Nonseparability and Quantum Logic

This talk is about quantum logic, and before we engage in the subject proper let me say how much I appreciate the invitation to deliver it that was extended to me by the Japanese Society for the Philosophy of Science. In particular because I feel that such a meeting is really the place that is most adequate for the discussion of these matters. Let us introduce the subject by mentioning a few general points. First of all, logics deals with propositions. Hence we shall be concerned with propositions. But in fact our interest will be exclusively focused on what is-or what should be the simplest type of propositions: the propositions by means of which a physicist expresses what he knows about a physical system. A priori, our subject should then be very simple. Indeed the elementary books about logic tell us that the rules concerning these propositions can be formalized. That, for example, the propositions can be combined by means of two rules, corresponding to and and to or, and that the resulting structure is just that of a Boolean Algebra. We would expect this to hold for any system. However, as you know, a major difficulty already creeps in at this point when we want to deal with atomic systems. This is because a very simple word such as "and" may well have no obvious meaning in that case. And when we try to force a meaning to it was sometimes encounter quite unpleasant surprises, exemplified by the Heisenberg relations. Among the founders of quantum physics the reactions to such a fact were quite varied as is well known. Some of them sort of hoped that the difficulty just came from our using the wrong concepts. For example, it is quite obvious that if we try to describe as a particle something which is really a wave, we are heading for trouble and we are bound to formulate some meaningless propositions. However, this remark did not lead to a satisfactory solution in the end. Other physicists notably the Copenhagen group took a very different standpoint. Substantially, what they said boiled to this: since we cannot "see" the elementary particles, let us refrain from formulating directly propositions bearing on them. Ultimately, there fore, all their propositions bear on the instruments; or should be interpreted in terms of such propositions. This is -it turned out a very good recipe. Of course, propositions bearing on instruments are propositions of classical, macroscopic physcis. As such, they fall