PHILOSOPHY OF PHYSICS — MILNE 237 



of the entropy-increase breaks down. Now, the expansion of the 

 universe, with bodies separating at different speeds, is a phenomenon 

 which goes on of itself and aifects the relations of all the separate 

 [)arts continuously; it may be described as a nonuniform radial 

 dilatation, resulting in increasingly perfect velocity segregation of 

 the separate parts. But the universe is not an enclosed system. Un- 

 like the systems considered in thermodynamics, it has no confining 

 boundary, though as we have seen it has an apparent though unat- 

 tained boundar3\ Whether it is surrounded by '' empty space " or 

 not is a. meaningless question, since it can be shown that there is no 

 possible causal connection between the objects (if any) outside the 

 sphere of observation and those inside it. 



The expanding universe may be described as creating space as it 

 expands, or alternatively as expanding into empty space. This 

 external unobservable space need not be actually empty; its contents 

 can be readily described mathematically, but they automatically make 

 room for the observable part to expand into, so that the space behaves 

 in effect as empty. The external occupants are genuine wills-o'-the- 

 wisp. In either case the system is totally different from an enclosed 

 system, and it acts as its own Maxwell's sorting demon. Maxwell 

 pictured a demon capable of opening and closing a door in a parti- 

 tion in a gas-filled vessel in such a way as to segregate fast-moving 

 molecules from slow ones. The natural expansion of a cloud of 

 objects such as nebulae into " empty " space is precisely such a type 

 of segregation. For it effects and then accentuates a complete sort- 

 ing-out of velocities, more and more completely concentrating the 

 faster objects at the greatest distances. Just as Maxwell's sorting 

 demon could cause the gas on one side of a partition to become hot 

 and the other cold without expanding mechanical work, and so 

 could avoid the consequences of the second law of thermodynamics, 

 so the universe as a whole avoids the heat death. It does this in 

 virtue of the expansion and the infinity of particle number, taking 

 into account the relativity of time. 



To summarize, the passage of time is a definite part of the experi- 

 ence of each individual, and from it may be constructed both time 

 measures and space measures without the introduction of the concept 

 of the rigid body as a length-measuring tool. Different individuals 

 assign different epochs and different distances to the same event, and 

 the relation between the epochs they assign is perfectly definite for 

 any two observers (in uniform relative motion) who stand in the 

 same relation to the rest of the universe. This relation, predicted 

 long ago by the special theory of relativity, is derived here from a 

 different observational basis. It is applicable as it stands to the 

 different bodies forming constituents of the expanding universe, 

 which presumably contains, and on a reasonable basis for extrapola- 



