12 B AXEMAN, The Physical Aspect of Time. 



in order that an observer P who is at a point (-I'l, J\, -i) 

 at time A may be in a position to record the effect of a 

 disturbance which issued from a point (a;, ;'., ;:.,) at time /,. 



It should be remarked that the conditions given 

 above with regard to the possibility oi P seeing Q at the 

 given times are necessary, but not sufficient. This accounts 

 for the fact that the transformations for which the condition 



{x^ - x^ + 0\ -y.y + (^. - s.)= = r{f, - ff 

 is invariant are limited to a certain group. 



It is clear that P is able to see Q if there is a 

 flow of energy from P to Q. If {s„ s,„ s) denotes the 

 direction in which energy is flowing from Q at time/*,, and 

 we regard the differences -Vi—x.,, etc., as small, so that 



x^- x.,^ dx, j»'i -ji'„ = ^v, z^-z., = dz, t^-/., = dt 



we may consider transformations such that the equations 



dx _dy __ dz 



dx" + dy- + dz- - trdi' = O 

 are invariant. Since the flow of energy depends upon 

 the state of the electromagnetic field, the formulae of 

 transformation will depend upon the character of the 

 electromagnetic field, but it can be shown that if the 

 above equations are invariant, the fundamental equations 

 which describe the sequence of electromagnetic disturb- 

 ances are also invariant.* The description of any series 

 of phenomena is thus qualitatively the same in the two 

 series of coordinates. 



It is interesting to compare the result just obtained 

 with some ideas with regard to the way in which 

 experience is interpreted by the mind. 



If we suppose that some physical process taking place 



* These are not the onl}' transformations which may be used to transform 

 a particular electromagnetic field into another, there appear to be man)- 

 different types of transformation which are suitable for this purpose. 



