We may note that in a world in which coincidences were relative, that is, in a world in which two cars would appear to collide and all the passengers killed when viewed from the road whereas no such collision would take place when viewed from the train, science would be quite impossible; for the opinions of the various observers would be relative to the point of being inconsistent. In the squirming world of relativity something at least must be absolute, and one of these absolutes is found to reside in the coincidences of events. [Pg 171] We may contrast the teachings of classical science and of relativity in the following way: Just as classical science recognised that there was no physical significance in speaking of the same point of space at different times until, by selecting a frame of reference, we had objectivised, as it were, the space we were discussing, so now relativity compels us to add: “There is no meaning in speaking of the same instant of time in different places until we have objectivised time, as it were, by specifying our frame of reference.” In both sciences, however, the classical and the relativistic, the coincidence of events remains an absolute, transcending the choice of a frame of reference. From a philosophical point of view, this discovery of the relativity of simultaneity marks a date of the same momentous importance as did the discovery of the Copernican system in astronomy.[55] [Pg 172] Having established the relative nature of physical simultaneity, we find it an easy matter to rediscover that other consequence of the theory, namely, the contraction of length. Consider, for example, an observer at rest on a track observing a train also at rest. What is the length of the train as referred to the observer’s frame, namely, to the earth? Obviously it is the difference in his distance from the engine and from the rear car. But if now we consider the more general case where the train or the observer with his reference frame is in relative motion (either choice comes to the same thing, so long as the motions are Galilean), it becomes imperative to state that the measurements must be performed at the same instant of time. It would be absurd to measure our distance from the rear car at one o’clock, then our distance from the engine at two o’clock; for we might find that the train had a length of over sixty miles owing to its displacement during the interval. But whereas in classical science the significance of the same time in two different places was absolute, the same for all observers, in relativity it becomes indeterminate. According to the relative motion of the observer, different simultaneity determinations will be obtained, and as a result the length of the same train will vary in value. This is what is meant by the relativity of length. Calculation proves that the greater relative velocity, the shorter will the train measure out.