Page:BatemanTime.djvu/4

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Bateman, The Physical Aspect of Time.

view is really not sound, because the universal time we are endeavouring to define is essentially quantitative in character. The best way of establishing the existence of a consistent method of comparison is to give an example of one, and so we shall consider Galileo's method of light signals,[1] which was used in a first but unsuccessful attempt to measure the velocity of light.

The way in which this method is applied is as follows. An observer situated at a point A observes at time t an event which has taken place at another point B. If τ is the time which light takes to travel from B to A, the universal time to be associated with the event at B according to A's measurements is . As soon as A has observed the event he makes a signal, and it is clear that by a series of signals the two measures of an interval of time may be compared.

By means of this rule the clocks belonging to a number of observers can be regulated in a consistent manner, provided light always takes the same time to travel from an observer to an observer .

Let us suppose that a large number of observers find that their observations of one another's experiences give a consistent universal time as far as they are concerned; they can then regard themselves as being at constant distances from one another, the distance between two observers , being defined as , where is the time light takes to travel from to , and C is a constant called the velocity of light.

These observers may then form a standard system for the measurement of time and distances at other points of space. The measurements of four standard observers should suffice to determine the position and time of any

  1. This method is used for the purpose of studying the properties of time by A. Einstein, Ann. der Physik, vol. 17 (1905).