Space-time trigonometry and formalization of the "Twin Paradox" for uniform and accelerated motions
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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.
18 pages, 4 figures
18 pages, 4 figures