﻿Einstein and (jfrossmann's Theory of Gravitation. ( J5 



Of fundamental importance is the conclusion of the theory 

 as to the relativity of inertia. Our classical conception of 

 inertia dates from Galilei, and can be said to be derived from 

 the observed behaviour of bodies acting upon one another. 

 But the underlying tacit assumption was that the bodies 

 would behave just the same if they were an isolated system, 

 and cut off from the remaining part of the universe. This 

 is corrected by the theory of Einstein, which makes an 

 influence of this remaining part of the universe responsible 

 for the inertia! properties of single systems. 



Still more essentially in favour of the theory are the 

 following considerations, which really form the very nucleus 

 of all conceptions of relativity. 



In order to describe physical phenomena we must construct 

 systems of coordinates, space-coordinates, and a time-co- 

 ordinate. With reference to these systems we can express 

 physical relations by certain equations. Now there are two 

 possibilities. Either the equations exist only with reference 

 to certain specialized systems of coordinates, or they exist 

 independent of our choice of coordinates, and retain their 

 form after an arbitrary transformation of coordinates*. In 

 the first case the equation can be suspected to owe its 

 existence to a special artifice of choosing the coordinates, 

 and not to correspond to a real relation. In the second case 

 the equation can only owe its existence to a real relation 

 existing in the nature of things. 



That the real relations in nature, and the equation ex- 

 pressing them, are to be independent of any choice of 

 coordinates whatever, is the principle of relativity in its 

 purest and most general form. 



This principle was in the older theory of relativity limited 

 to those systems of coordinates connected by the linear ortho- 

 gonal transformations for which the Euclidean four-dimen- 

 sional element dr 2 — dx 2 + dx 2 + dun 2 + dx 2 was an invariant. 

 The Verallgemeinerte RelativiUltstheorie tries to apply the prin- 

 ciple in its full extent for all transformations which leave 

 the non-Euclidean general form ds 2 = 1(jf^ v dx^ dx v invariant. 

 It is for being able to express the laws in their covariant 

 forms that the complicate "absolute differential calculus" 

 with its tensors is worked out. 



In fact, the fundamental equations (2) and (3) presen e 

 their form unchanged whatever transformation of coordinate> 

 is executed. So do equations (5) and (6). The same cannot 

 be said of the equations (4) and (7). These preserve their 

 form only when the transformation is a linear one. The 

 * A. Eiustein, P/iys. Zeitschr. xv. p. 170, Feb. 1914. 



