﻿80 Dr. A. D. Fokker : A Summary of 



reason to admit the possibility of his room being accelerated. 

 There would be no reason to suspect that there was anything 

 the matter with his room, affecting all bodies in the same 

 way. Again, there could be no reason for doubt, if he could 

 find an inertial mass which did not gravitate. Yet, as far 

 as the experiments of Eotvos have gone *, they seem to 

 confirm that bodies which are attracted by the earth with 

 the same force have equal inertial masses as measured by 

 the centrifugal forces excited by their motion in the earth's 

 daily rotation. 



It is clear, that when we consider the motions of bodies, 

 using the ordinary mechanics, no distinction can be made 

 between a homogeneous gravitation field and a uniformly 

 accelerated system of coordinates. 



4. We may put the equivalence hypothesis in another 

 form. If we know the laws of motion in a field without 

 gravitation, we know the differential equations connecting 

 the time and the coordinates referred to a certain system of 

 coordinates. We are not obliged to describe the motion 

 with reference to this system. If we choose to do so, we 

 /nay describe the motion with reference to another system 

 which relatively to the first is uniformly accelerated. Of 

 course we shall have then to introduce alterations in our 

 equations. 



The equivalence hypothesis states that the alterations to 

 be introduced are the same as those which we have to make 

 when there is a homogeneous gravitation field affecting the 

 motion. 



It extends this statement beyond the region of mechanics. 

 It assumes that for all physical phenomena, when we give 

 the laws referred to an accelerated system of coordinates, the 

 differential equations will undergo the same variations from 

 what they were in the resting systems as they would suffer 

 if we produced a gravitation field. 



5. Starting from this idea, it is easy to deduce in an 

 elementary manner some important consequences f . 



For example, consider two sodium atoms, placed one above 

 the other at a certain distance A, and fixed on the Z-axis of 

 a system of coordinates that has a constant acceleration (7) 

 upwards. Let at some instant a signal, consisting of a train 

 of wavelets, be sent from the upper sodium atom to the 



* B. Eotvos, Mathem. u. naturivissensch. Berichte aits Ungarn. vii. 1890. 

 Wiedemann, Beiblatter, xv. p. 688 (1891). 

 t A. Einstein, Annalen der Phi/sik, xxxv. p. 898 (1911). 



