In this paper, we present a further discussion of the role of electromagnetic potentials in the quantum theory, aimed at clarifying some of the points made in earlier papers, and indicating some extensions of these earlier ideas. In addition, we go into the problem of subsidiary conditions and questions concerning the full observability of the potentials. In the course of our discussion, we answer certain recent objections of Belinfante and De Witt.
In this paper, we present a further discussion of the role of electromagnetic potentials in the quantum theory, aimed at clarifying some of the points made in earlier papers, and indicating some extensions of these earlier ideas. In addition, we go into the problem of subsidiary conditions and questions concerning the full observability of the potentials. In the course of our discussion, we answer certain recent objections of Belinfante and De Witt.
In this article, we discuss in further detail the significance of potentials in the quantum theory, and in so doing, we answer a number of arguments that have been raised against the conclusions of our first paper on the same subject. We then proceed to extend our treatment to include the sources of potentials quantum-mechanically, and we show that when this is done, the same results are obtained as those of our first paper, in which the potential was taken to be a specified function of space and time. In this way, we not only answer certain additional criticisms that have been made of the original treatment, but we also bring out more clearly the importance of the potential in the expression of the local character of the interaction of charged particles and the electromagnetic field.
Abstract The purpose of this book is to present an interpretation of quantum mechanics. But what are we talking about when we speak of “quantum mechanics?” Are we talking about a single theory or about many related theories? And what do we mean by “interpretation” here? In this chapter, I will address these questions in an introductory way. Of course, I do not intend to take part in the extensive discussions about what a scientific theory is, what is meant by interpreting a theory, in what situation we encounter equivalent theories, and many other questions related to or derived from these. My aim here is to present some preliminary ideas in a way that I hope will be sufficient to avoid misunderstandings in the following chapters. But, above all, I will state my position as to why, after so many years and so much literature on the subject, the interpretation of quantum mechanics deserves further discussion.
Introduction Bohm's 1952 papers on quantum mechanics were for me a revelation. The elimination of indeterminism was very striking. But more important, it seemed to me, was the elimination of any need for a vague division of the world into ‘system’ on the one hand, and ‘apparatus’ or ‘observer’ on the other. I have always felt since that people who have not grasped the ideas of those papers … and unfortunately they remain the majority … are handicapped in any discussion of the meaning of quantum mechanics. When the cogency of Bohm's reasoning is admitted, a final protest is often this: it is all nonrelativistic. This is to ignore that Bohm himself, in an appendix to one of the 1952 papers, already applied his scheme to the electromagnetic field. And application to scalar fields is straightforward. However until recently, to my knowledge, no extension covering Fermi fields had been made. Such an extension will be sketched here. The need for Fermi fields might be questioned. Fermions might be composite structures of some kind. But also they might not be, or not all. The present exercise will not only include Fermi fields, but even give them a central role. The dependence on the ideas of de Broglie and Bohm, and also on my own simplified extension to cover spin, will be manifest to those familiar with these things. However no such familiarity will be assumed.
In this paper, we discuss some interesting properties of the electromagnetic potentials in the quantum domain. We shall show that, contrary to the conclusions of classical mechanics, there exist effects of potentials on charged particles, even in the region where all the fields (and therefore the forces on the particles) vanish. We shall then discuss possible experiments to test these conclusions; and, finally, we shall suggest further possible developments in the interpretation of the potentials.
More them any other topic in the foundations of physics, the problem of the arrow (or arrows!) of time seems to be characterized by a unique ‘slipperiness’: it is not only difficult to find answers to the questions once posed, but difficult to find meaningful questions to ask in the first place. Perhaps this is because an asymmetry with respect to the sense of time is built into us at an even deeper level than other ‘synthetic a priori’ conceptions about the world such as the continued existence of unknown objects. However that may be, in this situation, rather than trying to pose general questions which may turn out in the end to be ill-defined, there may be something to be said for trying to formulate much less speculative, indeed perhaps in retrospect trivial questions to which at least we have a hope of finding a definite answer. This is what I shall do in this essay: to be specific, I shall ask whether a test which is currently being designed concerning the validity of a certain ‘common-sense’ view of the macroscopic world (‘macrorealism’) would be affected if we were to relax our common-sense assumptions about the direction of causality in time. Let me start with a very brief review of established ideas concerning the formal (a)symmetry of the quantum theory with respect to the direction of time. The classic works on this subject are the paper of Aharonov et al. (‘ABL’) and the book by Belinfante. In these discussions the notion of ‘measurement’ is taken as primitive and undefined.
SUMMARY. — In this article, I examine Einstein's objections to quantum mechanics, with the formalism's interpretation in terms of complementarity as the historical setting. From 1924 to 1927, the period of development of a formalised quantum theory, Einstein raised certain questions that kept him from joining the throng of ardent supporters. Against the theory and its interpretation of 1927, he at first advanced arguments with the idea of eventually finding a flaw in quantum mechanics, and casting doubts upon its pretensions of completeness. Finally acknowledging, in 1931, the theory's coherence and accuracy at describing phenomena, he then tried to put forth objections to the theory's interpretation, which aimed at demonstrating the theory's incompleteness. These arguments culminated in the « Einstein-Podolsky-Rosen » article of 1935, and Einstein repeated them continually until his death. The analysis here calls, of course, for assessments of both the import of Einstein's arguments in relation to physics today, as well as to Einstein's own conceptions where theoretical physics is concerned, but these go beyond the aims of the present article.