Thierry Paul gives a non-technical talk!
In fact, the quantum evolution contains two parts, totally disjointed: the first one is the evolution of the wave function driven by a differential equation leading to a natural principle of causality, and the second is the indeterministic phenomenon of measurement, whose random result values are taken from a set of possible ones associated to the wave function.
You change your paradigm. You forget about the continuum of space that you have in Newton. You have a discrete things because you have vectorial space. You have two-dimensional space.
AWARDING OF THE "TULLIO LEVI CIVITA PRIZE 2021" TO THE PROFESSOR THIERRY PAUL
latest Thierry Paul lecture, 2023
Species of spacesby Paul Thierry
https://hal.science/hal-03707142v1/file/pouralex21_springer.pdf
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of noncommutativity, witness of an emblematic feature of quantum mechanise remains when the Planck constant vanishes, in the framework of noncommutative geometry.
https://link.springer.com/article/10.1007/s40574-024-00428-5
Quantum optimal transport aims to extend this success story to non-commutative systems, where density operators replace probability measures.
Citing Connes 1992
OK Googletranslate hacked up the French!
I feel confused cracks, hiatuses, points of friction, we sometimes have the vague feeling that it's stuck somewhere, or that it's bursting, or that it hits.quoting this book
https://monoskop.org/images/b/b0/Perec_Georges_Species_of_Spaces_and_Other_Pieces.pdf
It's some avant-garde minimalist play...funny that googletranslate
changed the French meaning of hiatus in English!!
We vaguely feel cracks, gaps, points of friction, we sometimes have thevague impression that it is stuck somewhere, or that it is bursting, or that..............................
Hiatus, in prosody, a break in sound between two vowels that occur together without an intervening consonant, both vowels being clearly enunciated.
I'm not sure why I'm attracted to this concept of silence between two separate vowels. It's not the same as a dramatic pause for effect. It's more subtle yet more powerful. Both vowels resonate overtones and undertones via the silence that hides a deeper noncommutative meaning.
The two vowels may be either within one word, as in the words Vienna and naive, Vienna and naive or the final and initial vowels of two successive words, as in the phrases “see it” and “go in.”And so the diacritical mark ◌̈, known as the combining diaeresis or umlaut,
Diaeresis[a] (/daɪˈɛrəsɪs, -ˈɪər-/ dy-ERR-ə-siss, -EER-)[1] is a diacritical mark consisting of two dots (◌̈) that indicates that two adjacent vowel letters are separate syllables – a vowel hiatus (also called a diaeresis)For example, in the spelling "coöperate", the diaeresis reminds the reader that the word has four syllables, co-op-er-ate, not three, *coop-er-ate. In British English this usage has been considered obsolete for many years, and in US English, although it persisted for longer, it is now considered archaic as well.[3] Nevertheless, it is still used by the US magazine The New Yorker.[4] In English language texts it is perhaps most familiar in the loan words naïve, Noël and Chloë,
Math entities with no objects - Paul Thierry
that temporarily possibly creates a kind of non-existing objects that we
named entities. Weak solutions of PDEs, almost everywhere defined flows,
noncommutative manifold are such examples of entities without clear underlying identified objects.
The reader can consult [10, 12, 13] for a similar attempt concerning mathematics versus music and mathematics versus quantum mechanics.
On the musical drum!!
Sweet.
I think he worked on this with Alain Connes?
https://apps.dtic.mil/sti/tr/pdf/ADA302229.pdf
Wow my Alma Mater - as a Military project!!
negative time.....
Paul Thierry in action!
ten years ago....he emphasizes the SAME point that Basil J. Hiley emphasized - that you can not go from the classical to the quantum because Planck's Constant can not go to zero due to "nonlocal objects" that are noncommutative dynamics.
phase space is something like time-frequency.....
https://zbmath.org/authors/?q=ai%3Apaul.thierry
Mathematics and music: loves and fights (2020)
https://hal.science/hal-02194739v2/file/rissetrevu.pdf
realism emerge in music as a consequence of,
among other things but necessary including it, the rigour present in the process
of composing. reading a fugue without playing it is a real experience, after all.
And conversely, considering that the mathematical realism calls only the rigorous
part of mathematics is too simple, too reductive. Let us quote Ren´e Thom: “Ce
qui limite le vrai, ce n’est pas le faux, c’est l’insignifiant”3.
The conclusion of this short section could be expressed by saying that, both
in music and in mathematics, the rigour has the role of providing a kind of
“emergence of realism”.
This reminds me of musical notation where you get something extremely powerful from redundancy.
Thierry Paul, youtube talk
it breaks the invariance of time because at negative infinity time you go to an unstable manifold...
Our ear...[switches naturally from location to momentum as direction of frequency]....since you have this quantum correction....unstable [noncommutative] manifold...you have a kind of delocalization....
non-technical Thierry Paul talk two years ago
flow at infinite time escapes from the classical paradigm because it does not preserve the geometrical structure of points in space: after infinite evolution, single points would “become" extended objects as manifolds.
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