﻿742 Prof. Rackett on Relativity- Contraction in a Rotating 



Moving System. — On the theory o£ restricted relativity, if 

 the apparatus is transferred to a system $' moving with 

 speed v along the axis of z and parallel to the axis of the 

 shaft, the properties of the system remain unaltered. For 

 the moving observer there are, therefore, definite speeds of 

 rotation for which 



(1) light rays parallel to the axis of the shaft can 



pass through the apertures in the disks in either 

 direction, 



(2) the measured speed of light in this hypothetical 



experiment is c. 



To an observer in the stationary system, this is impossible 

 unless compensations take place. He knows 



(3) the velocity of the moving system, 



(4) the distance between the two disks modified by 



motion to l^\ — v 2 jc 2 . 



Reasoning on these data, he concludes that the experiment 

 can only succeed if the forward end of the shaft when in 

 rotation is twisted, with respect to the rear end, in the 

 opposite sense to the rotation through an angle, say 6 ; and 

 this twist must be such as to compensate for the different 

 light-times between the disks in and opposite to the direc- 

 tion of motion. During the light-time for the former 

 direction the shaft turns through an angle </) + #, while the 

 light has the relative velocity c — v. In the other direction, 

 the shaft running at the same speed turns through an angle 

 <f> — 0, but the light has the relative velocity c-\-v. At this 

 speed, condition (1) is satisfied, since light, emitted through 

 an aperture in one disk towards the other, reaches it just as 

 an aperture is passing across the path of the ray in the plane 

 of (#, z). The period of rotation T' and the twist required 

 to satisfy this condition can be determined by the fixed 

 observer using his own units from the equations : — 



(c-v) (</> -f <9) T72tt = I \Zl-v 2 /c 2 = (c + v) (</>-0)T72tt, 

 which give 



0/<f> = vie, 



(jy.c. (l-v 2 /c 2 ) T'/2tt = I %/l-v 2 /c 2 . 



