Spacetime and Euclidean geometry
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 twodimensional 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.
 Publication:

General Relativity and Gravitation
 Pub Date:
 April 2006
 DOI:
 10.1007/s1071400602549
 arXiv:
 arXiv:grqc/0407022
 Bibcode:
 2006GReGr..38..643B
 Keywords:

 Special relativity;
 Line element;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Physics  Physics Education
 EPrint:
 11 pages, 9 figures