The problem of time determination may be divided into two parts: First, we wish to define equal successive durations at the same point of space, for instance, at the point where we happen to be standing. Secondly, we wish to co-ordinate our time reckonings with those computed by other observers situated at different points of space.
As we have already considered the problem of time-congruence at a point, we will not dwell on it unduly. Suffice it to recall that our direct intuition of time-congruence is far too vague and uncertain to be of any use in scientific investigation. Accordingly, throughout the course of history we find men relying on physical processes of one sort or another, the burning of candles, sand clocks, mechanical clocks, rotation of the earth, vibrations of atoms, etc. Newton gave a theoretical definition of time-congruence when he formulated the law of inertia, according to which a perfectly free body described equal distances in equal times. According to this definition, by measuring equal distances along the body’s path, we were enabled to mark out successive equal durations. But in common practice it was more convenient to appeal to chronometers regulated ultimately by the earth’s rotation. We may now pass to the problem of synchronisation in classical science.
Let us assume that we are in possession of a number of chronometers which, when placed side by side, beat out their hours, minutes and seconds in perfect unison, hence advance at the same rate. Suppose now that having drawn a circle of, say, ten miles’ radius, we maintain one chronometer at the centre and carry the remaining chronometers to various points distributed on the circumference of the circle. If some one were to play a prank and displace the hands of the chronometers located on the circumference, we should be faced with the problem of re-establishing synchronism. Classical science suggested various methods for obtaining this result.
First, we might transport our centre chronometer to each of the circumference chronometers in turn, and thus re-establish synchronism. But this method was open to the objection that by displacing a chronometer back and forth we might in some way disturb its working.
A second method was to appeal to the earth’s rotation on its axis. By ascribing a value of 24 hours to the complete rotation of our planet, we could divide its surface with equally distanced meridians, and then assert that the passage of the same star from one meridian to the next would always take the same time. Suppose, then, for argument’s sake, that the earth’s surface had been divided by 24 half meridians, all equally spaced. Then if a star passed a certain meridian at
at a certain time
, it would pass the contiguous meridian
