Macroscopic Observability of Spinorial Sign Changes

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

Macroscopic Observability of Spinorial Sign Changes

Postby gill1109 » Sat Mar 06, 2021 10:53 pm

Christian's IJTP paper https://arxiv.org/abs/1211.0784, https://link.springer.com/article/10.1007%2Fs10773-014-2412-2 (paywall) contains a fascinating section on the differential geometry of SU(2) and SO(3), resulting in Figure 3, which is the usual graph of the triangle wave and the negative cosine! But the legend to the figure is: "Fig. 3 Comparison of the geodesic distances on SU(2) and SO(3) as functions of half of the rotation angle ψ. The dashed lines depict the geodesic distances on SO(3), whereas the red curve depicts their horizontal lift to the covering group SU(2)".

This is really interesting. I also think that the relation of this graph with Pearle's model is worth understanding.

Image

It's a strange paper. It has the incredible exploding balls experiment which someone really ought to do. That would lay a lot of ghosts to rest.

Negative distances do not exist, so the legend to the graph isn't quite accurate
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Re: Macroscopic Observability of Spinorial Sign Changes

Postby gill1109 » Sun Mar 07, 2021 2:10 am

I suppose that if the difference between two angles is delta then the distance between the two points is the total variation of the curve between 0 and delta (up to an arbitrary multiplicative constant).
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Re: Macroscopic Observability of Spinorial Sign Changes

Postby Joy Christian » Sat Apr 03, 2021 7:28 pm

.
I have used Geometric Algebra (GA) in many of my papers on Bell's theorem since 2007. Here is a nice tutorial on Geometric Algebra on YouTube that covers almost all of known physics:

https://www.youtube.com/watch?v=60z_hpEAtD8
.
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Re: Macroscopic Observability of Spinorial Sign Changes

Postby gill1109 » Tue Apr 06, 2021 5:06 am

Joy Christian wrote:.
I have used Geometric Algebra (GA) in many of my papers on Bell's theorem since 2007. Here is a nice tutorial on Geometric Algebra on YouTube that covers almost all of known physics:
https://www.youtube.com/watch?v=60z_hpEAtD8

An excellent introduction.
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