238 ANNUAL REPORT SMITHSONIAN INSTITUTION, 19 30 



This is a representation of 2 electrons as a single point in a con- 

 figuration space of 6 dimensions. Now it turns out from Schroe- 

 dinger's theory that the motion of electrons, or rather of the waves 

 corresponding to them, can be completely described in the case of 

 the helium atom by. a quantity which has a particular value at each 

 point in this 6-dimensional space or configuration space. The 

 helium atom, however, can be described in terms of the motion of 

 2 electrons in 3-dimensional space if we are content merely to know 

 the probabilities that the electrons may be found at any point in 

 this space. 



These matters undoubtedly seem very abstract to those of you 

 who have not previously become familiar with them. I give them 

 here mainly in order to illustrate how far the modern concepts of 

 physics differ from those of 20 years ago. 



If we must thus abandon our ordinary ideas of cause and effect, 

 it may be asked why have the physicist and chemist so long believed 

 that the whole teaching of science gave proof that every phenomenon 

 resulted inevitably from the causes that led to it. I think the 

 answer is that in the past scientists chose as the subjects for their 

 investigations almost wholly those phenomena in which such definite 

 relations as cause and effect could be found. These phenomena are 

 those in which such enormous numbers of individual quantum phe- 

 nomena are grouped together that the result is determined only 

 by their averages. For example, when we study the variation of 

 the pressure with the volume of a gas, the forces that we measure 

 result from the impacts of great numbers of molecules, the average 

 force remaining steady and definite. If, however, we only had one 

 molecule in a small volume, the pressure exerted on the walls would 

 be zero except for those instants at which the molecules struck the 

 wall. It would then be impossible to predict in advance what the 

 pressure would be at a particular time. 



I think in trying to estimate the reliability of any of our scientific 

 loiowledge we should keep in mind that the whole complexion of a 

 science may be made to change by the psychology of the investi- 

 gators which governs the choice of the subjects that are investigated. 



Our best knowledge of time and its relation to other concepts is that 

 which we have obtained through Einstein. Yet in the whole rela- 

 tivity theory there is nothing to distinguish between positive and 

 negative time, that is, between future and joast, any more than there 

 is between different directions in space, such as right and left. There 

 thus appears to be something curiously incomplete in our knowledge 

 of time, for every one of us knows the vast practical difference be- 

 tween past and future. Eddington, in his recent book, the Nature of 

 the Physical World, discusses the " arrow of time " at some length. 



