234 ANNUAL REPORT SMITHSONIAN INSTITUTION, 193 3 



occupied, but representative points occur within arbitrarily small 

 distance of them. The important results for my present purpose 

 are that the total number of members of the world system is not 

 finite, and the most distant are receding with all but the velocity 

 of light, i.e., we can find members moving with speeds arbitrarily 

 close to that of light. 



Let us now put together the four considerations: (1) the relativity 

 of time; (2) the running down of any finite portion of the universe 

 according to the second law of thermodynamics; (3) the expansion 

 of the universe, with members moving at all speeds up to (but just 

 not including) that of light; (4) the infinitude of particles in the 

 universe. 



Consideration (4), which is implied by the analysis of world 

 structure just discussed, seems to me to be necessary if we are to 

 avoid the philosophical difficulties which would crop up if the number 

 of particles in the universe were finite. For they could always be 

 mapped in a flat constructed space, and if this space were finite the 

 particles would possess a center of position, and so absolute location 

 in this space would have a meaning. We should want to ask, but be 

 unable to answer the question, why the universe came to be asso- 

 ciated with this particular standard of absolute position and absolute 

 rest. We should in fact have found a frame of reference that was 

 specific, yet we could not mention anything to distinguish this frame 

 from any number of physically equivalent ones, except that the 

 universe happened to select it for occupation. In crude language, 

 how could the universe possibly know what frame it was adopting — 

 how could it identify it in the desert of featurelessness. A universe 

 possessing an infinite number of particles does not necessarily possess 

 a mass center, and in the case of the model I am discussing definitely 

 does not possess one. Each particle is equally a center of symmetry. 

 But if the universe were supposed mapped in a finite curved space, 

 and consisted of a finite number of particles, it would still determine 

 an absolute standard of rest in this completely featureless medium, 

 and no one could say how it does it ! In the model I am considering, 

 relative position and velocity alone have a meaning. 



Now let us compare our own experiences with the experiences of 

 an observer situated on a very distant nebula moving with nearly 

 the speed of light. The clock of the moving distant observer will be, 

 to us, almost standing still, and the epoch at which it stands will 

 be little removed from the epoch at which synchronization occurred, 

 that is, the epoch of separation. Thus whilst our own clock records 

 2,000,000,000 years as the time that has elapsed since all the nebulae 

 were close together, for a nebula moving at 9/10 of the velocity 

 of light, the time now read by the moving clock (our now) will be 

 2,000,000,000 X VI - 81/100 = 870,000,000 years; for a nebula moving 



