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A New Copernican Revolution

by Bill G.P.H. Bash and George P. Coatimundi

286 pages; quality trade paperback (softcover); catalogue #03-1913; ISBN 1-4120-1535-9; US$29.95, C$39.00, EUR25.35, £17.57

A book about both material's and space's non-local geometric relation to fiber groups of principle fiber bundles, it subsequently reveals the fundamental structure of life's intent and our perception.

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about the book      about the authors      sample excerpts or Table of Contents      catalogue info

About the Book What A New Copernican Revolution is about 1. What problems of modern physical science the main ideas of the book address 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. 2. The new mathematical structure (What the book really addresses) 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. 3. Science and religion are the same: namely, to describe what exists and to place mankind in that context 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. ---------------------------------------------------------------------------------------- A NEW COPERNICAN REVOLUTION Are You Ready for New Ideas? Only a Handful of People Read Copernicus! 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 ------------------------------------------------------------------------------------------------ NEW IDEAS IN A NUTSHELL 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. The metric space of our experience is a 3-dimensional flow (the same flow that stabilizes the planetary orbits) on a 4-dimensional space-form. The 3-dimensional metric-space time state contains 2-dimensional material structures. These 2-dimensional material structures interact through 3-dimensional space-forms which are projected into the 3-dimensional metric flow of our experience. These projected 3-dimensional space-forms give the structure of local curvature. The compact 2-dimensional space-forms are nuclei and some atoms and molecules. Note: There are as many metrics spaces in the description as there are differential material types.

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About the Authors 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.

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Sample Excerpts

Part 1; The Context of the New Ideas, and/ or Communicating these New Ideas
0. What The New Copernican Revolution, Is About

This book presents a new paradigm for physics and mathematics, that alters not only physics, but it also alters the notion of life, and the position of life in the universe. Life is modeled mathematically as a non-local structure, similar to how material and space are modeled, but life oscillates and sets up a resonance with a vacuum (a vacuum with a new structure). Existence depends on this resonance between spectral forms, defined on metric spaces, and a vacuum contained within the fiber groups. With this model of life and existence, the axiomatic structure of mathematics is taken to its edges. Furthermore, this new paradigm of physics, no longer needs probability for its basis, yet, the new, non-local structure, can also account for wave-particle duality.

The new paradigm answers the questions of: Why is the nucleus stable? Why is the solar system stable? What distinguishes a state (or quantum) description from a classical (or smooth) description? (The answer is related to the geometric structure of our metric space, in a dimensional hierarchy of spaces.) What is the "real" solid state theory of superconductivity? What is the structure of the sun, and what fuels it? How are we "really" connected to other worlds, or other universes? How does (semi-local) geometric shape affect the inertia of mass? (That is, material is successfully placed within the context of General Relativity.) Why is spherical symmetry so important for low dimensions? Why does there exist an external order, within which the ideas of complexity can (or do) work? and What is a morphogenetic field, ie what is life? The currently accepted paradigm has no verifiable answers to any of these questions.

The currently accepted paradigm tries to deal with the following questions, but its own axiomatic pre-conditions keep its answers formal and essentially, dysfunctional: What really are spin, super symmetry, matter, anti-matter, charge and monopoles, other than formal mathematical notions? How are material and metric symmetry connected?, ie general relativity. and How can the red shifts of distant stars be explained? The new paradigm gives clear (geometric) answers to these questions, and it also provides a new context in which to place the description of both molecular shape, and molecular dynamics, especially in living systems. Furthermore, within the new paradigm, the mathematical structures of internal symmetries are given their proper geometric context, without the need for the notion of the probability of occupation of the infinitesimal harmonic oscillators. These infinitesimal harmonic oscillators have been supplanted, in the new theory, with non-local geometries, dimensional hierarchies, and causality.

This new paradigm is based on a more consistently put together, set of mathematical ideas and physical interpretations that, essentially, includes the mathematical structure of the currently accepted paradigm.

The basics ingredients of physical description are:
(1) material and (2) space (or coordinates) and its number field, (3) its vector structures, (4) using local changes of coordinates (that are related to; mass and/ or a system of fields, or to material-spectral constraints [or boundary conditions]) to describe material (This is done with) (5) differential operators, (6) symmetries of the differential operators and/ or of the coordinates, and (7) the functions (or spectral space) upon which a relatively stable systems' differential operators act. (8) The geometric models of atoms, molecules, and crystals.

