Quaternionic Rays instead of Complex

[Antizzio]

TL;DR

This guy fixed quantum mechanics like Kelly fixed Al Bundy's work bench.
Instead of Complex rays as states, he used quaternionic rays. Each quaternionic ray: (1) is a copy of spacetime (called a "possible world"); (1) is 4-dimensional, (2) has a natural FLRW metric built in; (3) is a Lie Group with a natural Haar measure; (4) looks loke an hourglass, flaring out towards past and future. And all this from a single requirement that logic of the observer is Boolean.

It's in Chapter 2 of the book
"Focus on Quantum Mechanics", Editors David E. Hathaway et al.
Chapter 2, "Geometric Modification of Quantum Mechanics"
Nova Publishers, Physics Research and Technology, N.Y. 2011, pp. 15-34,
ISBN 978-1-62100-680-0. Since it's $90, I was looking for pointers to a cheaper version. Thank you!
It does not look like standard Quaternionic Quantum Mechanics (as far as I know, it does not work very well, it just complicates computations enormously).

 

[PeterDonis]

Moderator's note: Moving thread to the Beyond the Standard Models forum.

 

[renormalize]

Chapter 2, "Geometric Modification of Quantum Mechanics"

Can you list the author(s) of this chapter?

 

[Antizzio]

Vladimir Trifonov

 

[renormalize]

Vladimir Trifonov

I don't know if it will be helpful, but the author has written an earlier, easily available paper on this this topic:
GR-friendly description of quantum systems. I took a quick look and have to say, compared to a typical paper written by a theoretical physicist, this work is framed from the perspective of a mathematician, and dare I say, a philosopher. You might search Google Scholar to find follow-up citations.

 

[Antizzio]

Thank you!

 

[mitchell porter]

Can he use this new formalism to describe black holes, the hydrogen atom, anything real?

 

[Antizzio]

Looks like it incorporates standard QM as a "degenerate case": two out of four dimensions are collapsed in each possible world. I couldn't get through the category-theoretic diagrams, but Grok, Gemini and ChatGPT all say it checks out OK

 

[berkeman]

but Grok, Gemini and ChatGPT all say it checks out OK

Please keep in mind that AI cannot be used as a reference in the technical PF forums. Thanks.

 

[Antizzio]

Right, you cannot trust those guys, my apologies.

 

[Antizzio]

Goodness, it was something! But I think I've got it: If we accept for a second that spacetime is H* (nonzero quaternions), we get this in exchange: (1) natural Haar measure on H* (group multiplication, the author thinks it is more fundamental than Lebesgue, because it does not depend as much on Axiom of Choice, and can be build conctructively; (2) natural FLRW metric, which shapes it into an hourglass with the "waist" (3-sphere slice) going through the identity of H*; (3) FLRW metric induces a standard Lebesgue measure, which, the author feels, is less fundamental.

At the end of the paper he hints on Haar being responsible for structures at large scales, but it is not developed further in the paper (perhaps the book version is more complete? Please check this, if you have access to it). But if we roughly continue along these lines, Haar is responsible for pure spacetime (vacuum) volume, while Lebesgue measures matter density. Haar volume of the "waist" is nonzero, and since all other 3-sphere slices are produced by translations along left (and right) invariant vector fields, and Haar is also invariant, this means that Haar volume of 3-slices is constant. In the early universe matter density is huge compared to Haar. But Lebesgue dilutes rapidly and Haar catches up and eventually overtakes it, producing accelerated expansion. Please tell me where I am wrong on this, but doesn't it look like exactly like dark energy? Another thing, you can make the Haar volume as small as you wish, but it is never zero. This looks to me like a solution of the Fine Tuning problem.

 

[renormalize]

This looks to me like a solution of the Fine Tuning problem.

I applaud your enthusiasm, but the reality is, in the nearly 20 years since its publication, this paper has garnered a mere 7 citations in total. And of those, just 3 are (apparently) authored by physicists. The remaining cites appear to be from philosophers and a biologist(!). The brutal truth is that this work evidently has had no influence on any practicing relativist, cosmologist or particle physicist.

 

[Antizzio]

Exactly, sounds like normal statistics, considering contemporary fundamental physics situation.
I know about cosmology as much as the next guy, but are there any cosmologists in this forum, to address some of the stuff I mentioned?