TITLE:
The Vertical Projection Model of Hyperbolic Space and Geometric Illustration of Special Relativity
AUTHORS:
Weiyu Luo
KEYWORDS:
Lorentz Transformation, Einstein Velocity Addition, Hyperbolic Space
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.1,
January
25,
2024
ABSTRACT: In this article, new visual and intuitive interpretations of Lorentz transformation and Einstein velocity addition are given. We first obtain geometric interpretations of isometries of vertical projection model of hyperbolic space, which are the analogues of the geometric construction of inversions with respect to a circle on the complex plane. These results are then applied to Lorentz transformation and Einstein velocity addition to obtain geometric illustrations. We gain new insights into the relationship between special relativity and hyperbolic geometry.