80 THE RUNNING-DOWN OF THE UNIVERSE 



The conclusion is that whereas other statistical 

 characters besides entropy might perhaps be used to 

 discriminate time's arrow, they can only succeed when 

 it succeeds and they fail when it fails. Therefore they 

 cannot be regarded as independent tests. So far as 

 physics is concerned time's arrow is a property of 

 entropy alone. 



Are Space and Time Infinite? I suppose that everyone 

 has at some time plagued his imagination with the 

 question, Is there an end to space? If space comes to 

 an end, what is beyond the end? On the other hand the 

 idea that there is no end, but space beyond space for 

 ever, is inconceivable. And so the imagination is tossed 

 to and fro in a dilemma. Prior to the relativity theory 

 the orthodox view was that space is infinite. No one 

 can conceive infinite space; w r e had to be content to 

 admit in the physical world an inconceivable concep- 

 tion — disquieting but not necessarily illogical. Einstein's 

 theory now offers a way out of the dilemma. Is space 

 infinite, or does it come to an end? Neither. Space 

 is finite but it has no end; "finite but unbounded" 

 is the usual phrase. 



Infinite space cannot be conceived by anybody; 

 finite but unbounded space is difficult to conceive but 

 not impossible. I shall not expect you to conceive it; 

 but you can try. Think first of a circle; or, rather, not 



Detailed Balancing." This principle asserts that to every type of process 

 (however minutely particularised) there is a converse process, and in 

 thermodynamical equilibrium direct and converse processes occur with 

 equal frequency. Thus every statistical enumeration of the processes is 

 unaltered by reversing the time-direction, i.e. interchanging direct and 

 converse processes. Hence there can be no statistical criterion for a 

 direction of time when there is thermodynamical equilibrium, i.e. when 

 entropy is steady and ceases to indicate time's arrow. 



