interval between two events is small, the events are not necessarily near together in the ordinary sense.
Between any two neighbouring point-events there exists a certain relation known as the interval between them. The relation is a quantitative one which can be measured on a definite scale of numerical values[1]. But the term "interval" is not to be taken as a guide to the real nature of the relation, which is altogether beyond our conception. Its geometrical properties, which we have dwelt on so often in the previous chapters, can only represent one aspect of the relation. It may have other aspects associated with features of the world outside the scope of physics. But in physics we are concerned not with the nature of the relation but with the number assigned to express its intensity; and this suggests a graphical representation, leading to a geometrical theory of the world of physics.
What we have here called the world might perhaps have been legitimately called the aether; at least it is the universal substratum of things which the relativity theory gives us in place of the aether.
We have seen that the number expressing the intensity of the interval-relation can be measured practically with scales and clocks. Now, I think it is improbable that our coarse measures can really get hold of the individual intervals of point-events; our measures are not sufficiently microscopic for that. The interval which has appeared in our analysis must be a macroscopic value; and the potentials and kinds of space deduced from it are averaged properties of regions, perhaps small in comparison even with the electron, but containing vast numbers of the primitive intervals. We shall therefore pass at once to the consideration of the macroscopic interval; but we shall not forestall later results by assuming that it is measurable with a scale and clock. That property must be introduced in its logical order.
Consider a small portion of the world. It consists of a large (possibly infinite) number of point-events between every two of which an interval exists. If we are given the intervals between
- ↑ There is also a qualitative distinction into two kinds, ultimately identified as time-like and space-like, which for mathematical treatment are distinguished by real and imaginary numbers.
