MATTER, A MODE OF MOTION 365 



of the second particle, the nucleus. Since the stability conditions for the 

 electron pattern particle are most strongly influenced by the effective con- 

 stants of the medium near its center, we would expect its energy and fre- 

 quency to be controlled largely by that part of the nuclear pattern which is 

 near its center. Let us assume that, through some external agency, the 

 center of the electron pattern is transferred from one position of rest to 

 another which is difTerently placed relative to the nucleus. Owing to the 

 different effect of the nuclear pattern on the effective constants of the 

 medium as viewed by the electron pattern, the stable energy of the latter 

 would be different at the second position. This change in rest energy with 

 position may be interpreted as a measure of the change in a field of static 

 potential associated with the massive nucleus. The similarity between this 

 relationship and that which exists between the electron and the nuclear 

 potential in wave mechanics is obvious. 



In speaking of a change in the effective constants of the medium, we refer 

 to an average value taken over a number of cycles and wave lengths of the 

 oscillations which make up the second pattern, or nucleus. Calculations 

 based on this concept should not therefore be expected to give valid results 

 when the time intervals involved in the averages are comparable to the 



// 



period ;, of the second particle at rest, or the distances are comparable to 



nioc- 



the corresponding wave length of the pattern. For a proton this period 



is 4.38 X 10~ seconds and the wave length is 1.31 X 10~ cms. If, then, 

 an electron is to be subject to the kind of nuclear potential field just de- 

 scribed, the linear dimensions of that part of it which is controlled by the 

 potential field of the proton must be at least of the order of 10~ cm. This is 

 consistent with Gamow's^ observation that "It seems, in fact, that a length 

 of the order of magnitude of 10 centimeters plays a fundamental role in 

 the problem of elementary particles, popping out wherever we try to esti- 

 mate their physical dimensions." 



The variations in the medium due to the nucleus might be treated in 

 terms of their effect on the progressive wave components, the interference 

 of which gives rise to the wave pattern of the electron. The component waves 

 as so influenced should combine to form an interference pattern which 

 represents the behavior of the electron in the field of the nucleus. It is also 

 possible that a technique may be found for treating their effect on that 

 factor of the electron wave which is similar to the DeBroglie wave. This 

 should be more nearly like the techniques now used in wave mechanics. 



If two particles are brought so close together that the central cores of 

 their patterns overlap, the departure from linearity becomes so great that 



* G. Ganiow, Physics Today, 2, p. 17, Jan., 1949. 



