Linearity of space-time transformations without the one-to-one, line-onto-line, or constancy-of-speed-of-light assumptions
Document Type
Article
Publication Date
12-2000
Department
Department of Mathematical Sciences
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 Rn onto itself which maps every timelike line ℓ into an arbitrary line so that the image of every future ray of ℓ contains at least two distinct points or the same holds for every past ray of ℓ. 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.
Publication Title
Communications in Mathematical Physics
Recommended Citation
Chubarev, A.,
&
Pinelis, I.
(2000).
Linearity of space-time transformations without the one-to-one, line-onto-line, or constancy-of-speed-of-light assumptions.
Communications in Mathematical Physics,
215(2), 433-441.
http://doi.org/10.1007/PL00005542
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/4620
