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Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession: The Theory of Gyrogroups and Gyrovector Spaces (Fundamental Theories of Physics) epub

by Abraham A. Ungar


Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession: The Theory of Gyrogroups and Gyrovector Spaces (Fundamental Theories of Physics) epub

ISBN: 0792369092

ISBN13: 978-0792369097

Author: Abraham A. Ungar

Category: Science

Subcategory: Mathematics

Language: English

Publisher: Springer; 1 edition (March 31, 2001)

Pages: 464 pages

ePUB book: 1942 kb

FB2 book: 1473 kb

Rating: 4.2

Votes: 400

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Evidence that Einstein's addition is regulated by the Thomas precession . The application of gyrogroup-theoretic techniques clearly tilt the balance in favor of Einstein.

Evidence that Einstein's addition is regulated by the Thomas precession has come to light, turning the notorious Thomas precession, previously considered the ugly duckling of special relativity theory, into the beautiful swan of gyrogroup and gyrovector space theory, where it has been extended by abstraction into an automorphism generator, called the Thomas gyration. The gyrogroup-theoretic techniques developed in this book for use in relativity physics and in hyperbolic geometry allow one to solve old and new important problems in relativity physics.

Fundamental Theories of Physics. Table of contents (13 chapters). The Ungar Gyrovector Space. Ungar, Dr. Abraham A. Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession. The Theory of Gyrogroups and Gyrovector Spaces.

Series: Fundamental Theories of Physics (Book 117). Gyrogroups, also known as k-loops by some authors, is one of the few exceptions. Dr. Ungar has done an outstanding job in producing textbooks explaining the basics of gryogroups and how they may be applied to relativistic physics and hyperbolic geometry. His approach is different from those who usually work in loop theory. His approach and notations take advantage of the fact that Einstein's relativistic vector addition forms a gyrogroup. A weak-associative law is obtained by means of Thomas precession which is rarely studied in special theory of relativity.

PDF On Nov 30, 2001, Abraham A. Ungar and others published Beyond the . Ungar and others published Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession. The laws of propagation of electromagnetic waves modify Newtonian formalism for fast free motions within each spatial domain of its validity for slow motions and introduce the extended concept of time by uniting those of Newtonian which can exist in different spatial domains of their validity. A boost direction for a pair of frames is that spatial direction in one frame along which the other frame moves

The Theory of Gyrogroups and Gyrovector Spaces. 2001 ISBN 0-7923-6909-2 118. R. Miron, D. Hrimiuc, H. Shimada and . Sabau: The Geometry of Hamilton and Lagrange Spaces. 2001 ISBN 0-7923-6926-2. 2001 ISBN 0-7923-7006-6 120. . Santilli: Foundations of Hadronic Chemistry. With Applications to New Clean Energies and Fuels. 2001 ISBN 1-4020-0087-1 121.

2. Gyrogroups: Modeled on Einstein's Addition. 3. The Einstein Gyrovector Space. 4. Hyperbolic Geometry of Gyrovector Spaces. 5. 6. The Mobius Gyrovector Space. 2. 8. Gyrooperations - The SL(2,C) Approach. 10. The Lorentz Group and its Abstraction.

Thomas Precession: Its Underlying Gyrogroup Axioms and Their Use in Hyperbolic Geometry and Relativistic Physics, Abraham A. Ungar, Foundations of Physics, Vol. 27, No. 6, 1997. Hyperbolic Barycentric Coordinates, Abraham A. Ungar, The Australian Journal of Mathematical Analysis and Applications, AJMAA, Volume 6, Issue 1, Article 18, pp. 1–35, 2009.

Einstein's theory of relativity is a famous theory, but it's little understood. The theory of relativity refers to two different elements of the same theory: general relativity and special relativity. Fundamental Principles of Relativity. Learn all about the concepts that make up the theory of relativity. The theory of special relativity was introduced first and was later considered to be a special case of the more comprehensive theory of general relativity. General relativity is a theory of gravitation that Albert Einstein developed between 1907 and 1915, with contributions from many others after 1915. Theory of Relativity Concepts.

Series Statement: Fundamental theories of physics. Download DOC book format

Series Statement: Fundamental theories of physics. Download now Beyond the Einstein addition law and its gyroscopic Thomas precession the theory of gyrogroups and gyrovector spaces: Download PDF book format. Download DOC book format.

Evidence that Einstein's addition is regulated by the Thomas precession has come to light, turning the notorious Thomas precession, previously considered the ugly duckling of special relativity theory, into the beautiful swan of gyrogroup and gyrovector space theory, where it has been extended by abstraction into an automorphism generator, called the Thomas gyration. The Thomas gyration, in turn, allows the introduction of vectors into hyperbolic geometry, where they are called gyrovectors, in such a way that Einstein's velocity additions turns out to be a gyrovector addition. Einstein's addition thus becomes a gyrocommunicative, gyroassociative gyrogroup operation in the same way that ordinary vector addition is a commutative, associative group operation. Some gyrogroups of gyrovectors admit scalar multiplication, giving rise to gyrovector spaces in the same way that some groups of vectors that admit scalar multiplication give rise to vector spaces. Furthermore, gyrovector spaces form the setting for hyperbolic geometry in the same way that vector spaces form the setting for Euclidean geometry. In particular, the gyrovector space with gyrovector addition given by Einstein's (Möbius') addition forms the setting for the Beltrami (Poincaré) ball model of hyperbolic geometry. The gyrogroup-theoretic techniques developed in this book for use in relativity physics and in hyperbolic geometry allow one to solve old and new important problems in relativity physics. A case in point is Einstein's 1905 view of the Lorentz length contraction, which was contradicted in 1959 by Penrose, Terrell and others. The application of gyrogroup-theoretic techniques clearly tilt the balance in favor of Einstein.