Note 159 — Chapter XL · THE GENERAL SIGNIFICANCE OF THE THEORY OF RELATIVITY

The difference is, however, exceedingly minute, as we can judge by reverting to the expression for the invariant space-time distance . If is expressed in metres and in seconds, will be 300,000,000. Suppose, then, that the two signals, as measured from the embankment, are ten metres apart, and that the two light flashes are separated by an interval of one second. If these two events are viewed from a train travelling at the rate of ten metres a second, that is, at approximately 22 miles an hour, it will be possible for the observer in the train to pass before each of the two flashes just as they are produced, with the result that as referred to his train the two events will occur at the same spot. The time separation of the two events as referred to the train will then be given by (since ). Substituting our numerical values, we find which is very nearly one second, as it would rigorously have been in classical science. We see, furthermore, that it is owing to the enormous value of that the difference between the two sciences is so hard to detect in practice. It is for this reason that the fundamental continuum, though one of space-time, reduces for all practical purposes to the separate space and time of our forefathers, unless very high velocities are considered.