220 THE NEW QUANTUM THEORY 



the number of systems of the kind considered must 

 have one of a discrete series of values. In Dirac's 

 problem the series turns out to be the series of integers. 

 Accordingly we infer that the number of systems must 

 be either i, 2, 3, 4, . . ., but can never be 2% f° r 

 example. It is satisfactory that the theory should give 

 a result so well in accordance with our experience ! 

 But we are not likely to be persuaded that the true 

 explanation of why we count in integers is afforded by a 

 system of waves. 



Principle of Indeterminacy. My apprehension lest a 

 fourth version of the new quantum theory should 

 appear before the lectures were delivered was not ful- 

 filled; but a few months later the theory definitely 

 entered on a new phase. It was Heisenberg again who 

 set in motion the new development in the summer of 

 1927, and the consequences were further elucidated by 

 Bohr. The outcome of it is a fundamental general 

 principle which seems to rank in importance with the 

 principle of relativity. I shall here call it the "principle 

 of indeterminacy". 



The gist of it can be stated as follows : a particle may 

 have position or it may have velocity but it cannot in any 

 exact sense have both. 



If we are content with a certain margin of inaccuracy 

 and if we are content with statements that claim no 

 certainty but only high probability, then it is possible 

 to ascribe both position and velocity to a particle. But 

 if we strive after a more accurate specification of position 

 a very remarkable thing happens; the greater accuracy 

 can be attained, but it is compensated by a greater 

 inaccuracy in the specification of the velocity. Similarly 

 if the specification of the velocity is made more accurate 

 the position becomes less determinate. 



