OUTLINE OF SCHRODINGER'S THEORY 217 



Attention must be called to one highly important 

 consequence of this theory. A small enough stormy 

 area corresponds very nearly to a particle moving about 

 under the classical laws of motion; it would seem there- 

 fore that a particle definitely localised as a moving point 

 is stricdy the limit when the stormy area is reduced to 

 a point. But curiously enough by continually reducing 

 the area of the storm we never quite reach the ideal 

 classical particle; we approach it and then recede from 

 it again. We have seen that the wave-group moves like 

 a particle (localised somewhere within the area of the 

 storm) having an energy corresponding to the frequency 

 of the waves; therefore to imitate a particle exactly, not 

 only must the area be reduced to a point but the group 

 must consist of waves of only one frequency. The two 

 conditions are irreconcilable. With one frequency we 

 can only have an infinite succession of waves not ter- 

 minated by any boundary. A boundary to the group is 

 provided by interference of waves of slightly different 

 length, so that while reinforcing one another at the 

 centre they cancel one another at the boundary. Roughly 

 speaking, if the group has a diameter of 1000 wave- 

 lengths there must be a range of wave-length of o-i per 

 cent., so that 1000 of the longest waves and 1001 of 

 the shortest occupy the same distance. If we take a 

 more concentrated stormy area of diameter 10 wave- 



seems to depend on whether you are considering the probability after 

 you know what has happened or the probability for the purposes of 

 prediction. The ijj 2 is obtained by introducing two symmetrical systems 

 of ij>-waves travelling in opposite directions in time; one of these must 

 presumably correspond to probable inference from what is known (or 

 is stated) to have been the condition at a later time. Probability neces- 

 sarily means "probability in the light of certain given information", so 

 that the probability cannot possibly be represented by the same function 

 in different classes of problems with different initial data. 



