CONTEMPORARY ADVANCES IN PHYSICS, XXVIII 611 



causes of the transmutation, I mean the immediate cause as well as 

 the underlying one {la cause occasionnelle aussi Men que la cause pro- 

 fonde) are to be found in the interior of the atom fread, in the nucleus!] ; 

 for otherwise, external circumstances would affect the coefficient in 

 the exponent. . . . The chance which governs these transmutations 

 is therefore internal; that is to say, the nucleus of the radioactive 

 substance is a world, and a world subject to chance. But, take heed ! 

 to say 'chance' is the same as to say 'large numbers' — a world built 

 of a small number of parts will obey laws which are more or less com- 

 plicated, but not statistical. Hence the nucleus must be a com- 

 plicated world." 2^ 



Well! the advent of quantum mechanics has made unnecessary 

 the conclusion which Poincare was obliged to draw; for according to 

 this doctrine, the statistical law is characteristic as much of a single 

 particle confronted with a potential-hill, as of the greatest conceivable 

 number of particles mixed up together. It must be admitted that 

 Poincare's conclusion is probably right enough for the radioactive 

 nuclei of which he knew, all of which must be conceived to comprise 

 several hundreds of particles, protons and electrons and neutrons and 

 the like; but it is not enforced by the reason which he gives, if quantum 

 mechanics is valid. For reversing the argument of previous pages: 

 if in the valley-enclosed-by-hills which is illustrated (for the oversim- 

 plified one-dimensional case) by Fig. 16, we postulate a particle and 

 the waves associated with that particle, then the quantum-mechanical 

 boundary-conditions require waves beyond the hills as well, and the 

 coexistence of waves without and within implies a tendency — -a 

 tendency governed by the "laws of chance," a probability — for the 

 particle to escape from within to without. As soon as the physicist 

 has successfully made the effort of consenting to quantum mechanics, 

 he is dispensed from the further effort of contriving nuclear models 

 with special features to account for the law of decay of radioactive 

 substances. 



Like the probability of entry, the probability of escape of the 

 particle from the confined valley is governed by the ratio of the 

 squared amplitudes -^^if* within the valley and beyond the hill (the 

 latter in the numerator). It thus is governed by the exponential 

 function, 



exp. [- (47r//?.) f^2m{NeVm - E)dx'], 



of which we have already made the acquaintance, multiplied by a 



2^ H. Poincare: "Dernieres Pensees," pp. 204-205 (he credits Debierne with the 

 idea). 



