But it now appears that the time-stretches defined by the ticking of a clock at rest in the frame of reference would appear to an observer in relative motion to be longer than they would appear to . The result is quite general and applies to all processes. Thus, the duration of the revolution of a top will be possessed of varying values according to the relative motion of the observer. Arguments similar to those we elaborated in the case of space go to show that time is no longer unique. A multiplicity of different time directions, variously tilted, must coexist, each one referring to some particular frame of reference, hence to some particular observer. As a result, the simultaneity of two events occurring at different points of space can no longer be absolute, since simultaneity depends essentially on the time which we select, and therefore on our frame of reference. Just as each frame had its own space, so also would it now have its own time and its own definition of simultaneity. We may summarise these various discoveries by stating that there can exist no universal definition of practical congruence either for space or for time; there can exist, therefore, no geometry for a universal space or for a universal time. The philosophical consequence of these new points of view is to deprive universal space and time of the objective significance with which they were formerly credited. Henceforth, in the words of Minkowski, “space and time, by themselves, sink to the position of mere shadows.” Thus, consider a yardstick. If this same yardstick is measured by various observers passing it with different velocities, it will be possessed of different lengths. The space this rod occupies can then be credited with no particular magnitude, since this magnitude itself depends as much on the point of view of the observer as on the characteristics of the rod. This is what is meant by the relativity of distance. We must not confuse this discovery of Einstein’s with the fundamental relativity of all distance in conceptual space. For while classical science recognised that there was no such thing as absolute distance in conceptual space, yet it believed that in the real space of the physicist the distance between two given points in a frame of reference could be defined unambiguously for all observers, by means of rigid rods. It is this last opinion which is shattered by Einstein’s discoveries. It is the same for duration when we remember that the duration of any phenomenon will be possessed of varying values according to the relative motion of the observer; and it is this fact which is expressed by the statement that time or duration is relative. [Pg 191]