PHILOSOPHY OF PHYSICS MILNE 229 



nize the three-dimensionality of our possible observations; i.e., that 

 we can determine direction in terms of two independent measures. 



We now want to correlate or compare the clocks of two different 

 observers. When we repeat our measures of the distance X of an 

 object we may find that X remains constant or that X chanj^es. 

 If X happens to remain constant, it is not difficult to show how, 

 if the object also carries an observer with a clock, the two clocks 

 may be synchronized. And if three observers. A, B, C, by such 

 synchronized clocks agree that they are at constant distances apart, 

 it can be shown that the time numbering of their clocks is unique. 

 This time numbering they will call uniform time. Wliether it co- 

 incides with what we ordinarily mean by uniform time is another 

 matter, but this unique time numbering is as far as three such ob- 

 servers can get when they pay attention only to the reception time 

 of signals. The unique time numbering they arrive at would coincide 

 with what we ordinarily mean by uniform time when the strength 

 of the signals returned are also constant in time, provided we can say 

 what we mean by comparing the strengths of signals. This involves 

 the construction of a piece of apparatus capable of measuring signal 

 strengths, whose properties remained constant in time. These prop- 

 erties would include length measures of its parts, measured with the 

 same arbitrary clock (now uniquely graduated). Now if another 

 observer, B', were, in our ordinary language, receding from A, he 

 could be made to appear at a constant distance from A by letting 

 A's clock run slow. This is equivalent to letting the unit of length 

 conventionally adopted by A increase, so that the size of a signal- 

 strength-measuring receiver would appear to decrease and the weaker 

 signals now received would be estimated as weaker simphT- due to the 

 smaller instrument used. I have not carried out all the mathe- 

 matical details of this process, but the general inference is clear. 

 Just as it is generally recognized that no observable differences 

 would be produced in the universe if we had a length measure arbi- 

 trarily changing, so when we base length measures primarily on time 

 measures, uniform time cannot be defined. Uniform time is a con- 

 vention based on the simplest description of a set of phenomena 

 occurring in nature — as is obvious when we examine its astronomical 

 definition in terms of the earth's rotation, or in terms of dynamical 

 clocks assumed to remain invariable. 



All we can do then is to correlate different ways of time-keeping. 

 The next problem of interest is then to correlate the time-keojiing of 

 observers in motion. Suppose, then, that /, whom I call observer 

 A, repeat my observations on an object B, and find that X, its dis- 

 tance, changes as T, the assigned epocli. changes. Let us assume for 

 simplicity that its direction remains constant. This assumes that a 



