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Complex Quantum Mechanics

Complex Quantum Mechanics is an extension to Classical Quantum Mechanics that has arisen as a result of rewriting complex mathematics. There was a conviction that there was a need to rewrite complex mathematics as the general impass in physics research could not be breached through scientific endeavour alone. While complex mathematics is used extensively in Classical and other versions of Quantum Mechanics its application is naturally limited because there are features of this mathematics that defy explanation. Complex Quantum Mechanics goes to the heart of these problems by interpreting:

1> How i^2 = -1 by using it as a translation between a spherical to a cubic geometry.

2> How the set of complex numbers can be ordered upon a three dimensional manifold.

3> How Eigenvalues map onto linear forces in complex space.

Complex Quantum Mechanics then goes farther by defining complex space as a valid space with a valid vector system. This in turn is used to validate the existence of complex forces.

Alexander Ross' Yahoo Group for CQM

This article paraphrases the section introducing quantum mechanics at this site to draw attention to the advances made by Complex Quantum Mechanics. No infringement of copyright is intended in this draft.

Comparative Historical background

The section on the Interpretation of Quantum Mechanics gives some reference points to show how Complex Quantum Mechanics takes Classical Quantum Mechanics much further. For instance Schrödinger originally viewed the wavefunction associated to the electron as the charge density of an object smeared out over an extended, possibly infinite, volume of space. This wave function is redefined as an F wave (Father's wave) that alternates phases between the third (3rd D) and fourth (4th D) SPATIAL dimensions. This is a major depature from current versions of Quantum Mechanics that all use time as the fourth dimension. The possibility of time being another non-spatial dimension is not seen as an essential part of Complex Quantum Mechanics. Max Born interpreted it as the probability distribution in the space of the electron's position. Albert Einstein had great difficulty in accepting some of the consequences of the theory, such as quantum indeterminacy. Even if these matters could be treated as 'teething troubles', they have lent importance to the activity of interpretation. It is this view that Complex Quantum Mechanics takes to new horizons by REMOVING probability and substituting the distortion of space and time instead.

In fact it may be said that Complex Quantum Mechanics has "shut up and calculated". An examination of Classical Quantum Mechanics Mathematics does nothing to disallow Complex Quantum Mechanics and in fact is achieving more evidence independently validating it although at this stage in the emergence of Complex Quantum Mechanics that is expected to be 'modest' in quantity.

Clarifying the Current Interpretations

The difficulties of interpretation reflect a number of points about the orthodox description of quantum mechanics, including:

The abstract, mathematical nature of the description of quantum mechanics. Complex Quantum Mechanics is a very abstract interpretation but it does achieve clarity in describing processes involved in Quantum Mechanics.
The existence of non-deterministic and irreversible processes in quantum mechanics are treated as exactly that in Complex Quantum Mechanics.
The phenomenon of entanglement, and in particular, the correlations between remote events that are not expected in classical theory. Complex Quantum Mechanics deals with this by removing the Uncertainty Principle and showing how entanglement is really a vague description of what is happening in complex space.
The complementarity of possible descriptions of reality. Complex Quantum Mechanics defines and reveals the 'new' reality based upon higher spatial dimensions and complex space.

First, the accepted mathematical structure of quantum mechanics is based on fairly abstract mathematics, such as Hilbert spaces and operators on those Hilbert spaces. In classical mechanics and electromagnetism, on the other hand, properties of a point mass or properties of a field are described by real numbers or functions defined on two or three dimensional sets. These have direct, spatial meaning, and in classical theories there seems to be less need to provide a special interpretation for those numbers or functions. This a source of confusion that Complex Quantum Mechanics resolves by introducing a new hypergeometry (geometry of higher spatial dimensions. In fact this has been the 'holy grail' for topologists who study fabricating the surfaces of higher dimensions.

