7 - More Mathematics

Abstract

This chapter elaborates the Newtonian and special relativistic physics. One very important reason for the relative simplicity of the mathematics is that it has been possible to presuppose that the space of physics has a flat or Euclidean character. It is found that when space is Euclidean, it is always possible to represent it by means of a Cartesian coordinate system in which the various mathematical operations take on a particularly simple form. It merely happens that they are conveniences to be exploited when the physical system of interest has a spherical symmetry. It is found that when one approaches special relativity from the four-dimensional or space-time standpoint, it is found that the geometry was not quite Euclidean. Accordingly, it became more convenient to have recourse to Minkowski coordinates to represent the inertial frames of special relativity. The Minkowski coordinates, although unfamiliar, were essentially hardly more difficult to handle than the customary Cartesian ones.