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.Comment: 6 pages, no figure
