194 AISTNUAL REPORT SMITHSONIAN INSTITUTION, 1950 



This explains that, in favorable circumstances, long strings of suc- 

 cessively occupied states may be produced, similar to those contem- 

 plated in sections 7 and 8. Such a string gives the impression of an 

 identifiable individual, just as in the case of any object in our daily 

 surrounding. It is in this way that we must look upon the tracks in 

 the cloud chamber or in a photographic emulsion, and on the (prac- 

 tically) simultaneous discharges of Geiger counters set in a line, 

 which discharges we say are caused by the same particle passing one 

 counter after another. In such cases it would be extremely incon- 

 venient to discard this terminology. There is, indeed, no reason to 

 ban it, provided we are aware that, on sober experimental grounds, 

 the sameness of a particle is not an absolute concept. It has only a 

 restricted significance and breaks down completely in some cases. 



In what circumstances this restricted sameness will manifest itself 

 is fairly obvious: namely, when only few states are occupied in the 

 region of the state-manifold with which we are concerned, or, in other 

 words, when the occupied states are not too crowded in that region, 

 or when occupation is a rare event — the terms "few," "crowded," and 

 "rare" all referring to the state-manifold. Otherwise, the strings 

 intermingle inextricably and reveal the true situation. In the last 

 section we shall formulate the quantitative condition for the prevailing 

 of restricted individuality. Now we ask what happens when it is 

 obliterated. 



12. CROWDEDNESS AND WAVE ASPECT 



One gains the impression that according as the individuality of the 

 particles is wiped out by crowding, the particle aspect becomes alto- 

 gether less and less expedient and has to be replaced by the wave 

 aspect. For instance, in the electronic shell of an atom or molecule the 

 crowding is extreme, almost all the states within a certain region being 

 occupied by electrons. The same holds for the so-called free electrons 

 inside a metal. Indeed, in both cases the particle aspect becomes en- 

 tirely incompetent. On the other hand, in an ordinary gas the mole- 

 cules are extremely rare in the wide region of states over which they 

 spread. No more than one state in 10,000 or so is occupied. And in- 

 deed, the theory of gases, based on the particle aspect, was able to 

 attain great perfection long before the wave nature of ordinary mat- 

 ter was discovered. (In the last remark I have been speaking of the 

 molecules as if they were ultimate particles ; this is legitimate as far 

 as their translatory motion is concerned.) 



It is tempting to assign to the two rivals, the particle aspect and the 

 wave aspect, full competences in the limiting cases of extreme "rare- 

 faction" and extreme "crowding" respectively. This would separate 

 them, as it were, with only some sort of transition required for the 



