The Problem: An Axiomatic Basis for Quantum Mechanics

Abstract

The historical path of discovery for a new physical theory is, for the most part, a complicated one. At first new concepts are tentatively introduced. By a lengthy process, involving trial, error, insight, and revision, these concepts are modified and become more clearly defined and familiar. As an understanding of the postulated structure of the theory develops, it is possible by careful application of the new concepts to learn how to avoid error and to develop an interpretation of the new theory. Such has been the case for quantum mechanics. In this book we shall not present a heuristic path to quantum mechanics as a means of developing a theory of electrons, atoms, ... (in general: microsystems). Instead, we shall assume that the reader has already had extensive contact with quantum mechanics, and has studied one or more of the elementary texts. If this is not the case, we recommend that the reader either study such a text before reading this book, or use one of the elementary texts in conjunction with this book. In this way, the reader will discover the vagueness inherent in the usual fundamental concepts which are used to formulate quantum mechanics. For the reader who seeks an elementary text which considers some of the problems to be discussed in this book, we recommend Volume 3 of [2].