Quantum Sense vid on intuitive understanding=noncommutative nonlocality Fundamental time-info-torque

"If you take very seriously that the origin of variability doesn't come from the passing of time but comes simply from the formalism of quantum mechanics, from the Hilbert Space. Then it's absolutely vital that you can relate to ordinary time and time evolution as we know. What I'm saying is...this solution depends on the fact that you have a subsystem, it depends on the factorization... [noncommutative]....
You need to understand intuitively...this is the most difficult to explain...that this time evolution is UNavoidable....You can not suppress it... It's not an inner automorphism. It has the amazing property....it's in the center of the group of inner automorphisms. Any other automorphisms of the algebra will commute with it. It's canonical. It doesn't depend on any choice. ...
You take a system that you repeat... it repeats everywhere ...to infinity...it's repetition that allows you to see time evolution...it's the factorizations which are infinite repetitions that give you this time evolution... Otherwise you wouldn't see it. ...Hilbert space and Hilbert Space operators KNOW and know a lot more than we think....the passing of time is due to our partial knowledge, because we don't know the full system....
What are the observables for gravitation? Who can we say where we are? The answer is spectral [frequency]. ...It's not enough to know the spectral operators... ...Two noncommutative shapes that are Isospectral [i.e. both Perfect Fifth]...They have the same spectrum but they do not have the same second invariant. [Second-order tensors may be described in terms of shape and orientation.]"
You find three types of notes of the spectrum. Integers plus 1/4 [Perfect Fourth], Integers plus 1/2 [Perfect Fifth] and Integers in the square of the spectrum [Octave] there are three kinds of NOTES. When you look at the possible chords - this is like the piano in which you can play...because they are three kinds of notes. The chords of two notes are possible for some shapes [Perfect Fifth] but not other shapes [Perfect Fourth]. The point is spectral, given by correlations between the eigenvalues (frequencies) of the Dirac operator.
There are factorizations with infinite degrees of freedom, that they generate, their own time; and this is a partial knowledge and of course it's related to thermodynamics and temperature and all that. ...The time evolution would not be the same if you changed T to Minus T. If it were the same when you changed T to Minus T then it would be trivial.
What I want is to transmit a mathematical fact...it's extremely striking. It suggests a philosophical fact ...which is that the fundamental variability is quantum other than the passing of time.
It's unique up to inner automorphisms; it means you have the flexibility to change it locally. So you can be locally out of equilibrium. You can have a pure density matrix which on the subalgebra in the factorization you see something which is not pure of course. Factor 4 x 4 matrices as 2 x 2 matrix times 2 x 2 matrix. Now take a vector, pure in four dimensional Hilbert Space... And then you do the inner transfer product of the four dimensional Hilbert space. ...That will be a factorization of Type III. ...A corresponding vector and you just repeat it. That's enough to get the time evolution....The time evolution is in the Subparts, it's not in the full thing.
By the way, I should say, of course this was the motivation for why I spent many years studying noncommutative geometry..."
Chris Dewdney - Quantum Trajectories and the Nature of Wholeness in David Bohm’s Quantum Theory
This is a very rare explanation of de Broglie's Ph.D. thesis! Thanks so much - and yes we all can learn to pronounce his name as "de Broy"!! hahaha. "And then they just retained this relationship between the momentum of a particle (its mass times its velocity) and the wavelength of the associated wave. And It's a great, in a sense injustice that Louis de Broglie is just reduced to this one formula when he was really thinking about pilot waves right from the start."
Understanding Heisenberg’s “magical” paper of July 1925: A new look at
the calculational details
Ian J. R. Aitchison, David A. MacManus, and Thomas M. Snyder
Citation: Am. J. Phys. 72, 1370 (2004)
This is what Alain Connes talks about and so the Pythagorean Comma is actually the same noncommutative exponential as the inverse for the matrices math!
So Professor Hiley points out there no longer is "time" in the exponential but rather his noncommutative nonlocal phase as the "unfolding parameter"!
So then Hiley explains when you use the noncommutative complex conjugate that you get the Jordan Product.

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Alain Connes revolutionized John von Neumann's theory of algebras. The famous mathematician is giving this Friday evening in Gif-sur-Yvette an exceptional conference as part of the Open University. An event that offers more than 70 conferences each year, including that of Alain Connes who will focus on "the music of forms", in other words the relationship between form and music. The scientist, who received the Fields medal in 1982 (the most prestigious award in the discipline), reassures the public: “You don't need to know math to come.

