© 2001

Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession

The Theory of Gyrogroups and Gyrovector Spaces


Part of the Fundamental Theories of Physics book series (FTPH, volume 117)

Table of contents

  1. Front Matter
    Pages i-xlii
  2. Abraham A. Ungar
    Pages 1-34
  3. Abraham A. Ungar
    Pages 35-71
  4. Abraham A. Ungar
    Pages 73-94
  5. Abraham A. Ungar
    Pages 95-139
  6. Abraham A. Ungar
    Pages 141-160
  7. Abraham A. Ungar
    Pages 161-210
  8. Abraham A. Ungar
    Pages 211-252
  9. Abraham A. Ungar
    Pages 253-278
  10. Abraham A. Ungar
    Pages 279-311
  11. Abraham A. Ungar
    Pages 313-328
  12. Abraham A. Ungar
    Pages 329-370
  13. Abraham A. Ungar
    Pages 371-380
  14. Abraham A. Ungar
    Pages 381-401
  15. Back Matter
    Pages 403-419

About this book


"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.


Algebra Group theory Vector space geometry model transformation

Authors and affiliations

  1. 1.Department of MathematicsNorth Dakota State UniversityFargoUSA

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