Indefinite Quadratic Forms and the Invariance of the Interval in Special Relativity
نویسنده
چکیده
In this note, 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 diagonalizability of semi-definite real quadratic forms is given.
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عنوان ژورنال:
- The American Mathematical Monthly
دوره 117 شماره
صفحات -
تاریخ انتشار 2010