Speed of light or composition of velocities

Maciej Sablik
https://orcid.org/0000-0003-1194-1327


Abstract

We analyze in our paper questions of the theory of relativity. We approach this theory from the point of view of velocities and their composition. This is where the functional equations appear. Solving them leads to a world where velocities are bounded from above, the upper bound being exactly the “speed of light”.


Keywords

functional equations; relativity theory; conditional associativity; Hilbert’s fifth problem

J. Aczél, Sur les opérations définies pour nombres réels, Bull. Soc. Math. France 76 (1948), 59–64.

W. Benz, A characterization of relativistic addition, Abh. Math. Sem. Univ. Hamburg 70 (2000), 251–258.

N. Brillouët and J. Dhombres, Equations fonctionnelles et recherche de sous-groupes, Aequationes Math. 31 (1986), no. 2–3, 253–293.

R. Craigen and Zs. Páles, The associativity equation revisited, Aequationes Math. 37 (1989), no. 2–3, 306–312.

M. Sablik, The continuous solution of a functional equation of Abel, Aequationes Math. 39 (1990), no. 1, 19–39.

M. Sablik, On some local topological semigroups, Aequationes Math. 44 (1992), no. 2–3, 194–219.

M. Sablik, A functional equation of Abel revisited, Abh. Math. Sem. Univ. Hamburg 64 (1994), 203–210.

R.D. Sard, Relativistic Mechanics: Special Relativity and Classical Particle Dynamics, W.A. Benjamin, Inc., New York, 1970.

A. Sommerfeld, On the composition of velocities in the theory of relativity [Über die Zusammensetzung der Geschwindigkeiten in der Relativtheorie], Verh. Dtsch. Phys. Ges. 21 (1909), 577–582.

A. Szymacha, Szczególna teoria względności, Alfa, Warszawa, 1985.

P. Volkmann and H. Weigel, Über ein Problem von Fenyő, Aequationes Math. 27 (1984), no. 1–2, 135–149.

Download

Published : 2024-03-20


SablikM. (2024). Speed of light or composition of velocities. Annales Mathematicae Silesianae, 38(1), 111-119. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/17253

Maciej Sablik  maciej.sablik@us.edu.pl
Instytut Matematyki, Uniwersytet Śląski w Katowicach  Poland
https://orcid.org/0000-0003-1194-1327



Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The Copyright Holders of the submitted text are the Author and the Journal. The Reader is granted the right to use the pdf documents under the provisions of the Creative Commons 4.0 International License: Attribution (CC BY). The user can copy and redistribute the material in any medium or format and remix, transform, and build upon the material for any purpose.

  1. License
    This journal provides immediate open access to its content under the Creative Commons BY 4.0 license (http://creativecommons.org/licenses/by/4.0/). Authors who publish with this journal retain all copyrights and agree to the terms of the above-mentioned CC BY 4.0 license.
  2. Author’s Warranties
    The author warrants that the article is original, written by stated author/s, has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author/s.
  3. User Rights
    Under the Creative Commons Attribution license, the users are free to share (copy, distribute and transmit the contribution) and adapt (remix, transform, and build upon the material) the article for any purpose, provided they attribute the contribution in the manner specified by the author or licensor.
  4. Co-Authorship
    If the article was prepared jointly with other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.