Note 97 — Chapter XXIX · THE GENERAL LAWS OF MOTION

We shall see (Appendix I) that the geodesics of space-time are of two major varieties: the so-called time-like and the so-called space-like geodesics. The transition between the two is given by the null-lines or minimal geodesics; these correspond to the paths and motions of light rays. The space-like geodesics would correspond to the paths and motions of bodies moving with a speed greater than that of light. As such motions cannot exist, according to the theory of relativity, we see that free bodies can follow only the time-like geodesics. In future, therefore, when referring to the geodesics of space-time, we shall always have in mind the time-like geodesics. Also we may note that whereas the time-like geodesic defines the longest space-time distance between two points, the null-line or minimal geodesic has always a zero space-time length.