Further, the process of measurement plays an apparently essential role in classical theory. However it seems contradictory to then relates the abstract elements of classical theory, such as the wavefunction, to operationally definable values, such as probabilities. Complex Quantum Mechanics resolves this by using a more practical measure of spatial distortion.

The Demise of the Uncertainty Principle

As a consequence of introducing the F wave and removing probabilty as a feature of Quantum Mechanics Complex Quantum Mechanics has disproved the Uncertainty Principle. The Uncertainty Principle states that it is not even possible TO SHOW that there is a way to describe a particle's position and state at the same time. This is exactly what the F wave does.

In addition the phenomenon of entanglement, as illustrated in the EPR paradox, which seemingly violates principles of local causality is brought into question with Complex Quantum Mechanics providing conjugate complex vectors or complex forces that allow for some mimicry rather than entanglement.

Another obstruction to direct interpretation is the phenomenon of complementarity, which seems to violate basic principles of propositional logic. Complex Quantum Mechanics seems like an answer to physicists' prayers in this regard. The thoery arose as a need to advance modern mathematics in the area of calculus and complex mathematics. The rewriting of complex mathematics achieves a new appreciation of calculus although it remains largely unchanged.

Complementarity means that composition of physical properties for S (such as position and momentum both having values in certain ranges) using propositional connectives does not obey rules of classical propositional logic. As is now well-known (Omnès, 1999) the "origin of complementarity lies in the noncommutativity of operators" describing observables in quantum mechanics. This is cited as independent support for Complex Quantum Mechanics.

Instrumentalist interpretation

Any modern scientific theory requires at the very least a description which relates the mathematical formalism to experimental practice and prediction. In the case of quantum mechanics, the most common instrumentalist description is an assertion of statistical processes. The bare instrumentalist description explicitly avoids any explanatory role; that is, it does not attempt to answer the question of what quantum mechanics is talking about. This is a great strength of Complex Quantum Mechanics and can be seen to strengthen Classical Quantum Mechanics by greatly expanding the applicability of Quantum Mechanics to experimental observations.

Summary of common interpretations of QM

Properties of interpretations

The interpretation given by Complex Quantum Mechanics satisfy certain necessary conditions, such as:

Realism
Completeness
Local realism
Determinism

To explain these properties, we need to be more explicit about the kind of picture an interpretation provides. An interpretation as a correspondence between the elements of the mathematical formalism M and the elements of an interpreting structure I, is still developing in Complex Quantum Mechanics

The current use in physics of "completeness" and "realism" is often considered to have originated in the paper (Einstein et al., 1935) which proposed the EPR paradox. In that paper the authors proposed the concept "element of reality" and "completeness" of a physical theory. Though they did not define "element of reality", they did provide a sufficient characterization for it, namely a quantity whose value can be predicted with certainty before measuring it or disturbing it in any way. EPR define a "complete physical theory" as one in which every element of physical reality is accounted for by the theory.

Complex Quantum Mechanics clearly conforms to these criteria although it's elements tend to overlap and can therefore lead to a more complex view that might have been anticipated for any one particular aspect of the work.

Determinism is a property characterizing state changes due to the passage of time, namely that the state at an instant of time in the future is a function of the state at the present (see time evolution). Complex Quantum Mechanics is clear in using a particular interpreting structures that are deterministic providing a clear choice for a time parameter. The F wave is an example of how a photon moves in time as it follows this wave pattern

Bell's theorem supports Complex Quantum Mechanics

A precise formulation of local realism in terms of a local hidden variable theory was proposed by John Bell.

Bell's theorem , combined with experimental testing, restricts the kinds of properties a quantum theory can have. For instance, the experimental rejection of Bell's theorem implies that quantum mechanics cannot satisfy local realism. This can now be seen as a mistake and Complex Quantum Mechanics does satisfy local realism.

