Space-time trigonometry and formalization of the "Twin Paradox" for uniform and accelerated motions
Classical Physics
2007-05-23 v1
Abstract
The formal structure of the early Einstein's Special Relativity follows the axiomatic deductive method of Euclidean geometry. In this paper we show the deep-rooted relation between Euclidean and space-time geometries that are both linked to a two-dimensional number system: the complex and hyperbolic numbers, respectively. By studying the properties of these numbers together, pseudo-Euclidean trigonometry has been formalized with an axiomatic deductive method and this allows us to give a complete quantitative formalization of the twin paradox in a familiar "Euclidean" way for uniform motions as well as for accelerated ones.
Keywords
Cite
@article{arxiv.physics/0509161,
title = {Space-time trigonometry and formalization of the "Twin Paradox" for uniform and accelerated motions},
author = {Dino Boccaletti and Francesco Catoni and Vincenzo Catoni},
journal= {arXiv preprint arXiv:physics/0509161},
year = {2007}
}
Comments
18 pages, 4 figures