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Communications in Mathematical Physics

, Volume 215, Issue 2, pp 433–441 | Cite as

Linearity of Space-Time Transformations¶Without the One-to-One, Line-onto-Line, or Constancy-of-Speed-of-Light Assumptions

  • Alexander Chubarev
  • Iosif Pinelis

Abstract:

Using a version of the fundamental theorem of geometry without the 1-to-1 assumption, recently obtained by the authors, the following is proved: Let n≥ 2 and T be a mapping of n onto itself which maps every timelike lineℓ into an arbitrary line so that the image of every future ray ofcontains at least two distinct points or the same holds for every past ray ofℓ. Then T is affine.

A version of the Pappus theorem under minimal assumptions is also given, which is then used as a tool in this paper.

Related results have been obtained by Borchers and Hegerfeldt.

Keywords

Related Result Distinct Point Fundamental Theorem Minimal Assumption Arbitrary Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Alexander Chubarev
    • 1
  • Iosif Pinelis
    • 1
  1. 1.Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931, USAUS

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