222 ANNUAL REPORT SMITHSONIAN INSTITUTION, 19 3 3 



observables, and regard the fact that this policy is not only prac- 

 ticable but amazingly successful as one of the discoveries of the 

 century. 



Once an unnecessary concept is dismissed, it does not return. 

 Nevertheless, new different concepts may then make their ap- 

 pearance. Heisenberg's discoveries were quickly followed by 

 Schrodinger's development of the wave mechanics, which presented 

 a new unobservable ^, the subject of mathematical propositions but 

 not otherwise defined. Certain aspects of ^ — its absolute magnitude, 

 for example — had physical interpretations and were equivalent to 

 physical measures, but if/ itself remained mysterious. Dirac, in his 

 profound volume, has constructed a complete mechanics which 

 begins by introducing a new set of concepts, not defined in terms 

 of immediate experience. Certain nonnumerical magnitudes typi- 

 fied by symbols i}/ (or (f>) and a are introduced as representing 

 " states " and " observables ", respectively, where a distinction is 

 made between the " observable " a and the number that is obtained 

 when an observation of this observable a is made on the system in 

 the state ip. Thus the state and the observable are conceptual things, 

 capable of being roughly described but not defined or directly ex- 

 perienced. A purely symbolic mathematics is then constructed on 

 the basis of defined operations between observables and states, and 

 formulae are obtained embodying the fact that under certain circum- 

 stances observations assign definite numerical values to observables. 

 Probability interpretations are then placed on certain symbols, 

 capable of a meaning whatever systems or observations are in ques- 

 tion. Next, in a most beautiful manner the equations of classical 

 mechanics are used to suggest relations between observables which 

 are cases of the general abstract theory, and thus certain operations 

 conducted on them are capable of interpretation. Lastly, the con- 

 structed abstract theory and the introduced abstract mechanics are 

 applied to particular physical systems, themselves involving such 

 concepts as the point mass and the point charge, and the predicted 

 properties of these specific physical systems can then be obtained 

 from the interpretation of the abstract relations. This imperfect 

 summary is only intended to illustrate the development of physics 

 by the successive use of old concepts, then things observed, and then, 

 in turn, new concepts, the last being possibly very strange ones. 



Though the Einstein-Heisenberg policy is fairly new to physics, 

 it is far from new to philosophy. This was the policy of Locke and 

 Hume. Hume in particular irrevocably damaged the idea of efficient 

 causation by examining the evidence by which a particular " cause " 

 was assigned to a particular " effect." Though we may not accept 

 his solution in terms of habit, we owe a great debt to his exposure 



