88 ANNUAL REPORT SMITHSONIAN INSTITUTION, 19 3 4 



they are very like the waves by which Maxwell described the flow of 

 radiation through space, so that matter and radiation are much more 

 like one another in the new physics than they were in the old. 



In other cases, ordinary time and space do not provide an adequate 

 canvas for the wave picture. The wave picture of two currents of 

 electricity, or even of two electrons moving independently, needs a 

 larger canvas — six dimensions of space and one of time. There can 

 be no logical justification for identifying any particular three of these 

 six dimensions with ordinary space, so that we must regard the wave 

 picture as lying entirely outside space. The whole picture, and the 

 manifold dimensions of space in which it is drawn, become pure men- 

 tal constructs — diagrams and frameworks we make for ourselves to 

 help us understand phenomena. 



In this way we have the two coexistent pictures — the particle pic- 

 ture for the materialist, and the wave picture for the determinist. 

 When the cartographer has to make two distinct maps to exhibit the 

 geography of, say, North America, he is able to explain why two maps 

 are necessary, and can also tell us the relation between the two — he 

 can show us how to transform one into the other. He will tell us, for 

 instance, that he needs two maps simply because he is restricted to flat 

 surfaces — pieces of jDaper. Give him a sphere instead and he can show 

 us North America, perfectly and completely, on a single map. 



The physicist has not yet found anything corresponding to this 

 sphere ; when, if ever, he does, the particle picture and the wave pic- 

 ture will be merged into a single new picture. At present some kink 

 in our minds, or perhaps merely some ingrained habit of thought, 

 prevents our understanding the universe as a consistent whole — just 

 as the ingrained habits of thought of a " flat-earther " prevent his 

 understanding North America as a consistent whole. Yet, although 

 physics has so far failed to explain why two pictures are necessary, it 

 is, nevertheless, able to explain the relation between the particle pic- 

 ture and the wave picture in perfectly comprehensible terms. 



The central feature of the particle picture is the atomicity which 

 is found in the structure of matter. But this atomicity is only one 

 expression of a fundamental coarse-grainedness which pervades the 

 whole of nature. It crops up again in the fact that energj' can 

 only be transferred by w^hole quanta. Because of this, the tools with 

 which we study nature are themselves coarse-grained ; we have only 

 blunt probes at our disposal, and so can never acquire perfectly 

 precise knowledge of nature. Just as, in astronomy, the grain of our 

 photographic plates prevents our ever fixing the position of a star 

 with absolute precision, so in physics we can never say that an elec- 

 tron is here, at this precise spot, and is moving at just such and such 

 a si>eed. The best we can do with our blunt probes is to represent 



