Basil J. Hiley confirms Alain Connes noncommutative nonlocal truth of reality: inner cross products

I got a nice reply from Professor Basil J. Hiley when I asked him about the Poisson Bracket in a noncommutative context.
Dear Drew,

In my approach there is no need to refer to any wave function. Each individual process is described by the non-commutative elements of the phase-space algebra itself. Classical physics uses a commutative phase-space algebra. Classical physics has the Poisson brackets as a vital part of the description. What we have to understand is how that bracket emerges from the non-commutative structure. Now the non-commutative algebra contains two types of bracket, a commutator or Lie bracket (or Lie product to give it its proper mathematical name) and an anti-commutator or Baker bracket ( known as the Jordan product). The Lie bracket becomes the Poisson bracket as we go to the classical limit, while the Jordan product becomes the normal inner product. In symbols (AB + BA)/2 — AB. The Jordan product is the most neglected product in the whole discussion of the foundations of quantum mechanics. "

It is the spin that led me to the idea of no ‘waves’. One of the important things which keeps the ‘wave’ idea alive is the notion of ‘phase’, of interference, but in the case of non-relativistic spin there two ‘phases’— R(1)expiS(1) and the second component R(2)expiS(2). So how do you think of two ‘phases’ in interference phenomena; in Dirac there are four 'phases’. OK so you can think of 'four waves’. Why ‘four’, but what has happened to the simple idea of interference? The whole picture has suddenly become more complicated and confused. Four waves to be ‘collapsed’? The story seems bogus to me, but that is just my opinion. The simple picture loses it appeal, like the epicycles of Ptolemy. They work but nobody now believes in that story.

Of course you have to explore the algebraic way and see if it makes more sense. I do and to me it fits more naturally into the mathematical scheme I am developing. By the way it is not just me. Look, for example, at Rudolf Haag’s book, “Local Quantum Physics, Fields, particles and Algebras.” Chapter III onwards is the area I have been studying. But there is much more interesting ideas being developed i.e. Alan Connes “Noncommutative Geometry."

Basil Hiley.
Could you please give me the reference where Alan Connes shows "how the Type II inner product discrete numbers are actually not random”.

Basil.
In this paper we examine in detail the non-commutative symplectic algebra
Connes:

And if the cardinality of the Set X is a continuum, then it means that any other variable on the same set X – so if I take another variable X goes to R, then if that variable G happened to be discrete and we take only a countable set of values, then some of these values would have infinite multiplicity. And not only countable infinity multiplicity but in fact uncountable infinity multiplicity.

So this means this formulism, as good as it looks at first sight, is in fact excluding the coexistence of continuous variables with discrete variables. So at first this looks very bothering, but it turns out that this problem has a beautiful solution, that this solution is given by the quantum formalism, as written by Von Neumann.

So this is like the piano, if you want, in which you can play, in both cases, because there are three different kinds of notes. But somehow I will call something a chord if there exists a point at which the corresponding eigenfunctions both don't vanish. OK? So and either it could be three Perfect Fifth on the piano. It turns out that the chord which is blue-red is not possible for shape two but it is for shape one.

We are wrong to try to write things in time. Because of our minds, which are logical, we always trying to reconstitute a logical past... Just because we want to feel happy about it. What I'm saying is that things might be different and that there could be a fundamental quantum variability...

Type One does not involve infinitely degrees of freedom. Type Two - evolution is unavoidable, it occurs infinitely.... You can not suppress it. It's not an inner automorphism. It has the amazing property that, it is in the center of the group of automorphisms....it doesn't depend on any choice. ....It is repetition that will allow you to SEE this time evolution... factorizations as infinite repetitions - otherwise you would not see it.

My feeling is that the passing of the time could very well come from the fact that we UNable to know all observables in the quantum mechanics.... we are unable to control all the observables of the universe. We are only able to control a small part of them which is a factorization of this kind. And because of our lack of knowledge of the full observables, we have the feeling that time is passing.

SpaceTime is emergent and a corollary of our lack of knowledge.... There is a relation between thermodynamics and the Big Bang...

[branchesNine]

What does it mean when the ground shakes after a few weeks of heaven to earth sets.