254 PHYSICAL SCIENCE 



Fitzgerald. The time-scale undergoes a corre- 

 sponding change. A clock, to an observer 

 moving with it, goes steadily, but, if it were 

 carried past the observer at great speed, it would 

 seem to slow down. 



But, while both space and time separately 

 are relative to the observer, Minkowski, in 1908, 

 pointed out that there is a combined space-time 

 which is absolute : a space-time of such a nature 

 that the velocity of light is a true natural 

 constant. Hence, instead of the familiar three 

 dimensions of space, length, breadth, and height, 

 with time as a completely independent quantity, 

 we must add time as another dimension, and 

 picture the universe in terms of an inseparable 

 space-time involving four dimensions. Any given 

 particle is moving through both space and time. 

 The distance it moves depends on the observer, and 

 the time it takes to traverse that distance depends 

 on the observer, but its track through four dimen- 

 sional space-time, what is called the *' interval" 

 between its first state and its last, does not depend 

 on the observer, but is the same for all observers 

 — a true characteristic quantity for the particle. 



Since clocks are timed by pendulums or heavy 

 balance wheels which possess mass, the slowing 

 down of time suggests that mass, like length 

 and time, changes with the observer, and that 

 the mass of a fast moving body becomes greater 

 to an observer at rest. The amount of this 

 increase may be calculated from Minkowski's 

 space-time ''interval" which we have just 

 described. The velocity of a body may be 

 written as z^ = Ijt, where / is the length described 

 in a time t. But, if instead of t we write the 



