## 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

Cool! Thank you for the link and info. Will read both tomorrow with great interest.
local

Posts: 83
Joined: Mon Aug 05, 2019 1:19 pm

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

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

Code: Select all
`neg_adotb = 0.574949theta = 234.903931correlation = 0.574949neg_adotb = 0.386546theta = 247.260223correlation = 0.386546neg_adotb = 0.006321theta = 90.362167correlation = 0.006321neg_adotb = -0.487911theta = 60.796616correlation = -0.487911neg_adotb = 0.196614theta = 101.339050correlation = 0.196614neg_adotb = -0.526722theta = 58.215748correlation = -0.526722neg_adotb = 0.898704theta = 153.988235correlation = 0.898704neg_adotb = -0.832386theta = 33.655334correlation = -0.832386neg_adotb = 0.113726theta = 96.530151correlation = 0.113726neg_adotb = 0.461435theta = 242.520279correlation = 0.461435neg_adotb = 0.399192theta = 246.472336correlation = 0.399192neg_adotb = 0.532410theta = 122.168465correlation = 0.532410neg_adotb = -0.392552theta = 66.886620correlation = -0.392552neg_adotb = 0.254378theta = 104.736710correlation = 0.254378mean = 0.001660 + 0.004355*e2^e3 + -0.001763*e3^e1 + -0.002109*e1^e2aveA = 0.004108aveB = 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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FrediFizzx
Independent Physics Researcher

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

Happy Thanksgiving to all!

And thank you FrediFizzx for the great forum.
local

Posts: 83
Joined: Mon Aug 05, 2019 1:19 pm

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

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 $S^3$ sign flip, it would be a really great Thanksgiving.
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FrediFizzx
Independent Physics Researcher

Posts: 1700
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

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

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.

***
Joy Christian
Research Physicist

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

***
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

***
Joy Christian
Research Physicist

Posts: 2132
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

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