1B6 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1950 



tary state of a particle, two independent data were required : its co- 

 ordinates and their first time derivatives, or ubiety and velocity. 

 According to the new theory less is required, and less is obtainable. 

 Either of the two data can be given with arbitrary accuracy, provided 

 that no store is set on the other, but both cannot be known together 

 with absolute precision. One may not even conceive of both as having 

 absolutely sharp values at the same instant. They mutually blur each 

 other, as it were. Broadly speaking, the product of the latitudes of 

 their respective inaccuracies cannot be reduced below a fixed constant. 

 For an electron, this constant happens to be about 1 if the uni'ts 

 centimeter and second are used. Thus, if the velocity of an electron 

 is considered sharp with a latitude of only 1 centimeter per second, 

 its location has to be considered as blurred within the latitude of 1 

 centimeter. The strangeness does not lie in the mere existence of 

 inaccuracies, for the particle might be a thing of vague and change- 

 able extension, within which slightly different velocities prevailed at 

 different spots. Then, however, a sharp location or ubiety would 

 probably entail a sharply defined velocity and vice versa. Actually 

 it is just the other way round. 



5. CURRENT VIEWS: THE MEANING OF THE UNCERTAINTY 



RELATION 



Two links connect this strange and certainly very fundamental 

 statement to other parts of the theory. It can be arrived at by de- 

 claring that a particle is equivalent to its guiding wave, and has 

 no characteristics save those indicated by the guiding wave according 

 to a certain code. The code is simple enough. The ubiety is indi- 

 cated by the extension of the wave, the latitude in the velocity by the 

 range of wave numbers. "Wave number" is short for reciprocal of 

 the wavelength. Each wave number corresponds to a certain velocity 

 proportional to it. That is the code. It is a mathematical truism 

 that the smaller a wave group, the wider is the (minimum) spread of 

 its wave numbers. 



Alternatively, we may scrutinize the experimental procedure for 

 determining either the ubiety or the velocity. Any such measuring 

 device implies a transfer of energy between the particle and some 

 measuring instrument — eventually the observer himself, who has to 

 take a reading. This means an actual physical interference with the 

 particle. The disturbance cannot be arbitrarily reduced, because 

 energy is not exchanged continuously but in portions. We are given 

 to understand that, when measuring one of the two items, ubiety or 

 velocity, we interfere with the other the more violently the higher 

 the precision we aim at. We blur its value within a latitude inversely 

 proportional to the latitude of error allowed in the first. 