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Let us immediately dismiss one worry that always arises at this point.
Surely we cannot have an (x, p) phase space in the quantum domain because
of the uncertainty principle. The problem here is that in changing from α to
x and β to p, one immediately assumes the symbols (x, p) mean the position
and momentum of a point particle. But a deeper investigation shows that the
x and p are coordinates of the centre of an extended region of phase space,
a region that de Gosson has called a ‘blob’ [21]. A similar extended notion
of a particle was also proposed by Weyl [44] when he writes’
Hence a particle itself is not even a point in field space, it is
nothing spatial (extended) at all. However, it is confined to a
spatial neighbourhood, from which its field effects originate.
This idea of an extended region in phase space becomes much more com-
pelling if we evoke the “no squeezing theorem” of Gromov [23]. This deep
theorem reveals a new topological invariant that arises even in a commutative
symplectic geometry. It can be regarded as the “footprint” of the uncertainty
principle that quantum mechanics leaves in the classical domain [19, 20]. It
is only in the classical limit that the ‘blob’ becomes a point particle. Thus
to make the whole formalism work, we are forced to regard the ‘particle’, not as a point, but as a ‘blob’ with a finite extension in phase-space. In-
deed to accommodate this structure we need a product that is translation
and symplectic covariant, associative and non-local as was emphasised by
V ́arilly and Gracia-Bondia [42]. As we will see it is this non-local feature
that mathematically captures Bohr’s notion of wholeness.

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I think YouTube blocked my comments for review? Anyway, great video!

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"Problem II asks whether or not two nonisometric domains i21and i2 can be isospectral with respect to solutions(2), (4a). ...Even before the appearance of Kac's paper, Milnor considered problems analogous to Problem I for compact manifolds.That is, suppose M1 and M2 are compact manifolds in Rn, n> 2. It is known that for each such manifold M there is a sequence of eigenvalues 0 = A1? A2 ? ...*?** A k ?< ... and eigenfunctions Ul, U2, , Uk, ... which solve ...s. It turns out that in all dimensions certain inequalities hold among the eigenvalues regardless of the size or shape of the domain.We call these universal inequalities, and we shall see that among all sequences
of positive numbers tending to infinity those which correspond to sequences of eigen-
values are highly restricted. In ?4 we describe bounds for the first eigenvalue, i.e., the
fundamental tone in Problem I....a low fundamental tone the shape must be such that it contains in its interior a large circular drum...properties of Lie algebras to show that the two domains are not isometric. As Urakawa points out, not only is the problem for n= 2 and 3 still open, but the fact that domains such as U and U' have sharp edges leaves unsolved the
question of whether or not smooth isospectral domains are always isometric." Can One Hear the Shape of a Drum? Revisted
M. H. Protter
SIAM Review
Vol. 29, No. 2 (Jun., 1987), pp. 185-197 (13 pages)
Published By: Society for Industrial and Applied Mathematics

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This is not the ket, | 〉, that is used throughout physics. It is
denoted by the symbol 〉 and has been barely noticed. It was, in fact, Dirac’s
attempt to introduce a primitive idempotent into the Heisenberg algebra."
f the algebra is non-commutative it is no longer possible to find a unique underlying manifold. The physicist’s equivalent
of this is the uncertainty principle when the eigenvalues of operators are
regarded as the only relevant physical variables.
What the mathematics of non-commutative geometry tells us is that in
the case of a non-commutative algebra all we can do is to find a collection of
shadow manifolds. The phase spaces constructed by the methods of Wigner
and Bohm are then examples of these shadow manifolds. Thus we should
not regard Wigner and Bohm as lying outside the quantum formalism. They
are central to it. They are simply constructing different representations of
the same formalism. The emotional arguments that surround discussions
about the Wigner and Bohm approaches are totally misplaced. The appear-
ance of shadow manifolds is a necessary consequence of the non-commutative
structure of the quantum formalism."
The nature of quantum processes is such that its very essence is such that we can only
display some aspects of the process at the expense of others. We are inside
looking out. We are participating in Nature. We are participating through
our instruments. Because of our activity not everything can be made manifest
together. "

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of classical phase space.
3. We do not need operators in a Hilbert space.
2. This reproduces all the standard results of quantum mechanics
4. This algebraic structure contains classical mechanics as a natural limit.
No fundamental role for decoherence
5. The structure is intrinsically non-local.
CM uses point to point transformations in phase space.
QM involve non-local transformations expressed through matrices
Basic unfolding and enfolding movements
Algebraic approach.
Everything is done in the algebra.
Wave functions replaced by elements in the algebra.
Advantage: Uses Clifford algebra therefore includes Pauli and Dirac.
Therefore we need to use two time development equations.
The Quantum Torque, Quantum Potential

