188 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1950 



themselves — so I believe — have the authority of forcing us to put an 

 end to the habit of picturing the physical world as a reality. 



I believe the situation is this. We have taken over from previous 

 theory the idea of a particle and all the technical language concerning 

 it. This idea is inadequate. It constantly drives our mind to ask 

 information which has obviously no significance. Its imaginative 

 structure exhibits features which are alien to the real particle. An 

 adequate picture must not trouble us with this disquieting urge; it 

 must be incapable of picturing more than there is ; it must refuse any 

 further addition. Most people seem to think that no such picture can 

 be found. One may, of course, point to the circumstantial evidence 

 (which I am sorry to say is not changed by this essay) that in fact 

 none has been found. I can, however, think of some reasons for this, 

 apart from the genuine intricacy of the case. The palliative, taken 

 from positivist philosophy and purporting to be a reasonable way out, 

 was administered fairly early and authoritatively. It seemed to re- 

 lieve us from the search for what I should call real understanding; 

 it even rendered the endeavor suspect, as betraying an unphilosophical 

 mind — the mind of a child who regretted the loss of its favorite toy 

 (the picture or model) and would not realize that it was gone forever. 

 As a second point, I submit that the difficulty may be intimately con- 

 nected with the principal subject of this paper, to which I shall now 

 turn without further delay. The uncertainty relation refers to the 

 particle. The particle, as we shall see, is not an identifiable individual. 

 It may indeed well be that no individual entity can be conceived which 

 would answer the requirements of the adequate picture stated above. 



It is not at all easy to realize this lack of individuality and to find 

 words for it. A symptom is that the probability interpretation, unless 

 it is expressed in the most highly technical language of mathematics, 

 seems to be vague as to whether the wave gives information about one 

 particle or about an ensemble of particles. It is not always quite clear 

 whether it indicates the probability of finding "the" particle or of 

 finding "a" particle, or indicates the likely or average number of par- 

 ticles in, say, a given small volume. Moreover, the most popular view 

 on probability tends to obliterate these differences. It is true that 

 exact mathematical tools are available to distinguish between them. 

 A point of general interest is involved, which I will explain. A 

 method of dealing with the problem of many particles was indicated 

 in 1926 by the present writer. The method uses waves in many-dimen- 

 sional space, in a manifold of 3iV dimensions, N being the number of 

 particles. Deeper insight led to its improvement. The step leading 

 to this improvement is of momentous significance. The many-dimen- 

 sional treatment has been superseded by so-called second quantization, 

 which is mathematically equivalent to uniting into one three-dimen- 



