Beggs, E. J., & Majid, S. (2020). Quantum Riemannian Geometry book

Not sure where this is coming from but if you are asking for my comment, thats true there is no evidence, its what I call the `quantum spacetime hypothesis’ yet to be proven by experiment. However, from a mathematicians

point of view it turns out that restricting geometry to commutative coordinates and differentials as Newton and Leibniz

did, while good enough for what they had in mind, was totally unnecessary and the mathematics is just as natural if a little unfamiliar without. So given the way nature peels back unnecessary assumptions as we probe deeper, the real question to my mind is what's so special about the commutative case that it should appear in a special case, that special case being classical GR as the macroscopic limit of quantum gravity. Moreover, if you accept 2+1

quantum gravity [two dimensions of space plus one of time] with point sources as physics in some special scenarios, well that one can be solved and we

can see exactly how quantum spacetime provides a natural effective description of some effect in the theory. 

 Best wishes, Shahn Majid

On 12 Jul 2020, at 16:25, Voidisyinyang Voidisyinyang <voidisyinyang@gmail.com> wrote:

Unlike quantum phase space in quantum mechanics, there is as yet no physical
evidence that the coordinates of spacetime themselves form a noncommutative
differential algebra.

Shahn Majid	4:05 AM (2 hours ago)
to me, Shahn

Beggs, E. J., & Majid, S. (2020). Quantum Riemannian Geometry. Grundlehren Der Mathematischen Wissenschaften. doi:10.1007/978-3-030-30294-8 

url to share this paper:
sci-hub.tw/10.1007/978-3-030-30294-8

 ‘quantum groups approach to noncommutative geometry’),

 connections for noncommutative algebras, as well as Hochschild
and cyclic cohomology, were a natural progression in this direction, culminating
in Connes’ famous notion of a spectral triple as an abstract ‘Dirac operator’ in
the early 1980s.

 s.majid@qmul.ac.uk

I emailed him about:

 Unlike quantum phase space in quantum mechanics, there is as yet no physical
evidence that the coordinates of spacetime themselves form a noncommutative
differential algebra.

Asking, "what about Yakir Aharonov"

 

and



and



and

Oh thanks Professor Majid - I had to look up that 2 +1. Makes sense. My interest is in what math professor Luigi Borzacchini called the "deep, pre-established disharmony" of commutative math as the "evoltive principle" secretly guiding science. So as Connes points out music theory is actually noncommutative (contrary to all the fancy music theory youtube channels, haha). So Borzacchini documented the "cognitive bias" of Western math against acknowledging the music theory origin of commutative math (from the wrong music theory!). So my claim then, in my master's thesis of 2000, is that there is a structural drive of the current ecological and social justice crisis on Earth. So we can enjoy our fancy science technology yet supposedly we can't observe the negentropy of the Universe (assuming a left-brain and right hand dominance bias of perception). Music frequency is right brain dominant and as per Connes, then noncommutative phase is the true origin of reality, despite the glories of commutative symmetric-based logic of Western science (going back to Vedic and Zoroastrian divide and average cipher logic).

Let me know if you think that is just bonkers or makes sense in its own way. haha. It could be that the (2 + 1) model then actually is the Holographic truth of reality and our 3-D visual bias from the Cambrian  Explosion of eyeballs evolving - and primates moving into the savannah as hominins - and later hominids - we developed what archaeologist Jacques Cauvin calls the "symbolic revolution" around the Younger Dryas Event - a mythological "ritual origin of geometry" (math professor Abraham Seidenberg) that developed into the Religion of Technology, as former MIT history professor David F. Noble titled his book. So as Eddie Oshins at Stanford Linear Accelerator Center emphasized, Karl Pribram was wrong about his holographic mind model of reality since Pribram could not understand noncommutative phase logic. So Pribram was stuck in Fourier Analysis - and even Sir Roger Penrose admits he's not good enough at noncommutative geometry maths.

Good luck with your research!

drew hempel