Ensemble interpretation, or statistical interpretation

The Ensemble interpretation, or statistical interpretation is an interpretation that can be viewed as a minimalist interpretation. That is, it is a quantum mechanical interpretation, that claims to make the fewest assumptions associated with the standard mathematical formalization. Complex Quantum Mechanics is true to this tradition in that it reduces probability to spatial distortion. The statistical interpretation becomes not one of probability but one of measurement of the distortion of space.

The attempt to conceive the quantum-theoretical description as the complete description of the individual systems leads to unnatural theoretical interpretations, which become immediately unnecessary if one accepts the interpretation that the description refers to ensembles of systems and not to individual systems.
— Einstein in Albert Einstein: Philosopher-Scientist, ed. P.A. Schilpp (Harper & Row, New York)

This comment can be helpful in certain experimental areas but Complex Quantum Mechanics is so good that it is now possible to consider individual systems in isolation.

The Copenhagen interpretation

The Copenhagen interpretation is the "standard" interpretation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg while collaborating in Copenhagen around 1927. Bohr and Heisenberg extended the probabilistic interpretation of the wavefunction, proposed by Max Born. The Copenhagen interpretation is flawed, as mentioned above in the Uncertainty Principle above, but is correct in rejecting questions like "where was the particle before I measured its position" as meaningless. In this respect it supports this feature of Complex Quantum Mechanics if not completely aware of it at the time of this collaboration.

Consciousness causes collapse

This is a weak area, but not on its own, in classical Quantum Mechanics that provides no proper means of validating its claims.

Objective collapse theories

In objective theories, collapse occurs randomly ("spontaneous localization"), or when some physical threshold is reached, with observers having no special role. In this respect it follows Complex Quantum Mechanics before departure. The physical threshold is described by waves making up a Grand Unification Theory connected to my Complex Quantum Mechanics. Complex Quantum Mechanics however gives this change has gradual and in waveform. This can be a little misleading though as the existence of quantum levels is not rejected by Complex Quantum Mechanics. In fact the positions of the electron shells can now be fixed.

The decoherence approach

Decoherence occurs when a system interacts with its environment, or any complex external system, in such a thermodynamically irreversible way that ensures different elements in the quantum superposition of the system+environment's wavefunction can no longer interfere with each other. Decoherence does not provide a mechanism for the actual wavefunction collapse; rather it provides a mechanism for the appearance of wavefunction collapse. Complex Quantum Mechanics can clarify this by using the F wave showing how the collapse is controlled.

The quantum nature of the system is simply "leaked" into the environment so that a total superposition of the wavefunction still exists, but exists beyond the realm of measurement. This is another supportative area for Complex Quantum Mechanics. The use of a fourth spatial dimension by Complex Quantum Mechanics explains the difficulty in measuring sub atomic events.

The Bohm interpretation

The Bohm interpretation of quantum mechanics is an interpretation postulated by David Bohm in which the existence of a non-local universal wavefunction allows distant particles to interact instantaneously. Complex Quantum Mechanics does not entirely agree with this introducing mimicry as an alternative solution. It is unlikely that complex forces could act like this INSTANTANEOUSLY but they could act like this otherwise given entexended periods of time and no interference between object and source.

The interpretation generalizes Louis de Broglie's pilot wave theory from 1927, which posits that both wave and particle are real. This is yet another suggestion that Complex Quantum Mechanics is correct.

References

1. Complex Waves in Classical Quantum Mechanics http://en.wikibooks.org/wiki/Quantum_Mechanics/Complex_Waves

2. Are Complex Numbers Essential to Quantum Mechanics? by Robert French http://www.quantumrealism.net/uploads/Complex_numbers.doc

3. Hermann Weyl's views uphold my Complex Quantum Mechanics http://publish.uwo.ca/~jbell/Hermann%20Weyl.pdf

4. Roger Penrose has written a paper titled: "Angular Momentum: An Approach to Combinatorial Space-time:" Keep your eye on this work it will probably be quite relevant to my Complex Quantum Mechanics. http://math.ucr.edu/home/baez/penrose/Penrose-AngularMomentum.pdf