A GEOMETRIC TREATMENT OF "DIMENSIONS" IN PHYSICS

Abstract

"Dimensional analysis" is an established and venerable subject, associated with such names as Fourier, Maxwell, and Lord Rayleigh. But only a genius can obtain dependable results with it, a state of affairs that is caused by the vague intuitionalistic way in which the subject has always been presented. The purpose of this paper is to formulate a precise theory.An idon or complete physical quantity is an entity with two attributes: quality and quantity. Formal rules are given for the manipulation of idons, and it is shown that they can be pictured as vectors in k-dimensional space. This geometrization is not necessary, of course, but it often gives added grasp of the subject; just as vector analysis is never necessary in physics, though it is often convenient. There are six practical applications of the theory, all of which are handled m a precise and dependable way by the geometric method.