rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Beyond the Einstein Addition Law and its Gyroscopic Thomas Precession
    sub title: The Theory of Gyrogroups and Gyrovector Spaces
  name:
    name part: Ungar, Abraham A.
    role:
      role term: creator
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: ne
    date issued: 2002
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: access
    form: remote
    extent: 1 online resource.
  abstract: 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 Thomas gyration, in turn, allows the introduction of vectors into hyperbolic geometry, where they are called gyrovectors, in such a way that Einstein's velocity additions turns out to be a gyrovector addition. Einstein's addition thus becomes a gyrocommutative, gyroassociative gyrogroup operation in the same way that ordinary vector addition is a commutative, associative group operation. Some gyrogroups of gyrovectors admit scalar multiplication, giving rise to gyrovector spaces in the same way that some groups of vectors that admit scalar multiplication give rise to vector spaces. Furthermore, gyrovector spaces form the setting for hyperbolic geometry in the same way that vector spaces form the setting for Euclidean geometry. In particular, the gyrovector space with gyrovector addition given by Einstein's (Mbius') addition forms the setting for the Beltrami (Poincar) ball model of hyperbolic geometry. 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. A case in point is Einstein's 1905 view of the Lorentz length contraction, which was contradicted in 1959 by Penrose, Terrell and others. The application of gyrogroup-theoretic techniques clearly tilt the balance in favor of Einstein.
  table of contents: Introduction / Abraham A. Ungar -- 1. Thomas Precession: The Missing Link -- 2. Gyrogroups: Modeled on Einstein's Addition -- 3. Einstein Gyrovector Space -- 4. Hyperbolic Geometry of Gyrovector Spaces -- 5. Ungar Gyrovector Space -- 6. Mobius Gyrovector Space -- 7. Gyrogeometry -- 8. Gyrooperations -- The SL (2, C) Approach -- 9. Cocycle Form -- 10. Lorentz Group and its Abstraction -- 11. Lorentz Transformation Link -- 12. Other Lorentz Groups -- 13. References.
  note: by Abraham A. Ungar.
  note: Electronic resource.
  note: Includes bibliographical references (pages 381-401) and indexes.
  subject:
    topic: Physics
  subject:
    topic: Algebra
  subject:
    topic: Geometry
  subject:
    topic: Mathematical physics
  subject:
    topic: Astronomy
  subject:
    topic: Algebra
  subject:
    topic: Astronomy
  subject:
    topic: Geometry
  subject:
    topic: Mathematical physics
  subject:
    topic: Physics
  subject:
    topic: Physics
  subject:
    topic: Science
  classification: QC19.2-20.85
  classification: 530.1
  related item:
    title info:
      title: Fundamental theories of physics ; 117
  identifier: 9780306471346 (electronic bk.)
  identifier: 0306471345 (electronic bk.)
  identifier: 0306471345
  identifier: 0792369092 (acid-free paper)
  identifier: 9780792369097 (acid-free paper)
  identifier: 9789401091220 (electronic bk.)
  identifier: 9401091226 (electronic bk.)
  identifier: 9780792369103
  identifier: 0792369106
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: Nz
    record creation date: 100301
    record change date: 20260420211903.6
    record identifier: in00003578863
    language of cataloging:
      language term: eng