The geometry of Minkowski space and the special theory of relativity
DOI:
https://doi.org/10.35819/remat2023v9i1id6351Keywords:
Special Relativity, Minkowski Geometry, Twin ParadoxAbstract
The Special Theory of Relativity, since it's emergence in 1905 with the famous paper "On the Electrodynamics of Moving Bodies" of Albert Einstein, has revolutionized the way we see the world. In this paper, we study concepts of the geometry of Minkowski space and how its structure is related to this theory. We also exhibit some of the main results and show the physical implications and consequences of the mathematical statements related to the relativistic phenomena. We also discuss the famous Twin Paradox, which unveils time dilation, one of the consequences of the Special Theory of Relativity.
Downloads
References
BRADLEY, Robert E.; SANDIFER, C. Edward. Cauchy's Cours d'analyse: An Annotated Translation. Sources and Studies in the History of Mathematics and Physical Sciences. New York: Springer, 2009. DOI: http://dx.doi.org/10.1007%2F978-1-4419-0549-9.
BROS, Jacques. From Euclid's Geometry to Minkowski's Spacetime. In: DAMOUR, Thibault; DARRIGOL, Olivier; DUPLANTIER, Bertrand; RIVASSEAU, Vincent (ed.). Einstein, 1905–2005. v. 47, Basel: Birkhäuser Verglag, 2006, p. 60-119. DOI: https://doi.org/10.1007/3-7643-7436-5_3.
CIPOLATTI, Rolci; GONDAR, Juan López. Iniciação à Física-Matemática: Modelagem de Processos e Métodos de Solução. 2. ed. Rio de Janeiro: IMPA, 2016.
EINSTEIN, Albert. On the Electrodynamics of Moving Bodies. Annalen der Physik, v. 17, p. 891-921, 1905.
HALLIDAY, David; RESNICK, Robert; WALKER, Jearl. Fundamentos de Física: Óptica e Física Moderna. v. 4. 10. ed. Rio de Janeiro: LTC, 2016.
LEE, Nam-Hoon. Geometry: from Isometries to Special Relativity. 1. ed. New York: Springer, 2020.
NABER, Gregory L. The Geometry of Minkowski Spacetime: An Introduction to the Mathematics of the Special Theory of Relativity. Applied Mathematical Sciences. v. 92. 2. ed. New York: Springer, 2012.
TOJO, Fernando Adrián Fernández. A Hyperbolic Analog of the Phasor Addition Formula. The American Mathematical Monthly, v. 123, n. 6, p. 574-582. jun./jul. 2016. DOI: https://doi.org/10.4169/amer.math.monthly.123.6.574.
WALTER, Scott. Minkowski, Mathematicians and the Mathematical Theory of Relativity. In: GOENNER, H.; RENN, J.; RITTER, J.; SAUER, T. (ed.). The Expanding Worlds of General Relativity. Einstein Studies. v. 7. p. 45-86. Boston/Basel: Birkhäuser, 1999.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 REMAT: Revista Eletrônica da Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
REMAT retains the copyright of published articles, having the right to first publication of the work, mention of first publication in the journal in other published media and distribution of parts or of the work as a whole in order to promote the magazine.
This is an open access journal, which means that all content is available free of charge, at no cost to the user or his institution. Users are permitted to read, download, copy, distribute, print, search or link the full texts of the articles, or use them for any other legal purpose, without requesting prior permission from the magazine or the author. This statement is in accordance with the BOAI definition of open access.