MODERN CONCEPTS IN PHYSICS — LANQMUIR 233 



thus have some justification in saying that two points are really 

 one kilometer apart. We do not attribute, however, much reality 

 to the concept of the diameter of an electron. 



Thirty years aijo the physical chemist doubted the existence of 

 atoms or believeil the com-ept was useless if nt)t pernicious. A few 

 years later the leader of this movement, Ostwald, in the preface of 

 one of his books stated that he believed that the existence of atoms 

 had been proved experimentally beyond question, althou^di in pre- 

 vious books he had stated that there are always an infinite number 

 of hypotheses that could be advanced to explain any given set of 

 experimental facts. 



To-day, what can we say in answer to the question " Does matter 

 really consist of atoms?" Must we say that this is one of those 

 meaningless questions? 



Of course, the amount of meaning that can be attached to any 

 such question depends upon the definitions of the words and con- 

 cepts which it contains. If we mean by atoms indivisible and in- 

 destructible infinitely hard, elastic spheres, we are compelled to 

 answer the question in the negative. In accordance with modern 

 usage, however, we do not attribute any such properties to the atom. 

 If, by the use of the word atom, we mean to imply principally the 

 concept that matter consists of discrete particles which can be 

 counted by the various methods which are now known for this 

 purpose, we have the very best of reasons for answering the ques- 

 tion in the affirmative. If in our studies of nature we discover 

 evidences of discontinuities or of the presence of discrete natural 

 units which can be correlated in a definite way with the numerical 

 integers, we have come, it would seem, about as close to something 

 absolute in nature as we can hope to get. Einstein in the relativity 

 theory has taught us to look upon the intersections of world lines 

 as the data upon which our observations of nature rest. Such 

 points of intersections, which can be called events, are essentially 

 discontinuities. In general they are all unlike one another. When 

 we find in nature discrete units which in many respects appear to 

 be identical with one another, and we can count these units, it would 

 seem that the number of these units which obtain as a result is apt 

 to be independent of our system of reference; therefore, they have 

 in general, a certain kind of absolute significance. 



In this respect, therefore, it seems that the atomic theory and the 

 quantum theory in which integers play such a fundamental role 

 may be considered as representing reality to a higher degree than 

 almost any other of our physical and chemical theories. 



Skepticism in regard to an absolute meaning of worils, concepts, 

 models or matheuuitical tlieories should not prevent us from using 



