Indefinite quadratic forms and the invariance of the interval in Special Relativity
General Mathematics
2009-08-04 v2
Abstract
A simple theorem on proportionality of indefinite real quadratic forms is proved, and is used to clarify the proof of the invariance of the interval in Special Relativity from Einstein's postulate on the universality of the speed of light; students are often rightfully confused by the incomplete or incorrect proofs given in many texts. The result is illuminated and generalized using Hilbert's Nullstellensatz, allowing one form to be a homogeneous polynomial which is not necessarily quadratic. Also a condition for simultaneous diagonalizabilityof semi-definite real quadratic functions is given.
Keywords
Cite
@article{arxiv.0904.3913,
title = {Indefinite quadratic forms and the invariance of the interval in Special Relativity},
author = {John H. Elton},
journal= {arXiv preprint arXiv:0904.3913},
year = {2009}
}
Comments
6 pages, no figures