2009/04/24 by John H. Elton, Elton, John H. · 1 citation
Mathematics · #Algebraic and Geometric Analysis #FOS: Mathematics #General Mathematics (math.GM) #Mathematical and Theoretical Analysis #Mathematics and Applications #math.GM
paper · pdf · doi:10.48550/arxiv.0904.3913
6 pages, no figures
openalex publication_date 2009/04/24 · arxiv created 2009/08/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.