,
, which, as we have seen, are characteristic of sensory continuity, be it in space, or in time, or in whatever domain we please. In the case of time, as in that of space, only by a process of abstraction can we remedy this inconsistency. We thereby conceive of mathematical duration, a duration in which mathematical continuity is assumed to have replaced sensory continuity.
Now, owing to the ordering relation or path of continuous transfer which appears to be imposed upon us by nature, perceptual time must be regarded as uni-dimensional, and by retaining the natural ordering relation, we will attribute the same uni-dimensionality to mathematical duration. It is, of course, to this mathematical duration that we appeal in all theoretical investigations in mechanics and physics.
Primarily the only time of which we are conscious is an “egoistic” time, the time of our stream of consciousness. But as a result of our perception of change and motion in the exterior universe of space, it becomes necessary to extend the concept of duration throughout space, so that all external events are thought of as having occurred at a definite instant in time as well as at a definite point in space.[22]
Now, when discussing space, we saw that the concept of the same point in space, considered at different times, was ambiguous; it was necessary to specify the frame of reference by which space was defined, and according to the frame selected, an object would continue to occupy the same point or else manifest motion. The analogous problem in the case of time would be to conceive of the same instant in time at two different places, i.e., of the simultaneity of two spatially separated events.
If we allowed ourselves to be guided by our analysis of position in space, we should be inclined to say that a determination of the simultaneity of spatially separated events must necessitate the choice of a frame of reference. The observer who was to pass an opinion on the simultaneity of the two events would then select that particular frame in which he stood at rest. But from this it would follow that a change in the motion of the observer, hence a change of frame, might bring about a modification in his understanding of simultaneity. Simultaneity would thus manifest itself as relative, just like position.
Although these possibilities cannot be discarded a priori on any rational grounds, classical science and common-sense philosophy refused to entertain them. The fact is that this thesis would have tended to surround with ambiguity the concept of time in physics, since the duration of the same event would vary with the motion of our frame of reference. It had always been felt that although, through an act of our will, we might change our motion through space, yet on the other hand the flowing of time transcended our action. These views were confirmed by the behaviour of physical phenomena known to classical science; hence the uniqueness of time and the absolute character of simultaneity had been accepted. In other words, the simultaneity and the order of succession of two spatially separated events were assumed to constitute facts transcending our choice of a system of reference.
This stand was fully justified in Newton’s day; for inasmuch as a priori arguments could not decide the question, so long as experiment did not compel us to recognise the relativity of simultaneity and the ambiguity of duration there appeared to be no good reason to hamper science with an unnecessary complication. But the point we wish to stress is that if perchance experiment were ever to suggest that simultaneity was not absolute, no rational argument could be advanced to prove the absurdity of this opinion. As we shall see, Einstein’s interpretation of certain refined electromagnetic experiments consists precisely in recognising the relativity of simultaneity and the ambiguity of duration.