Introduction

When I was a student I had much difficulty with quantum mechanics. It was comforting to find that even Einstein had had such difficulties for a long time. Indeed they had led him to the heretical conclusion that something was missing in the theory: ‘I am, in fact, rather firmly convinced that the essentially statistical character of contemporary quantum theory is solely to be ascribed to the fact that this (theory) operates with an incomplete description of physical systems.’

More explicitly, in ‘a complete physical description, the statistical quantum theory would … take an approximately analogous position to the statistical mechanics within the framework of classical mechanics …’.

Einstein did not seem to know that this possibility, of peaceful coexistence between quantum statistical predictions and a more complete theoretical description, had been disposed of with great rigour by J. von Neumann. I myself did not know von Neumann's demonstration at first hand, for at that time it was available only in German, which I could not read. However I knew of it from the beautiful book by Born, Natural Philosophy of Cause and Chance, which was in fact one of the highlights of my physics education. Discussing how physics might develop Born wrote: ‘I expect … that we shall have to sacrifice some current ideas and to use still more abstract methods. However these are only opinions.