£08 Does an Accelerated Electron radiate Energy ? 



In Dr. Milner's case, however, the electrons are moving 

 with a rapidity which appreciably departs from the velocity 

 of light only for a very short part of their total infinite path *, 

 so that except perhaps at the turning point in each path, 

 either the velocity or the acceleration would exceed the 

 limits laid down for proper radiation ; in other words, the 

 radiation shell created at any instant cannot in general 

 be expected to free itself from the electron, so that its field 

 would always remain mixed up with the velocity field 

 which properly determines the mass and energy of the 

 electron. Near the turning point the ordinary conditions of 

 small velocity and acceleration are realized, and here Milner 

 verifies the usual formula for an instantaneous irreversible 

 radiation. 



It is evident, therefore, that the solution presented does 

 not in reality contradict our previous notions of these matters 

 except in so far, perhaps, as the conditions in it are such as 

 are never presumed to be realized in actual practice. 



The subsequent question as to the complete suitability of 

 the retarded point potentials, and the consequent necessity 

 for boundaries of discontinuity in the electromagnetic field, 

 does not seem open to much doubt. Of course it involves 

 regarding the whole subject from the point of view which 

 concentrates mainly on the electrons and their motion. The 

 alternative is to regard the infinite field as the fundamental 

 entity, and then to deduce the motions of the various 

 electrons involved in it as one aspect of the conditions in the 

 field, but this is infinitely more difficult than the reverse 

 process, if only for the reason that it involves in any problem 

 an a priori specification for a quadruply infinite number of 

 space-time points instead of merely for a finite number 

 of electrons. And ultimately there can be no discrepancy in 

 the results for any given problem approached in the two ways; 

 for two field solutions satisfying the electromagnetic equations 

 and giving the same polar nuclei with the same motions must 

 be identical. 



The University, Manchester, l ^' 



July 29th, 1921. Gr. H. LlVENS. 



* A point moving with the velocity of radiation and starting from 

 infinity with one of the electrons, would only gain a finite distance in 

 the infinite time required for the motion. 



