THE PRESIDENTIAL ADDRESS 9 
speed. The best we can do with our blunt probes is to represent 
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 we 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 
different 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 
nothing 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 position 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 depict 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. 
B2 
