A New Copernican Revolution

About the Book

The geometries of polygons, polyhedrons, and polytopes can be used within a mathematical context of differential equations to describe the world. This is done in the new book A New Copernican Revolution. The physical world is currently being described so that a particular metaphysics is satisfied, namely, that material defines existence within a mythological coordinate system, namely, local space-time coordinates. This mythology gets tripped-up by the properties of the micro-world, such as spin, supersymmetry, and fixed energy levels of micro-systems, along with the mathematical property that coordinates and functions do not always coincide with one another. This has resulted in a relatively new aspect of existence to be added to the mythology of physical description, (or the academic contest [or investment concerns]) namely, the idea that everything is determined by probability, ie function spaces are the basis for physical description. Spin has been used as an extra, alternative, elementary event space which can carry surprises. This use of probability, both function spaces and internal spin symmetries, is not necessary, and the logic of a useful description requires actual descriptions of the physical world rather than a overly broad vision of the world, ie its metaphysics, and a probability structure through which "all" events can be fitted into this myth. In the current paradigm, the stability of micro-structures, (that is so obvious) cannot be described, instead the metaphysical material existence can be given probabilities within a mythological coordinate structure. The accepted metaphysics of physical description has jeopardized what can be described by fixing the terms within which the description must exist.

Using polygons, polyhedrons, and polytopes along with differential equations in a fiber bundle structure, which is a similar mathematical structure as quantum field theory uses, the hidden world of what really exists can be uncovered. A causal description of spin states and their relation to both "metric-states" and motion is given. It opens the real world up to explicit descriptions and rational thought. Supersymmetry becomes a necessity of the self-similar discrete group structures in a dimensional hierarchy of metric spaces.

The main mathematical idea is that, within a principle fiber bundle, one looks in the base space at the spectral structure of different signature metric spaces in a dimensional hierarchy of metric spaces. Within such a mathematical structure both material and spatial system properties can be identified. Furthermore, there exists in this description, a resonance relation between the base manifolds of the principle fiber bundle and their fiber groups. It is a maximal torus within the fiber groups which play the role of "the complete set of spectra" of all possibilities that are accessible to our awareness. These maximal tori contain the spectral information of all possibilities within a single galaxy. Within the base spaces of the principle fiber bundles, certain spectral shapes of metric spaces naturally oscillate. The base space's oscillation, and the fiber group's resonance, together form a filter for many worlds. This natural oscillation is both the essence fo life and the basis for life's intent.

The key elements of the shaman's world [as described by Carlos Castaneda in the "new" forward to his first book, "The Teachings of don Juan,"] are "the dark sea of awareness," and intent. Both of these abstract ideas are given a geometrical and quantative form (in a new mathematical theory) which yields to the quantitative structures of both mathematics and experiment. The context of life and death, within an existence that has many facets (or many worlds) to it, is also easily described in terms of geometry within a dimensional hierarchy.

The mathematical descriptions of this new book are not techniques that can lead a person to internal powers, rather they are descriptions of abstract existence itself, where life, mind, and material have both geometric and quantitative relations to one another, ie a quantitative description that has an easily identified geometric context.

The esssence of all life, (and mankind in particular) is to create. However, one's essence is also to attain the full realization of one's will or intent. To gain the direct attainment of one's will, is to be able to create a world, by one's own intent, as real as the world which we presently call real. How we place our attention on the "world" we call real, is filtered by how our attention (and belief) is hooked to the metaphysics (underlying beliefs) of what we think exists.
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A new, alternative rearranging of the mathematical structure of physical description, based on the same FIBER BUNDLE structures as QUANTUM FIELD THEORY, but WITHOUT a probabilistic interpretation, is given in the new book A New Copernican Revolution. With a causal basis, it answers questions about quantum interaction, stability of nuclei, how spectral structures define reality, the stability of the solar system, the nature of the sun's energy source, what the vacuum is, the geometry of local inertia, and gives a geometric model of both SPIN and SUPER-SYMMETRY.

The key concepts relate to:
• Hermitian space
• Isometry groups
• The signatures of real metric spaces
• DISCRETE ISOMETRY SUBGROUPS
• Physical (and/or material) interpretations of metric space spectra, [which become mathematical axioms]
• A DIMENSIONAL HIERARCHY of metric spaces [This dimensional hierarchy stops at space-time dimension 11, because of the properties of HYPERBOLIC DISCRETE SUBGROUPS]
• A new vacuum based on RESONANCE
• Differential operators with discrete group boundary conditions
• Inertia which has non-global, local origins

The mathematical rearrangements are as follows:
A base space of the principle fiber bundle is determined by the spectral structure of different signature metric spaces that are within a dimentional hierarchy of these same metric spaces, so that each different signature metric space has a material-geometric interpretation which allows the identification of the two [opposite (or inverse)] covering states of the isometry group's spin representations. There is also a dual real-Hermitian space description that coincides with a metric space-material duality, that is fundemental to both wave mechanics and supersymmetry.

The finite dimensional unitary fiber group and the real subgroups it contains, can form a resonance relation with the spectral structures of the hierarchy of geometric forms on the base space, so that this resonance determines the hierarchy's binding energy. The structure of this resonance process can be considered to be analogous to the vacuum.

Instead of the variation techniques of point particle Lagrangian's the (elliptically) equivalent Dirichlet Lapacian is used so that the boundary conditions are determined by the spectral shapes of the distinct metric spaces' (discrete isometry subgroup) spectral structures.

At dimension three and less there exists spherical symmetry.

About the Author

These new ideas stand on their own as Copernicus's ideas stood on their own without Copernicus being a full fledged member of his culture's dominant institutions. There are new scientific ideas that are outside both the metaphysics and dogmas of modern day big instritutional science. They create a complete, new world view, within which a new axiomatic structure for the language of physical description can be comprehended, just as Copernicus's ideas formed a new basis for the language of physical description in his day. B Bash first presented the two main ideas of: (1) using discrete isometry subgroups to model physical systems which are stable, with the non-local geometries of discrete groups, and (2) creating a new interacting notion of a vacuum. P Coatimundi extended these new ideas so that they consistently contain a model of motion.

B Bash and P Coatimundi both have PhD's in mathematics, one from ASU and the other from UC respectively. They were both interested (at first) in physical theory, and both found the ideas of modern physical theory to be unbelievable.