There is another feature of very great importance in the theory we have been considering, and that is that, although distances and times vary for different observers, we can derive from them the quantity called “interval,” which is the same for all observers. The “interval,” in the special theory of relativity, is obtained as follows: Take the square of the distance between two events, and the square of the distance traveled by light in the time between the two events; subtract the lesser of these from the greater, and the result is defined as the square of the interval between the events. The interval is the same for all observers, and represents a genuine physical relation between the two events, which the time and the distance do not. We have already given a geometrical construction for the interval at the end of Chapter IV; this gives the same result as the above rule. The interval is “time-like” when the time between the events is longer than light would take to travel from the place of the one to the place of the other; in the contrary case it is “space-like.” When the time between the two events is exactly equal to the time taken by light to travel from one to the other, the interval is zero; the two events are then situated on parts of one light ray, unless no light happens to be passing that way. When we come to the general theory of relativity, we shall have to generalize the notion of interval. The more deeply we penetrate into the structure of the world, the more important this concept becomes; we are tempted to say that it is the reality of which distances and periods of time are confused representations. The theory of relativity has altered our view of the fundamental structure of the world; that is the source both of its difficulty and of its importance.