2i 8 THE NEW QUANTUM THEORY 



lengths the range is increased to 10 per cent.; 10 of 

 the longest and 1 1 of the shortest waves must extend the 

 same distance. In seeking to make the position of the 

 particle more definite by reducing the area we make its 

 energy more vague by dispersing the frequencies of the 

 waves. So our particle can never have simultaneously 

 a perfectly definite position and a perfectly definite 

 energy; it always has a vagueness of one kind or the 

 other unbefitting a classical particle. Hence in delicate 

 experiments we must not under any circumstances expect 

 to find particles behaving exactly as a classical particle 

 was supposed to do — a conclusion which seems to be in 

 accordance with the modern experiments on diffraction 

 of electrons already mentioned. 



We remarked that Schrodinger's picture of the hy- 

 drogen atom enabled it to possess something that would 

 be impossible on Bohr's theory, viz. two energies at 

 once. For a particle or electron this is not merely per- 

 missive, but compulsory — otherwise we can put no limits 

 to the region where it may be. You are not asked to 

 imagine the state of a particle with several energies; 

 what is meant is that our current picture of an electron 

 as a particle with single energy has broken down, and 

 we must dive below into the sub-aether if we wish to 

 follow the course of events. The picture of a particle 

 may, however, be retained when we are not seeking high 

 accuracy; if we do not need to know the energy more 

 closely than I per cent., a series of energies ranging 

 over i per cent, can be treated as one definite energy. 



Hitherto I have only considered the waves correspond- 

 ing to one electron; now suppose that we have a prob- 

 lem involving two electrons. How shall they be repre- 

 sented? "Surely, that is simple enough! We have only 

 to take two stormy areas instead of one." I am afraid 



