https://www.youtube.com/watch?v=A7NEve8BAto
"In the noncommutative geometry, we don't have to take a square root, we add a square root which is the inverse of the Dirac Operator...The Dirac Operator is a mass and its inverse is a length. You send a wave from A to B and you look at the maximal shift of the wave with the condition that the wave doesn't vibrate to fast because the commutator is equal or less than 1.....The reason also why it can not commute with the coordinates. Imagine the line element [Fermion Propagator] commutes with the coordinates, because it's infinitesimal the coordinates have to take a specific value...It if is located somewhere what it means, if you want to measure something you have to go to this place and come back...Whereas the Dirac Propagator is not located anywhere and the price to pay is exactly that it does not commute with the coordinates."...
"That time is passing as a variable is not the right answer...when you take an observation at the quantum level - for instance the one slit experiment....you send an electron or photon through a tiny slit and after that slit it goes somewhere - there is a target...because it can't be reproduced."
"The fundamental variable is not in the passing of time but is in this noncommutativity.... it is this quantum uncertainty which is the source of the passing of time...the true origin of noncommutative geometry, ...which is the fact that noncommutativity creates time.... If you take purely imaginary time, this will be a switching of order from xy to yx....When you change the state...automorphisms which are never seen, because they are inner, because they are automatically there when you take the noncommutative algebra....
The message is very very strong. You don't limit a state. If you limit a state, this would be bad. .. It would not just be the algebra that gives you time. ...JUST the noncommutative algebra by itself generates its own time....The philosophical message tells you that time in fact can be a byproduct of noncommutativity. You don't need anything else. And it's related to quantum mechanics and it's related to what we know of Heisenberg evolution...It's supported by very precise physical equations. The philosophical message is much stronger. The philosophical message is much stronger, because of the coexistence of continuous and discrete that we are noncommutative. It's because of the noncommutativity that time emerges out of the group. Instead of trying to write things down in time, as we do normally. In fact we should start, there is a variability that is much more important than the passing of time and that's a variability that is constantly present by quantum mechanics. ...Every second that passes has an incredible amount of new variability which is unpredictable. I claim that this is why the clocks turn..."
Conférence faite à l'Académie Royale de Belgique. : La géométrie non commutative en physique et en théorie des nombres. 1. Introduction à la géométrie non commutative
A point is defined by the 2 x 2 matrices... that have an inner noncommutative transformation...as the noncommutative quotient.
In many places in mathematics we are taking inductive limits defined by quotients. There are billions of examples of inductive limits in which the quotient set is not a good set - there are billions of examples...[the limit is a quotient]
the correct power of 2pi x i (imaginary) the total curvature is an integer. The irrational number disappears.
The Lagrange transform is actually a Fourier transform and you only get one eigenvalue (continuous).
In noncommutative geometry we have inner endormorphisms for any algebra...
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