MODERN PHYSICS — JEANS 89 



the position of the electron by a smear, and its motion by a moving 

 smear which will get more and more blurred as time progresses. 

 Unless Ave check the growth of our smear by taking new observations, 

 it will end by spreading through the whole of space. 



Now the waves of an electron or other piece of matter are simply 

 a picture of just such a smear. Where the waves are intense, the 

 smear is black, and conversely. The nature of the smear — whether 

 it consists of printer's ink, or, as was at one time thought, of elec- 

 tricity — is of no importance; this is mere pictorial detail. All that 

 is essential is the relative blackness of the smear at different places — 

 a ratio of numbers which measures the relative chance of electrons 

 being at different points of space. 



The relation between the wave picture and the particle picture 

 may be summed up thus: The more stormy the waves at any point 

 in the wave picture the more likely we are to find a particle at that 

 point in the particle picture. Yet if the particles really existed as 

 points and the waves depicted the chances of their existing at dif- 

 ferent points of space — as Maxwell's law does for the molecules of 

 a gas — then the gas would emit a continuous spectrum instead of 

 the line spectrum that is actually observed. Thus we had better put 

 our statement in the form that the electron is not a point particle, 

 but that if we insist on picturing it as such, then the waves indicate 

 the relative proprieties of picturing it as existing at the different 

 points of space. But propriety relative to what? 



The answer is — relative to our own knowledge. If we know noth- 

 ing about an electron except that it exists, all places are equally 

 likely for it, so that its waves are uniformly spread through the 

 whole of space. By experiment after experiment we can restrict the 

 extent of its waves, but we can never reduce them to a point or, 

 indeed, below a certain minimum; the coarse-grainedness of our 

 probes prevents that. There is always a finite region of waves left. 

 And the waves which are left depict our knowledge precisely and 

 exactly ; we may say that they are waves of knowledge — or, perhaps 

 even better still, waves of imperfections of knowledge — of the posi- 

 tion of the electron. 



And now we come to the central and most surprising fact of the 

 whole situation. I agree that it is still too early, and the situation 

 is still too obscure, for us fully to assess its importance, but, as I see 

 it, it seems likely to lead to radical changes in our views not only 

 of the universe but even more of ourselves. Let us remember that 

 we are dealing with a system of waves which depicts in a graphic 

 form our knowledge of the constituents of the universe. The central 

 fact is this : The wave parable does not tell us that these waves depict 

 our knowledge of nature, but that they are nature itself. 



