PAPERS ON CHEMISTRY AND PHYSICS 323 



NOTES ON THE QUANTUM THEORY AND 

 . RELATIVITY 



Jakob Krxz, University of Illinois 



It has been shown by A. Sommerfeld that the fine 

 structure of the lines of the Balmer series of the hydro- 

 gen and helium spectrum can be explained by a simultan- 

 eous application of the quantum theory and of relativity 

 to the elliptic orbits of the electron revolving around the 

 nucleus. The mass of the electron varies in its stationary 

 elliptic motion according to the expression given by re- 

 lativity, but during the jump of the electron from one 

 stationary orbit to another one the mass is supposed to 

 be constant in spite of the fact that this motion is ac- 

 companied by radiation, i. e., by emission of energy, and 

 that the emission of energy is accompanied by a loss of 

 mass of the radiating system, according to the equation 



dE 



dm = — 

 c 2 



which holds in relativity as well as in classical electrody- 

 namics if we assume an electromagnetic momentum in a 

 beam of light. When the electron jumping from one 

 orbit to another one loses energy A E = E b — E e = hv, 



hv 

 then it should also lose mass A m = — in a discontinu- 

 es 



ous process. These masses Am would be the smallest 

 particles at present suggested by our theories. It is sur- 

 prising that they do not make themselves felt in the 

 theory of the fine structure of the helium and hydrogen 

 lines, nor in the doublets of the Roentgen spectra, where 

 they are of considerable magnitude. There is probably 

 a compensation in the mass. 



A second remark is related to the previous one. The 

 quantum theory and the theory of relativity seem to be 

 at variance. The experimental basis of the quantum 

 theory is much broader than that of the general theory of 



