250 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1930 



a radiation exchanges energy with matter, the exchange can be de- 

 scribed as being an absorption or emission by the matter of a photon, 

 and when we wish to describe the movement in space of corpuscles 

 of light we must speak of the propagation of a wave. Elaborating 

 further this conception, we are led to admit that the density of a 

 cloud of corpuscles, which constitutes a luminous wave, is always at 

 every point equal to the intensity of the associated wave. It thus 

 happens that we come to the synthesis of two old rival theories of 

 light. We thus explain at the same time both the interference phe- 

 nomena and the photo-electric effect. Great interest lies in this 

 s-ynthesis because it indicates to us that in nature both light waves 

 and the corpuscles of matter are intimately connected, at least in 

 the case of light. But if this is true with light, may we not also 

 expect it to be true with matter ? Until now all the efforts of physi- 

 cists have tended to reduce matter to a complicated structure of 

 corpuscles, photons, and electrons. But just as a photon can not be 

 conceived without its wave which travels with it, should we not also 

 suppose that the corpuscles of matter are always escorted by a wave ? 

 Such is the leading question now asked of us. 



Let us suppose that a corpuscle of matter, an electron, for example, 

 is always accompanied by a wave, the corpuscle and the wave being 

 intimately bound together. The movement of the corpuscle and 

 the propagation of the wave are not independent, and we should be 

 able to obtain a relationship between the mechanical magnitude of 

 the corpuscle — the velocity and the energy — and the magnitude 

 characterizing the wave — the velocity of propagation and the wave 

 length. In suggesting the connection which should exist between 

 the protons and their associated light waves, we can indeed estab- 

 lish a parallelism. This theory of the bond between the material 

 corpuscles and their associated waves is to-day know as wave me- 

 chanics. Naturally I can not to-day lay before you the details of 

 this mechanics. I will limit myself merely to telling you that it 

 leads to attributing a wave length to the wave associated with the 

 material corpuscle, a value which varies inversely with the velocity 

 of the corpuscle. The more rapidly the corpuscle moves, the smaller 

 is the wave length of the associated wave. 



When the wave moves freely in a portion of space whose dimen- 

 sions are large compared with the wave length, the new mechanics 

 attributes to the associated particle a movement identical with that 

 predicted by the classical mechanics. There is therefore here an 

 accordance between the old and the new mechanics. Particularly is 

 this the case with the electrons which we can observe directly, and 

 we thus explain why the study of the electron movements on a large 

 scale led to considering them as simple corpuscles moving according 

 to the laws of the classical mechanics. 