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You need to understand intuitively...this is the most difficult to explain...that this time evolution is UNavoidable....You can not suppress it... It's not an inner automorphism. It has the amazing property....it's in the center of the group of inner automorphisms. Any other automorphisms of the algebra will commute with it. It's canonical. It doesn't depend on any choice. ...
You take a system that you repeat... it repeats everywhere ...to infinity...it's repetition that allows you to see time evolution...it's the factorizations which are infinite repetitions that give you this time evolution... Otherwise you wouldn't see it. ...Hilbert space and Hilbert Space operators KNOW and know a lot more than we think....the passing of time is due to our partial knowledge, because we don't know the full system....
What are the observables for gravitation? Who can we say where we are? The answer is spectral [frequency]. ...It's not enough to know the spectral operators... ...Two noncommutative shapes that are Isospectral [i.e. both Perfect Fifth]...They have the same spectrum but they do not have the same second invariant. [Second-order tensors may be described in terms of shape and orientation.]"
You find three types of notes of the spectrum. Integers plus 1/4 [Perfect Fourth], Integers plus 1/2 [Perfect Fifth] and Integers in the square of the spectrum [Octave] there are three kinds of NOTES. When you look at the possible chords - this is like the piano in which you can play...because they are three kinds of notes. The chords of two notes are possible for some shapes [Perfect Fifth] but not other shapes [Perfect Fourth]. The point is spectral, given by correlations between the eigenvalues (frequencies) of the Dirac operator.
There are factorizations with infinite degrees of freedom, that they generate, their own time; and this is a partial knowledge and of course it's related to thermodynamics and temperature and all that. ...The time evolution would not be the same if you changed T to Minus T. If it were the same when you changed T to Minus T then it would be trivial.
What I want is to transmit a mathematical fact...it's extremely striking. It suggests a philosophical fact ...which is that the fundamental variability is quantum other than the passing of time.
It's unique up to inner automorphisms; it means you have the flexibility to change it locally. So you can be locally out of equilibrium. You can have a pure density matrix which on the subalgebra in the factorization you see something which is not pure of course. Factor 4 x 4 matrices as 2 x 2 matrix times 2 x 2 matrix. Now take a vector, pure in four dimensional Hilbert Space... And then you do the inner transfer product of the four dimensional Hilbert space. ...That will be a factorization of Type III. ...A corresponding vector and you just repeat it. That's enough to get the time evolution....The time evolution is in the Subparts, it's not in the full thing.
By the way, I should say, of course this was the motivation for why I spent many years studying noncommutative geometry..."

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less both the Wigner distribution theory [31] [29] [8] and the Bohm approach
[1] [5] [24] use such phase space pictures....The Bohm approach uses a different phase
space in which the momentum of a particle is given by p(x, t) = ∇S(x, t).
In this phase space particles are assumed to follow well-defined trajectories.
The ensemble of trajectories that correspond to a given initial probability dis-
tribution produce a final probability distribution which is again exactly the
same as that produced by ...The importance of this algebra is that in the limit of a small defor-
mation parameter (in this case ̄h) this algebra becomes the Poisson algebra
of classical mechanics. Indeed the star product can be written in terms of
two brackets, the sine or Moyal bracket and the cosine or Baker bracket. In
the limit the Moyal bracket becomes the Poisson bracket while the Baker
bracket becomes the ordinary product.
While all this is well-known, what is not so well-know is that these two
brackets have their exact analogue in the generalised algebraic formulation
of quantum mechanics as outlined for example in Emch [14] or for the more
mathematically inclined in Bratteli and Robinson [6]. I stumbled across the
connection while attempting to solve a different puzzle. Melvin Brown and
I [7]were trying find where the quantum potential arose in the Heisenberg
matrix form of quantum theory. We were led to a pair of algebraic equa-
tions, which were alternatives to the Schr ̈odinger equation and its dual in
the Hilbert space approach. One of these involved the commutator of the
density operator and the Hamiltonian. This equation is the exact analogue
of the equation of motion for the Moyal bracket.
The second equation involved the anticommutator or Jordan product of
these objects. This equation is clearly related to the Baker bracket but the
relation was not completely transparent. We will discuss this relation in more
detail later in this paper. This second equation is particularly interesting
because although it is an operator (representation-free) equation it contains
no quantum potential. However once it is projected into a representation, a
quantum potential immediately appears. Thus this potential is a consequence
of projection into a Hilbert space and plays no explicit role in the algebraic
structure as such. The projection splits the kinetic energy into two parts and
the quantum potential is a result of this split. This suggests that it is a kind
of internal energy as was discussed in Bohm and Hiley [5] and Hiley [17].he standard approach...."