Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession

The Theory of Gyrogroups and Gyrovector Spaces

Abraham A. Ungar (Autor)

Buch | Softcover

419 Seiten

2001
Springer (Verlag)
978-0-7923-6910-3 (ISBN)

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"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