Alain Connes: Dependence on Noncommutative nonlocal primitive time music harmony as ever new process

Fields Medal Math Professor Alain Connes says how he loved his grandmother who was a pianist....

Connes: "When I was five years old I began piano lessons, and I really loved it. But when we moved to Marseille, we could not have a piano in the house. My father told me I had to choose between music and studies. So I dropped the piano then. I of course always regretted immensely to have done that. When I was twenty, I started again to play the piano, but of course I had missed the most important years for learning. I have done a lot of work to recover from that, but I never recovered to the point that I would have been at. But okay — this is life.

Connes: You can’t do everything. I now see very well that I have a part of the brain that is musical. In fact I just wrote a paper for the Journal of Mathematics and Music. But I know that the part of the brain that is occupied by music is sort of competing with the part that is occupied by mathematics. Of course, they are extremely close. This might sound strange, but often I learn a lot in mathematics by studying scores of music.

Connes: In mathematics, you might in some cases have the impression that you have reached the highest level of sophistication. But then you study a great musical score, and you find that the composer has a level of sophistication that is about twice the level of sophistication of the best mathematics. This is what I have in mind. There are composers, especially of the Romantic period, who have reached a level of musical precision that I always find comforting and a source of energy to do mathematics. So I use musical scores as a source of sophistication, but I also like to improvise and to let things out.

Why is it natural to view a space spectrally and to define the action from a spectral invariant?
This action is simply measuring the spectrum of the line element. The formula for distance in noncommutative geometry will use the fact that the line element does not commute with the coordinates in the space.
We realized that if one takes a spectral point of view of geometry, then there is a natural manner of defining what is called in physics an “action”, for that geometry. This will measure how suitable the geometry is. This action turned out to be spectral and depends only upon the line element, upon its spectrum.
When I defined noncommutative geometry, I defined it as a spectral triple. The shift from the classical standpoint, which was the Riemann standpoint on geometry, to the new standpoint that I had defined, which is spectral, is exactly parallel to the shift that occurred in physics between the definition of the unit of length by means of the platinum bar, and the definition by means of comparison with wavelengths of a fixed chemical. It’s very striking.

The action principle, which we defined with Chamseddine, then allows you not only to recover gravity but to find gravity coupled with matter. This action is simply measuring the spectrum of the line element. The formula for distance in noncommutative geometry will use the fact that the line element does not commute with the coordinates in the space.
On the conceptual level, what this means is that a paradigm of noncommutative geometry, that of a spectral triple, in fact is very closely related to physics. It has a big advantage in the quest to unify gravity with other forces, which is that it is both quantum and geometric.

These things exist in the brain, and they send you signals. Similarly in music, you can have something that exists in your mind, a tune or a theme. This is something amazing and very hard to define.

Algebra is much more time-dependent and evolving. In algebra, when you are doing computations, there is a definite analogy with the time dependence in music, which is extremely striking.

The noncommutativity, which was discovered by people in quantum mechanics, in fact is a generator of time. I am still thinking about the fact that the passage of time, or the way we feel that time is going on and we cannot stop it, is in fact exactly the consequence of the noncommutativity of quantum mechanics

Something Heisenberg discovered, which is absolutely amazing, is that when you repeat certain microscopic experiments, the results will never be the same.

When you permute A and B, and you make the A pass on the other side, you have to make it evolve with time. And the time in which it has to evolve is in fact the purely imaginary number . This is what is behind the scenes.

This means that the notion of causality, or the notion of time, is totally upset by the phenomenon of entanglement. I interpret it as meaning that there is something more primitive than the passing of time, "

[simoncleret]

8:01 "Clef" is just French for "key" (though you'll often see it spelled "clé", which is how we generally pronounce it today).

[voidisyinyangvoidisyinyang]

transformation, which guarantees its total compatibility with de BROGLIE's phase harmony
theorem, which is itself established on purely relativistic bases....