ENGLISH

Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession: The Theory of Gyrogroups and Gyrovector Spaces

By Dr. Abraham A. Ungar (auth.)

Book information

Publisher
Springer Netherlands
Year
2001
ISBN
0792369092, 9780792369097, 9780306471346, 1402003536, 9781402003530
DOI
10.1007/978-94-010-9122-0
LCC
QC173.65 .U54 2001
Open Library ID
OL18325330M
Language
english
Format
PDF
Filesize
5 MB (5323545 bytes)
Series
Fundamental Theories of Physics 117
Edition
1
Pages
419\462
Topic
Physics
Library
Kolxo3
Time added
2009-07-20 03:45:11
Mathematical and Computational PhysicsTheoretical

Description

"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.

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