﻿Einstein and Grossmann's Theory of Gravitation. 79 



of energy, which seems to be a sufficiently trustworthy basis, 

 and admits that the principle of relativity shall be valid in a 

 particular case, that is, its formulae will be correct whenever 

 the gravitation potentials are constants independent of the 

 coordinates. To be complete, we state explicitly that it is 

 believed that the results of experiments in a laboratory are 

 not altered when the laboratory, as a whole, is taken to a 

 place where the gravitation potentials have other values. 



Starting from these ideas, Einstein has been able to give 

 the laws according to which matter is affected by a gravi- 

 tation field, and a gravitation field created by matter. It is 

 of special interest that his theory is not constructed after 

 the known model of the electromagnetic theory (though we 

 find certain analogies to be present). He places the phe- 

 nomena of gravitation on a higher plane, and accordingly 

 shows how the equations of the electromagnetic field are to 

 be altered when allowance must be made for the presence of 

 a gravitation field. 



It is characteristic of his theory, that the field of gravita- 

 tion is not given by a single potential, but by a set of ten 

 potentials, functions of the coordinates *. These ten poten- 

 tials are the components of a symmetrical tensor. Further, 

 the important thing which is acted upon by gravitation and 

 which produces the field, formerly the " mass " alone, is in 

 the present theory a tensor of stresses, momenta, currents of 

 energy, and energy. This will be made clearer afterward sf. 



The Equivalence Hypothesis. 



3. The equivalence hypothesis briefly assumes the equi- 

 valence of a homogeneous field of gravitation and a uniform 

 acceleration of the system of coordinates. 



Consider the case, that an experimenter is working in a 

 room without any window, so that he cannot know anything 

 about things outside, and does not know whether he is in 

 relative motion against an outside world or not. Let the 

 only remarkable thing he notices be this, that all bodies fall 

 down to the floor when he lets them loose, all with the same 

 acceleration, in the same direction. Shall he be able to 

 state whether his room is in a homogeneous gravitation field 

 or whether there is no gravitation field at all, the cause of 

 falling down and apparent weight of his bodies being a 

 uniformly accelerated motion of his room through space ? 



He cannot. He has no criterion. Of course, if all bodies 

 did not fall with the same acceleration, there would be no 



* See § 11. t See § 12, 



