Article
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Complex Numbers for Relativistic Operations
Version 1
: Received: 1 December 2021 / Approved: 6 December 2021 / Online: 6 December 2021 (17:38:41 CET)
How to cite: Kulyabov, D. S.; Korolkova, A. V.; Sevastianov, L. A. Complex Numbers for Relativistic Operations. Preprints 2021, 2021120094. https://doi.org/10.20944/preprints202112.0094.v1 Kulyabov, D. S.; Korolkova, A. V.; Sevastianov, L. A. Complex Numbers for Relativistic Operations. Preprints 2021, 2021120094. https://doi.org/10.20944/preprints202112.0094.v1
Abstract
When presenting special relativity, it is customary to single out the so-called paradoxes. One of these paradoxes is the formal occurrence of speeds exceeding the speed of light. An essential part of such paradoxes arises from the incompleteness of the relativistic calculus of velocities. In special relativity, the additive group is used for velocities. However, the use of only group operations imposes artificial restrictions on possible computations. Naive expansion to vector space is usually done by using non-relativistic operations. We propose to consider arithmetic operations in the special theory of relativity in the framework of the Cayley–Klein model for projective spaces. We show that such paradoxes do not arise in the framework of the proposed relativistic extension of algebraic operations.
Keywords
Cayley-Klein model; hypercomplex numbers; hyperbolic complex numbers; special relativity; superluminal motion
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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