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.