president's address — SECTION A. 13 



physicists in Bonn have discovered the shift. In view of the great 

 diversity of opinion, however, judgment must be suspended until 

 further evidence is forthcoming. 



The prediction of the shift is based on the assumption that the 

 atom is a natural clock giving the same value of ds for each vibration. 

 If this assumption is correct, and it appears to be justified by the 

 Principle of Equivalence, y-dt is constant. Therefore the period of 



vibration is proportional to y^^ or 1 -| 



At the surface of the sun, r = 697,000 kilometres and w = 1'47. 

 It follows that the ratio of the period of an atom at the sun's surface 

 to that of a similar atom on the earth is 1 '00000212. 



The radiation, however, is seen from the earth and not from the 

 surface of the sun, and the prediction of the Einstein efEect involves 

 the further assumption that the time period of the source is transmitted 

 by the radiation to the terrestrial observer. If this is so, the displace- 

 ment should be observed. 



An alternative hypothesis is that the interval Ss is transmitted 

 by the radiation. In this c^se the observed local time period of the 

 light will be the same whatever the situation of the radiating source. 



The latter hypothesis seems to be more in accordance with the ideas 

 of the Relativity than the former. 



Suppose a disturbance to leave A at time i^ and arrive at B at time 

 ts, and a second to follow at time ^^ + S<a, arriving at time /„ + S^u, 

 F'or each disturbance 8s = along tTie world line, and therefore s 

 is constant. Hence the interval y>}8t_^ which elapses between the 

 two departures from A is equal to the interval yB'S'u between the 

 two arrivals at B. 



The alternative view, that S/! is transmitted by the radiation, appears 

 to arise from a too hasty deduction from the three-dimensional optical 

 work by which the apparent deviation was established. You will 

 remember that the argument was based on the application of the 

 Principle of Least Time to the investigation of the path of a ray with 

 given velocity. A tempting line of argument is the following : — 

 " We know that the period of light traversing a region of varying 

 refractive index is constant along the path. Therefore the period 

 seen by an observer at B is the same as that seen by an observer at C" 



The fallacy appears to lie in this fact : the observer at B takes the 

 elements Sr, rS6, 8t as elements of a Euclidean system of co-ordinates, 

 the observer at C does the same with the corresponding elements at C. 

 Each builds up his space-time system on this basis, and the resulting 

 space systems are similar as are also the time systems ; but it is not 

 true to say that the scales of the two systems are the same. The corre- 

 lation between the two is found in the fundamental underlying quantity, 

 the interval. By comparing equal intervals at B and C it is seen that 

 Yf^Stfj = yji'^tji. That is, the time scale varies as y"^. 



