Spacetime and Euclidean Geometry
General Relativity and Quantum Cosmology
2009-11-10 v2 High Energy Physics - Theory
Physics Education
Abstract
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the "spacetime Pythagoras theorem".
Cite
@article{arxiv.gr-qc/0407022,
title = {Spacetime and Euclidean Geometry},
author = {Dieter Brill and Ted Jacobson},
journal= {arXiv preprint arXiv:gr-qc/0407022},
year = {2009}
}
Comments
11 pages, 9 figures; for a festschrift honoring Michael P. Ryan; v.2: References to related work added