Woolard — Generalized Relativity and Gravitation. 429 



would be no pressure between the lift floor and the 

 observer's feet; in fact, by a gentle spring the observer 

 could 'float up' to the ceiling of the lift; bodies placed 

 anywhere in the lift would remain there without sup- 

 port — in short; there would be no 'up' nor 'down'. If 

 now the motion of the lift were accelerated, all the 

 mechanical phenomena which we associate with, a field 

 of gravitation would supervene. If the acceleration is 

 maintained in a direction which is 'upwards' (in the 

 sense from feet to head), the lift floor w T ould exert a 

 pressure on the observer's feet in proportion to the mag- 

 nitude of the continuous, uniform, acceleration; bodies 

 would 'fall' (i. e., move towards the lift floor) with an 

 acceleration relative to the lift equal in magnitude and 

 opposite in direction to the acceleration of the lift." 9 



It would be impossible to distinguish between a system 

 at rest in a homogeneous gravitation field, and a system 

 in continuously accelerated motion in a space free from 

 gravitation. The Equivalence-Hypothesis states that 

 two such systems are completely equivalent for all phe- 

 nomena. This assumption is an application of our 

 postulate of general relativity 10 ; for, since at a given 

 point in any gravitation field, every material particle 

 receives the same acceleration, if we introduce at this 

 point a new system of coordinates which here has exactly 

 this acceleration relative to the old system, then the mate- 

 rial point subjected to gravitation would be at rest rela- 

 tive to the new coordinates, and, relative to them, 

 apparently not subject to gravitation; but by the pos- 

 , tulate of general relativity, these two systems must be 

 equivalent. 



7. One great result of the ' ' older ' ' relativity was Her- 

 mann Minkowski's dictum that "space and time each 

 separately must vanish to shadows, and only a union of 

 the two should preserve reality." Four-dimensional 

 space and mathematics are accordingly used throughout 

 the principle of relativity, time being treated as the 

 fourth dimension; this is measured in such a way that 

 the velocity of light in free space is unity. "If we 

 choose a new axis of t, we must choose a new axis of x, 

 just as if we choose a new axis of x, we must choose a new r 

 axis of y; 7 ' and the new choices must be such that the 



9 Bice, Kelativity and Gravitation, Sei. Amer. Sup., April 7, 1917. 



10 De Sitter, Monthly Not. E. A. S., vol. 76, No. 9, Sec. 3, 1916. 



