Today I learned about Alex Eskin, at U of Chicago, and his Magic Wand Theorem which was recently awarded $3 million in 2019 Breakthrough Prize in Mathematics. The results of this theorem are based on the work Article Invariant and stationary measures for the SL(2,R) action on ...
by Alex Eskin and the late Maryam Mirzakhani, submitted in 2013The rewarded breakthrough theory claims that its results are of enormous importance for studying dynamical processes in the Universe, however, the theory is "not easy to explain". This is further discussed in Article The Magic Wand Theorem of A. Eskin and M. Mirzakhani
, where the author Anton Zorich states " One can observe certain common phenomena in large classes of dynamical systems; in particular, ideal billiards might be interpreted as toy models of a gas in a chamber. Such toy models allow to elaborate tools to study original dynamical systems of physical nature."My question is, why have a geometric toy model to study dynamical processes, when you can have a real and simple dynamical model, known as the globotoroid, to address these processes?
It seems, Magic Wand Theorem is another example of hard to explain mathematical theory, which provides a "useful tool for physics". Can we be more real and pragmatic, or this is perhaps not academic enough? For instance, my recentArticle Curvatures and Dynamics of the Universe
addresses more realistically the topics Magic Wand Theorem attempts to do.Incidentally, I also used the term "Magical Wand" im my 2015 YouTube video, https://youtu.be/gbPaG9AHZfg, where I show how to wrap growth data, in this case the market data, onto a spheroid. Interesting coincidence in the use of term.
I think Alex Eskin, a mathematician at the University of Chicago, which won the $3 million 2019 Breakthrough Prize in Mathematics because of the extreme importance of his work. This workstudies various aspects of the motion of relativistic rotators, both in the presence and absence of external fields, using a toy model which, in a sense, can be regarded as a non-relativistic limit of the rotators.
Maged,
Thank you for your comment. However, I still have questions since it seems to me you are referring to the relativistic dynamics, which may apply to microscopic and submicroscopic processes, hence the ideal billiards. If that is the case, how do you generalize from there to large structures such as the black holes? Whether this is explained in the original 2013 article, which subsequently was revised in 2018 and now contains over 200 pages of mathematics, is not obvious even for the "toy models", especially since the nature of dynamics may have its own rules that do not necessarily follow geometric arguments.
Interesting coincidence or intersection of thoughts
Preprint Chaotic dynamics of an electron
Nikola Samardzija
By the way, did you know that 2-row complex matrices with a zero trace can be put in correspondence with linear vector fields tangent to classical tori that rotate in 4-dimensional space with a neutral and Euclidean metric? Thus, it turns out that in this case the torus moves on the surface of 3-dimensional hyperspheres of spaces with neutral and Euclidean metrics. In addition, the generators of these matrices can be mapped to vector fields whose current lines correspond to the metric properties of the coordinates of the Minkowski space.
Dear Igor Bayak,
Thank you for your comments, and recommendations.
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