Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession - Abraham A. Ungar

Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession

The Theory of Gyrogroups and Gyrovector Spaces
Buch | Softcover
419 Seiten
2001
Springer (Verlag)
978-0-7923-6910-3 (ISBN)
53,49 inkl. MwSt
"I cannot define coincidence [in mathematics]. But 1 shall argue that coincidence can always be elevated or organized into a superstructure which perfonns a unification along the coincidental elements. The existence of a coincidence is strong evidence for the existence of a covering theory. " -Philip 1. Davis [Dav81] Alluding to the Thomas gyration, this book presents the Theory of gy­ rogroups and gyrovector spaces, taking the reader to the immensity of hyper­ bolic geometry that lies beyond the Einstein special theory of relativity. Soon after its introduction by Einstein in 1905 [Ein05], special relativity theory (as named by Einstein ten years later) became overshadowed by the ap­ pearance of general relativity. Subsequently, the exposition of special relativity followed the lines laid down by Minkowski, in which the role of hyperbolic ge­ ometry is not emphasized. This can doubtlessly be explained by the strangeness and unfamiliarity of hyperbolic geometry [Bar98]. The aim of this book is to reverse the trend of neglecting the role of hy­ perbolic geometry in the special theory of relativity, initiated by Minkowski, by emphasizing the central role that hyperbolic geometry plays in the theory.

1. Thomas Precession: The Missing Link.- 2. Gyrogroups: Modeled on Einstein’s Addition.- 3. The Einstein Gyrovector Space.- 4. Hyperbolic Geometry of Gyrovector Spaces.- 5. The Ungar Gyrovector Space.- 6. The Möbius Gyrovector Space.- 7. Gyrogeometry.- 8. Gyrooperations — The SL(2, C) Approach.- 9. The Cocycle Form.- 10.The Lorentz Group and Its Abstraction.- 11.The Lorentz Transformation Link.- 12.Other Lorentz Groups.- 13.References.- About the Author.- Topic Index.- Author Index.

Erscheint lt. Verlag 12.3.2001
Reihe/Serie Fundamental Theories of Physics ; 117
Zusatzinfo 25 Illustrations, black and white; XLII, 419 p. 25 illus.
Verlagsort Dordrecht
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Algebra
Naturwissenschaften Physik / Astronomie Allgemeines / Lexika
Naturwissenschaften Physik / Astronomie Astronomie / Astrophysik
Naturwissenschaften Physik / Astronomie Relativitätstheorie
Naturwissenschaften Physik / Astronomie Theoretische Physik
ISBN-10 0-7923-6910-6 / 0792369106
ISBN-13 978-0-7923-6910-3 / 9780792369103
Zustand Neuware
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