226 ANNUAL REPORT SMITHSONIAN INSTITUTION, 19 3 3 



how to behave as if a definite time exists, Jeans is even led to con- 

 jecture that "our minds may be in contact with reality by other 

 than purely physical elements ", just because of their consciousness 

 of " a radical distinction between space and time which does not 

 appear to extend to physical phenomena." Yet he emphasizes an 

 apparently fundamental distinction between time and space when 

 he describes that physical phenomenon which is the running-down 

 of the universe. 



I want now to suggest that the impasse arises partly from our 

 forgetting the purely conceptual character of space-time and partly 

 from an unjustifiable application of the second law of thermody- 

 namics to the whole universe. Our experience of time is immediate, 

 not a concept; the experiments on which thermodynamics is based 

 are not concepts. But on the one hand " the whole universe " is a 

 concept, as De Sitter has pointed out, save in the case of the unin- 

 teresting possibility that the universe contains a finite number of 

 particles. And on the other hand, space-time is a concept of which 

 we have no experience, a mathematical invention, useful solely for 

 correlating experiences. We have no right to foist this invention on 

 nature and then complain that nature contains two contradictory 

 phenomena ; for the so-called " possession " of a space-time frame- 

 work in which time and space merge together is not a phenomenon 

 in nature. Our problem is to correlate the experience of one observer 

 (in which, in his time, the universe increases its entropy) with the 

 experience of another observer with a different time. Jeans is, I 

 think, right in suggesting that very large scale astronomical phe- 

 nomena afford a means of reconciling these experiences, but not, it 

 seems to me, by pointing to a unique or absolute space or time, which 

 involves grave difficulties in relation to the facts on which relativity 

 is based. We will attempt to remove our difficulties by building up 

 definitions of space and time, or rather building up measures of 

 space and time, from a basis of things experienced. We will pass 

 from concepts of space and time to observables, according to the 

 Einstein-Heisenberg policy. 



We begin with the observer. Each observer possesses, for macro- 

 scopic phenomena, a definite temporal experience of events at him- 

 self. I as an observer and chronicler can say of two events which 

 happen to me which precedes the other. For very small separations 

 of events it may, indeed, occur that I am unable to decide which is 

 earlier, and the indubitability of the time sequence may fail. But 

 this is not an exception in principle. I may suppose myself to have 

 constructed a clock, running no matter how irregularly, and to have 

 graduated it numerically in some perfectly arbitrary way. I can 

 make the graduations as small as is recognizable. Then when an 



