If, now, with these more homely units we were to set up Minkowski’s graph, we should find that it was virtually identical with the classical one. The world-lines of the light rays would appear to coincide with the space axis
, and it would need a graph thousands of miles in length to detect their deviations from this line. A light-cone would cover the entire graph; hence the permissible space directions lying outside the cone would appear to be limited to the
axis. To all intents and purposes, there would be but one permissible space direction entailing the absoluteness of simultaneity and of time. We see, then, that it is by our immediate needs rather than by cosmic conditions, or, again, because slow velocities predominate around us, contrasted with which the velocity of light appears infinite, that we have been misled into believing in a world of separate space and time.
APPENDIX II
THE CURVATURES OF SPACE-TIME
IT may be of interest to explain the significance of Einstein’s gravitational equations more fully. We will restrict our attention to the equations of the general theory in the case of an infinite universe. These equations may be written:
Here it must be noticed that
