Analytic Hyperbolic Geometry And Albert Einstein's Special Theory Of Relativity

Analytic Hyperbolic Geometry And Albert Einstein's Special Theory Of Relativity

AngličtinaEbook
Abraham Albert Ungar, Ungar
World Scientific Publishing Company
EAN: 9789814474016
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This book presents a powerful way to study Einstein's special theory of relativity and its underlying hyperbolic geometry in which analogies with classical results form the right tool. It introduces the notion of vectors into analytic hyperbolic geometry, where they are called gyrovectors.Newtonian velocity addition is the common vector addition, which is both commutative and associative. The resulting vector spaces, in turn, form the algebraic setting for the standard model of Euclidean geometry. In full analogy, Einsteinian velocity addition is a gyrovector addition, which is both gyrocommutative and gyroassociative. The resulting gyrovector spaces, in turn, form the algebraic setting for the Beltrami-Klein ball model of the hyperbolic geometry of Bolyai and Lobachevsky. Similarly, Mobius addition gives rise to gyrovector spaces that form the algebraic setting for the Poincare ball model of hyperbolic geometry.In full analogy with classical results, the book presents a novel relativistic interpretation of stellar aberration in terms of relativistic gyrotrigonometry and gyrovector addition. Furthermore, the book presents, for the first time, the relativistic center of mass of an isolated system of noninteracting particles that coincided at some initial time t = 0. The novel relativistic resultant mass of the system, concentrated at the relativistic center of mass, dictates the validity of the dark matter and the dark energy that were introduced by cosmologists as ad hoc postulates to explain cosmological observations about missing gravitational force and late-time cosmic accelerated expansion.The discovery of the relativistic center of mass in this book thus demonstrates once again the usefulness of the study of Einstein's special theory of relativity in terms of its underlying analytic hyperbolic geometry.
EAN 9789814474016
ISBN 9814474010
Typ produktu Ebook
Vydavatel World Scientific Publishing Company
Datum vydání 11. února 2008
Stránky 648
Jazyk English
Země Singapore
Autoři Abraham Albert Ungar, Ungar
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