LAW, CAUSE 379 



masses of appreciable size is very small, hence is practically 

 equal to zero. This accounts for the fact that no difficulties 

 of the kind here indicated are noticed in connection with 

 gross objects. But for particles of the size of electrons the 

 indeterminacy becomes larger. The essential meaning of 

 this principle for the deterministic view of nature is that 

 position and velocity (the necessary and sufficient condi- 

 tions for ascertainment of state) cannot be determined at 

 the same time with a high degree of accuracy. Position can 

 be determined accurately, but then velocity is measured 

 only very inaccurately; or velocity can be determined accu- 

 rately, but then position is measured only very inaccurately. 1 



The inferences from this fact to a general view of nature 

 are of two kinds, and physicists seem to be divided about 

 equally into two classes on the basis of their views as to 

 these consequences. On the one hand are such men as 

 Eddington and Compton, who conclude that the world 

 cannot be a rigidly deterministic system; on the other, such 

 men as Planck and Einstein, who insist that the difficulties 

 lie merely in our techniques of observation and not in nature 

 itself. A brief examination of these contrasting views may 

 be made. 



The former view, which may be called objective indeter- 

 minism, argues essentially as follows: The meaning of any 

 physical concept is determined by the operations which 

 are employed in locating the object to which the concept 

 refers. Concepts, to be meaningful, must refer to events 

 which can be produced in observation by describable tech- 

 niques. If the operations purporting to locate an event are 

 self -contradictory, or such as cannot be carried out without 

 violating recognized physical laws, the concepts which 



1 Professor Carl Eckart has called the author's attention to a very important 

 feature of the principle of indeterminacy. There is actually no way of measuring 

 the position and momentum of an electron or any other small particle accurately 

 enough to confirm or infirm this inequality. On the other hand there are actual 

 experiments that confirm the classical theory and thus contradict the principle of 

 indeterminacy. This is, indeed, a noteworthy fact, and weakens to a very great 

 extent the positions of all of those who argue for an objective indeterminacy upon 

 the basis of the principle. It is surprising that some of the popularizers of the theory 

 (Eddington, Compton, and Planck) have not chosen to emphasize this fact. 



