11 CONCEPTS OF SPACE AND TIME 27 



the most accurate experiments, that the velocity of light is 

 always the same, whatever the velocity of its source, and ; 

 however great may be the difference in velocities of the 

 moving observers who are trying to measure it. An 

 observer moving away from a flash of light at a rate which is 

 half that of light will see the flash at the same time as a \ 

 stationary observer, and not later as one might suppose. 

 The reason is that the time and space measures of the mov- 

 ing observer have changed jointly so as to neutralise the 

 results which his motion might have on his observation. 



The two salient facts to bear in mind as a result of the 

 above are: that to moving observers clocks and standards 

 of measurement in motion are no longer absolute but vary 

 according to the rates of motion of these observers or 

 of the clocks or standards, and that there is this curious 

 joint and opposite variation of the space and time 

 measures of moving observers or bodies. In fact separately 

 Space and Time must be mere abstractions, as in all actual 

 movements they are always found in inseparable conjoint 

 action. 



From this co-variation of Space and Time it is but a step . 

 to Minkowski's great idea, first formulated in 1908, that in 

 natural events Space and Time are not independent factors, 

 and that in the mathematical representation of events the 

 correct way is to introduce time as a fourth dimension, not 

 of space, but of the Space-Time continuum in which events 

 really take place. Time is, of course, in many ways unlike 

 space and is not another dimension of it, but this inseparable 

 co-variation in all events which happen in nature makes it 

 both feasible and proper that we should substitute the real 

 Space-Time continuum of events for the old abstract three- 

 dimensional space of bodies or points in space. In passing 

 it may here be pointed out that the old notion of the sepa- 

 rate reality of space and of time involved both the errors of 

 analysis and of abstraction to which attention was drawn in 

 the last chapter, and Minkowski's brilliant idea has simply 

 brought us back to the natural fact as it occurs in experience, 

 where nothing ever happens in space alone or in time alone, 



