.487911
theta = 60.796616
correlation = -0.487911
neg_adotb = 0.196614
theta = 101.339050
correlation = 0.196614
neg_adotb = -0.526722
theta = 58.215748
correlation = -0.526722
neg_adotb = 0.898704
theta = 153.988235
correlation = 0.898704
neg_adotb = -0.832386
theta = 33.655334
correlation = -0.832386
neg_adotb = 0.113726
theta = 96.530151
correlation = 0.113726
neg_adotb = 0.461435
theta = 242.520279
correlation = 0.461435
neg_adotb = 0.399192
theta = 246.472336
correlation = 0.399192
neg_adotb = 0.532410
theta = 122.168465
correlation = 0.532410
neg_adotb = -0.392552
theta = 66.886620
correlation = -0.392552
neg_adotb = 0.254378
theta = 104.736710
correlation = 0.254378
mean = 0.001660 + 0.004355*e2^e3 + -0.001763*e3^e1 + -0.002109*e1^e2
aveA = 0.004108
aveB = 0.000323


One can see that the correlation matches up perfectly to neg_adotb event by event so verifies the product calculation. And that the bivectors are vanishing in the "mean".
.
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Re: Dr Bertlmann's socks and the 3-sphere model of EPR-Bohm

Postby local » Thu Nov 28, 2019 10:41 am

Happy Thanksgiving to all!

And thank you FrediFizzx for the great forum.
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Re: Dr Bertlmann's socks and the 3-sphere model of EPR-Bohm

Postby FrediFizzx » Thu Nov 28, 2019 11:04 am

local wrote:Happy Thanksgiving to all!

And thank you FrediFizzx for the great forum.


You're welcome and Happy Thanksgiving to you and all.

Now, if I could just figure out the function for the sign flip, it would be a really great Thanksgiving. :)
.
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Re: Dr Bertlmann's socks and the 3-sphere model of EPR-Bohm

Postby Joy Christian » Mon Dec 02, 2019 8:07 pm

Joy Christian wrote:***
Ok., here is the new paper: https://arxiv.org/abs/1911.11578.

Title: Dr. Bertlmann's Socks in the Quaternionic World of Ambidextral Reality

Abstract:

In this pedagogical paper, John S. Bell's amusing example of Dr. Bertlmann's socks is reconsidered, first within a toy model of a two-dimensional one-sided world of a non-orientable Möbius strip, and then within a real world of three-dimensional quaternionic sphere, S^3, which results from an addition of a single point to R^3 at infinity. In the quaternionic world, which happens to be the spatial part of a solution of Einstein's field equations of general relativity, the singlet correlations between a pair of entangled fermions can be understood as classically as those between Dr. Bertlmann's colorful socks.


I have revised the pedagogical paper: https://arxiv.org/abs/1911.11578.

I have added an appendix proving the equivalence of the conservation of spin angular momentum and the twists in the Hopf bundle of S^3. This makes the paper more technical than I intended it to be, but the technicality (as beautiful as it is) is in the appendix and can be ignored in the first reading.

I have also added a couple of explanatory lines in the code presented in Section IV to bring the code more in line with the analytical derivation of the singlet correlations.

***
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Re: Dr Bertlmann's socks and the 3-sphere model of EPR-Bohm

Postby Joy Christian » Wed Dec 11, 2019 4:21 am

***
Quite independently of any cosmological model, for the past twelve years I have argued for a closed S^3 model for the 3D physical space. My argument comes from a local-realistic understanding of quantum correlations. It is good to know that cosmological data also now seem to support the closed model for the physical space:

"... the Planck cosmic microwave background spectra now preferring a positive curvature at more than 99% confidence level":

https://www.nature.com/articles/s41550-019-0906-9

***
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