The symmetries and the coordinates, together, compose a principle fiber bundle. This new theory models material as being related to both metric spaces of particular signatures, (see glossary) and these metric spaces' discrete group structure. The differential operator becomes a part of this discrete structure. The operator becomes defined on the set of functions, that are themselves defined on the non-local spectral shapes, which model both material and physical systems. One of those physical systems is the structure of metric space itself. The new (oscillating) metric structure of our experience gives one example of, how this new paradigm shows how the axioms of mathematics depend on how we describe our existence, and thus there is a need to extend (or alter) mathematics' axiomatic structure.

Though evolution is a force in the development of life, within this new paradigm, it is seen that evolution is not the only such force, nor even the main force, in life's development. This has implications for our present day ideas about social structure and social development. Furthermore, this new, technical theory, gives the context for life's relation to existence, and the relation between death and the creative impulse of life.

In the new paradigm, the vacuum is created by the oscillation of a bounded, 5-dimensional, spectral shape, (the sun) that identifies the spectral context of material, ie atoms, and space, which are in resonance with the "sun's" oscillations. This spectral information is projected down into the 3-dimensional metric structure of our experience, and this identifies the spectral inertia of the vacuum. This might be restated to mean; "That our material experience is being determined by the dream of the sun," which is what the 5-dimensional spectral shape models. Humans lives may be modeled as 3-dimensional, oscillating spectral shapes, this means that we have also have a spectral inertia associated with ourselves. This is the core of our dreaming and creative capacities.

Who Is This Book Addressed To?

It is written for a few intellectually disciplined people who want a new view of knowledge, science in particular, that is outside the domination of the dogmas of "Big Institutional Science." Modern physical science, burdened with its dogmas and its axiomatic interpretations, is no longer capable of answering practical questions about material systems. The audience of this book is exactly analogous to the audience, that the writings of Copernicus were designed for. Namely, a few disciplined intellects outside of the dominating influence of the church. The church was the domineering, dogmatic institution of the feudal system, in the day of Copernicus. Similarly, big institutional science, has a dominating role in its relation to corporate, commercial-military interests today.

However, this new paradigm, also alters our notions of life, hence, it is also relevant to issues of both societal structure and to spirituality. The language of technical science and math, is the language in which this new paradigm of science, is expressed. It is written in an instructive manner, for those interested in math and science (physics and math). However, it also supplies a context of life, and life's relation to existence. Hence, it should also be one of interest to those spirituality inclined. It places life in a new context, this means, it also creates a new relation between man and his society, that must be reconsidered. The material aspects of society's present focus, are placed in contrast to, the creative capacity of human life, which has influence throughout all of existence.

Accessibility

These ideas have not been accessible to the channels of institutional science, because big science is burdened with dogmas and axiomatic interpretations, that are held in place by big science's important personalities and the funding traditions, along with the interests of those investors. This new paradigm is outside their dogmatic structure, and their cultural traditions.

Technical Short

This book presents a new paradigm for physical theory. It describes a dimensional hierarchy of non-local shapes, that resonate with a spectral set on a maximal torus, which is contained in a fiber group of a principle fiber bundle. The spectral shapes emerge from different signature (real) metric spaces and their discrete isometry subgroups, to fill the base manifold of the principle fiber bundle, with material and space.

It describes spectral stability without probability, and it allows inertia to be related to both spherical symmetry and to other non-local geometric shapes.

It gives fundamental forms to both life and mind. It provides a new physical context for life's development.

Life is about creativity, and death can also be about creativity. It provides a context for the relation between death and the creative impulse of life.

Short

This book presents a new paradigm of physics and math, which alters not only physics, (allowing physics to once again provide answers to practical questions) but also the notion of life, and provides a context for life's relation to all of existence.

The Use of This Knowledge

Being the authors of these core ideas which form a new paradigm for physics, we can state how these ideas can be used. These ideas of the new paradigm, cannot be used for creating tools or instruments, which are to be used for (military) destructiveness and coercion, irregardless of whether it is called defense or offense, or intellectual or physical.

These ideas must be used to help both mankind, and our living planet. These ideas are not to be exploited for personal gain.

It is the nature of man to want to use knowledge to live in harmony with the planet.

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