1 98 THE QUANTUM THEORY 



of our theories arises from this misuse. For such states 

 space and time do not exist — at least I can see no reason 

 to believe that they do. But it must be supposed that 

 when high numbered states are considered there will 

 be found in the new scheme approximate counterparts 

 of the space and time of current conception — some- 

 thing ready to merge into space and time when the 

 state numbers are infinite. And simultaneously the inter- 

 actions described by transitions of states will merge 

 into classical forces exerted across space and time. So 

 that in the limit the classical description becomes an 

 available alternative. Now in practical experience we 

 have generally had to deal with systems whose ties are 

 comparatively loose and correspond to very high quan- 

 tum numbers; consequently our first survey of the 

 world has stumbled across the classical laws and our 

 present conceptions of the world consist of those enti- 

 ties which only take definite shape for high quantum 

 numbers. But in the interior of the atom and molecule, 

 in the phenomena of radiation, and probably also in the 

 constitution of very dense stars such as the Companion 

 of Sirius, the state numbers are not high enough to 

 admit this treatment. These phenomena are now forcing 

 us back to the more fundamental conceptions out of 

 which the classical conceptions (sufficient for the other 

 types of phenomena) ought to emerge as one extreme 

 limit. 



For an example I will borrow a quantum conception 

 from the next chapter. It may not be destined to sur- 

 vive in the present rapid evolution of ideas, but at any 

 rate it will illustrate my point. In Bohr's semi-classical 

 model of the hydrogen atom there is an electron de- 

 scribing a circular or elliptic orbit. This is only a model; 

 the real atom contains nothing of the sort. The real 



