and of the geodesics; and the entire geometry of the continuum is thereby established.
Thus far we have been reasoning as though the continuum possessed a structure; but in a purely amorphous continuum no such structure exists, and the mathematician must postulate it. When, however, we are dealing with physical space, we find that the laws of dispositions of material rods, as also the laws of moving bodies (law of inertia), suggest that space is three-dimensional and Euclidean. This implies that it is possible to obtain a particular co-ordinate system, called a Cartesian one, in which the
’s will have constant values equal to unity. Einstein’s and Minkowski’s great achievement was to prove that this conception of the world was incompatible with the verdict of the negative experiments. Instead it appeared necessary to assume that the fundamental continuum was four-dimensional, possessing one imaginary dimension, which was none other than time. In this four-dimensional space-time continuum, experiment proved that
had the following form when a Galilean frame of reference was resorted to:
We have reversed the sign of