ELEMENTARY PARTICLE — RCHRODINGER 191 



velopmeiit, and the feature which in the long run is bound to have the 

 most important consequences. If we wish to retain atomism we are 

 forced by observed facts to deny the ultimate constituents of matter 

 the character of identifiable individuals. Until recently, atomists of 

 all ages, for all I know, had transferred that characteristic from visi- 

 ble and palpable pieces of matter to the atoms, which they could not see 

 or touch or observe singly. Now we do observe single particles; we 

 see their tracks in the cloud chamber and in photographic emulsions; 

 we register the practically simultaneous discharges caused by a single 

 swift particle in two or three Geiger counters placed at several yards' 

 distance from each other. Yet we must deny the particle the dignity 

 of being an absolutely identifiable individual. Formerly, if a physi- 

 cist w^ere asked what stuff the atoms themselves were made of, he might 

 smile and shirk the answer. If the inquirer insisted on the question 

 whether he might imagine them as small unchangeable bits of ordinary 

 matter, he would get the smiling reply that there was no point in doing 

 so but that it would do no harm. The formerly meaningless question 

 has now gained significance. The answer is definitely in the nega- 

 tive. An atom lacks the most primitive property we associate with a 

 piece of matter in ordinary life. Some philosophers of the past, if 

 the case could be put to them, would say that the modern atom con- 

 sists of no stuff at all but is pure shape. 



10. THE MEANING OF THE NEW STATISTICS 



We must at last proceed to give the reasons for this change of atti- 

 tude in a more comprehensible form than at the end of section 6. It 

 rests on the so-called new statistics. There are two of them. One is 

 the Bose-Einstein statistics, whose novelty and relevance were first 

 stressed by Einstein. The other is the Fermi-Dirac statistics, of 

 which the most pregnant expression is Pauli's exclusion principle. I 

 shall try to explain the new statistics, and its relation to the old classi- 

 cal or Boltzmann statistics, to those who have never heard about such 

 things and perhaps may be puzzled by what "statistics" means in this 

 context. I shall use an instance from everyday life. It may seem 

 childishly simple, particularly because we have to choose small num- 

 bers — actually 2 and 3 — in order to make the arithmetic surveyable. 

 Apart from this, the illustration is completely adequate and covers 

 the actual situation. 



Three schoolboys, Tom, Dick, and Harry, deserve a reward. The 

 teacher has two rewards to distribute among them. Before doing so, 

 he wishes to realize for himself how many different distributions are 

 at all possible. This is the only question we investigate (we are not 

 interested in his eventual decision). It is a statistical question: to 

 count the number of different distributions. The point is that the 



