Negative Frequency nonlocal 1/2 spin antigravity negative resonance Pythagorean Law of Phase Harmony

"This lead him [Dirac] to the conclusion that he described two spin-1/2 particles, one pair with positive and one pair with negative frequencies. Thus the solutions with positive frequences can immediately be identified with particles of positive energy. As long as free particles are concerned you can just say that the negative-frequency solutions are unphysical."
A Note on "Extension, Spin and Non Commutativity"
B.G. Sidharth
"We show that the Dirac theory of the electron, corresponds to recent approaches based on a Non commutative spacetime. "
In this paper, we endeavor to extend the noncommutative relations between the coordinates and the momenta. We find that the momentum operators conform to anti-commutation rules. This helps us to explain the extra terms emerging in case of the Landau quantization and we find that the emerging magnetic term is a direct consequence of the noncommutative nature of space-time. This intuition has been further extended to explain the large magnetic fields arising from compact stellar bodies.
Physicist B.G. Sidharth points out, light has mass due to noncommutative spacetime (noncommutative phase). "Therefore, the underlying geometry behind the superluminal nature of a particle is simply the noncommutative geometry."
And Professor B.G. Sidharth again:
"Returning to the mass of the photon, it can be argued that this is a result of the non commutativity of spacetime at a micro scale."
And so therefore we confront the hidden truth of reality: Time-frequency uncertainty actually originates from non-local, noncommutative phase logic!
"Non commutativity is the central mathematical concept expressing the uncertainty."
Basil J. Hiley recent paper
"The connection with geometric aspects of quantum phenomena allows us to introduce Clifford algebras in a natural way so that it is possible to extend the Dirac–Bohm approach to include spin and relativity, offering new geometric insights into quantum phenomena. In particular the bi-vector aspects allow us to introduce the Gromov non-squeezing theorem in a new way, ultimately offering the possibility of relating our work to the non-commutative geometry of M-theory."

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Within this description the quantum potential plays the role of an internal
energy necessary because of the way we are constructing our shadow manifolds. This
potential is totally unlike any classical potential. It has features more akin to a self-
organising potential. Indeed this self-organisation occurs in response to the environment
in which the quantum process finds itself. In fact we have argued elsewhere that
expressing the process in a shadow manifold determines an information dynamics (Hiley
1999)

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What I want to suggest that it is in this pre-space that mind and matter appear as different aspects of the same underlying process.
Thus mind and matter are united through mutual participation in which separation
is not possible. They are two aspects of an indivisible totality, the implicate order.

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On the philosophical side, this non-commutative algebra is actually a
mathematical expression of Bohm’s implicate order [3]. The algebra is a
mathematical description of what Bohm calls the implicate order. The
shadow manifolds are examples of what Bohm calls explicate orders aris-
ing from the participation of ourselves or our measuring instruments in the
process itself. "

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As we have remarked earlier it is not possible to describe quantum processes in
terms of a classical phase space because x and p cannot be defined simultaneously. This
is a consequence of the non-commutative structure of the formalism. All we are able to
do is to construct shadow phase spaces, each one being an explicate order defined by the
context in which it is displayed.
Thus in the example we have discussed above we have two shadow phase spaces,
one based on the x-representation, the other based on the p-representation. These are
shown in figure below. Each, although different from the classical point of view, is
necessary for a full representation of the quantum process. The non-commutativity of the
underlying process produces an ontological complementarity."

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Notice we are not regarding the lack of precision as being due to an 'uncertainty'
as if everything is actually certain, but that we, as observers, are uncertain as to the
precise values because of some 'ham-fisted' use of apparatus. We are arguing that the
process itself is such that it is not possible in principle to define x and p together because
simultaneous x and p does not have a meaning.
The basic underlying assumption of this general approach is that the ontology is
based on process, a process that cannot be described explicitly. It can only be described
implicitly, hence the terminology 'implicate' order. This implicate order is a structure of
relationships, and this order of structures is described by an algebra, the algebra of
process (Hiley 1995). Here the implicate order is not some woolly metaphysical
construction, it is a precise description of the underlying process, mathematically
expressed in terms of a non-commuting algebra. This process only allows partial views
because nature is basically participatory."

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"This suggests that the appearance of the quantum potential, called “mystical” by Feynman [37] when it arises in the equation of motion that he obtains for a superconducting fluid, may not be so mysterious after all! Its source is related to gauge invariance, which we already know, plays an important role in quantum mechanics. We will develop the quantum aspects later. Here we merely want to point out how the extra term arises in the classical domain as a result of a constraint, namely, the conservation of energy.

It has been shown elsewhere [38] that the extra term
leads directly to the Coriolis force when a particle is constrained to move on the surface of a rotating sphere. Mathematically we have a problem as one cannot cover a sphere by a single coordinate system. Although locally we have no problem, we have a global difficulty because of the non-single valued nature of the rotation group."

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To give a flavour of the attitudes of the time, consider the title of Hamilton's (1837)
lecture "The Metaphysics of Mathematics-Algebra as Pure Time", a title that one would
expect from someone on the fringe, and not someone at the centre of things! In that
lecture he wrote:
In algebra relations are between successive states of some changing thing or thought. In other words algebra is not about material process but something more general that could be applied to both matter and mind.
Grassmann (1995) takes this further. He argues that mathematics is about thought,
not material reality. It is about relationships of form, not relationships of content.
Mathematics is to do with ordering forms created in thought. Thus since thoughts are not
located in space-time, mathematics is not necessarily about material things in space-time."

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Misfire is finally gone on the inline six engine!!

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The detailed calculations show that it is this non-local feature that is ultimately

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"It has been argued that spin is purely a quantum effect, but that conclusion is not correct. One can demonstrate the difference between and rotations in the macroscopic world as shown in the “belt trick” or variations of it [20]. "

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When we are faced with a non-commutative dynamics, we have a serious
problem. There is no unique underlying manifold, no unique underlying
phase space and therefore no unique underlying space-time. Such a situation
was already anticipated by Einstein [14] when he wrote
."...perhaps the success of the Heisenberg method points to a
purely algebraic description of nature, that is, to the elimina-
tion of the continuous functions from physics. Then, however, we
must give up, in principle, the space-time continuum."
Einstein here attributes the non-commutativity to Heisenberg.

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I am arguing here that these global structures are not merely properties of
the material world. They have ramifications for all forms of activity, in-

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The negative time derivative, which does not equal the positive time derivative in this case,

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Basically, due to the noncommutative feature we see that space and time are already

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The question is, can gravitation also be included in such a scheme, and if so can this point to the long sought after unification of gravitation and electromagnetism?
We will now argue that indeed this is so - it is an underlying non commu- tativity of the spacetime that has kept apart gravitation which relies on a smooth spacetime manifold on the one hand, and Quantum Theory on the other hand, though the latter also uses a smooth manifold as an approximation."

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At the deepest level the process has neither colour nor shape.