Communications in Mathematical Analysis

When Relativistic Mass Meets Hyperbolic Geometry

Abraham A. Ungar

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

It is admitted in the literature on special relativity that, being velocity dependent, relativistic mass is a wild notion in the sense that it does not conform with the Minkowskian four-vector formalism. The resulting lack of clear consensus on the basic role of relativistic mass in special relativity has some influence in diminishing its use in modern books. Fortunately, relativistic mechanics is regulated by the hyperbolic geometry of Bolyai and Lobachevsky just as classical mechanics is regulated by Euclidean geometry. Guided by analogies that Euclidean geometry and classical mechanics share with hyperbolic geometry and relativistic mechanics, the objective of this article is to tame the relativistic mass by placing it under the umbrella of the Minkowskian formalism, and to present interesting consequences.

Article information

Source
Commun. Math. Anal. Volume 10, Number 1 (2011), 30-56.

Dates
First available in Project Euclid: 19 May 2011

Permanent link to this document
http://projecteuclid.org/euclid.cma/1305810734

Mathematical Reviews number (MathSciNet)
MR2825952

Zentralblatt MATH identifier
06008769

Subjects
Primary: 83A05: Special relativity
Secondary: 51M10: Hyperbolic and elliptic geometries (general) and generalizations

Keywords
Hyperbolic Geometry special relativity relativistic mass particle system center of momentum

Citation

Ungar , Abraham A. When Relativistic Mass Meets Hyperbolic Geometry. Communications in Mathematical Analysis 10 (2011), no. 1, 30--56. http://projecteuclid.org/euclid.cma/1305810734.


Export citation