n CONCEPTS OF SPACE AND TIME 25 



plicity of statement only shows that the ultimate form 

 has not yet been reached. The day may yet come when the 

 ten recondite Einstein equations of gravitation may appear 

 as but the scaffolding of the simpler structure yet to arise, 

 the naturalness and inevitableness of which will be as evi- 

 dent to every educated person as the heliocentric conception 

 of Copernicus has become. 



The Einstein theory arose originally from mathematics, 

 and a brief reference to this mathematical origin will be 

 useful. Galileo and Newton were the fathers of the modern 

 classical mechanics; they (and especially Newton) formu- 

 lated the laws of moving bodies in an exact mathematical 

 science. Now the germ of the new Relativity mechanics is 

 the almost obvious fact that the motion of a body is never 

 absolute, but is always relative to some other body or point. 

 If this body or point of reference is stationary, Newton's 

 laws of motion apply completely, and the geometry of 

 Euclid also applies, so that the movements of bodies can be 

 represented by geometrical figures. Such bodies are said 

 to move in Euclidean space, which is the same and homo- 

 geneous all through and in all directions. Now since New- 

 ton's time a great deal of attention has been given to the 

 case where the body of reference or the observer is not 

 stationary but is also in motion. This case is important, 

 because it is actually that of all bodies in our universe, in 

 which all observers or points of reference are themselves in 

 motion. A point on the earth, for instance, rotates with a 

 certain velocity round the centre of the earth, while the earth 

 again rotates with another velocity round the sun. The sun 

 itself is not stationary but moving with reference to some 

 star, which is itself in motion with reference to some other 

 moving centre of reference. It is this case of the moving 

 observer or point of reference' with which Einstein's theory 

 deals, and it is therefore clear that this theory faces the 

 problem of motion as it actually exists in the universe. The 

 impression of rest or stationariness to us as observers in the 

 universe is a mere illusion, and the great service of Einstein 

 was to explore this illusion and to show in exact mathemat- 



