Mainly due to the EPR trio having declared quantum mechanics as ‘not complete’ and given the acid criticisms of Schrödinger, including his famous cat paradox , many physicists felt encouraged to introduce new interpretations to confront a vaguely assembled orthodox interpretation . Indeed, there are numerous interpretations of quantum mechanics, so numerous that we have decided not to even enter into the interpretational arena, leaving that to the professionals and citing their encyclopedic works instead. In this regard, we are compelled to quote Dyson: ‘We still have passionate arguments between believers of various interpretations… The reason for these arguments is that various interpreters are trying to describe the quantum world in words… and the language is inappropriate for the purpose.’ Here, a humble approach to this subject is taken whilst opting for pragmatism.
Mainly due to the EPR trio having declared quantum mechanics as ‘not complete’ and given the acid criticisms of Schrödinger, including his famous cat paradox , many physicists felt encouraged to introduce new interpretations to confront a vaguely assembled orthodox interpretation . Indeed, there are numerous interpretations of quantum mechanics, so numerous that we have decided not to even enter into the interpretational arena, leaving that to the professionals and citing their encyclopedic works instead. In this regard, we are compelled to quote Dyson: ‘We still have passionate arguments between believers of various interpretations… The reason for these arguments is that various interpreters are trying to describe the quantum world in words… and the language is inappropriate for the purpose.’ Here, a humble approach to this subject is taken whilst opting for pragmatism.
The problems of modern physics are man made.The Copenhagen version of quantum mechanics is formulated in a vague prosaic way, inconsistencies and paradoxes are the price.New interpretations try to solve the problem, however a reformulation rather than an interpretation is needed.In this manuscript I will point out, where the Copenhagen formulation of quantum mechanics is flawed and how one can make sense out of it.Then I will show, that it is possible to give a precise formulation of quantum mechanics without losing its compelling ability in describing experiments.
The problems of modern physics are man made. The Copenhagen version of quantum mechanics is formulated in a vague prosaic way, inconsistencies and paradoxes are the price. New interpretations try to solve the problem, however a reformulation rather than an interpretation is needed. In this manuscript I will point out, where the Copenhagen formulation of quantum mechanics is flawed and how one can make sense out of it. Then I will show, that it is possible to give a precise formulation of quantum mechanics without losing its compelling ability in describing experiments.
Long ago, and almost in parallel with the “orthodox” Copenhagen/standard interpretation, other interpretations of quantum mechanics were proposed. Giving an exhaustive discussion of all points of view that have been put forward since then would probably be an impossible task. Moreover, while one can distinguish big families among the interpretations, it is also possible to combine them in many ways, with an almost infinite number of nuances. The Copenhagen/standard interpretation itself, as we have seen, is certainly not a monolithic construction, but can be declined in various forms. In this chapter, we will therefore limit ourselves to a general description of the major families of interpretations. We will begin with a brief description of some frequent attitudes observed among scientists in laboratories, who do not necessarily pay extreme attention to the foundations of quantum mechanics, even when they do experiments in quantum physics. In practice, they often use pragmatic rules, which are sufficient to interpret all their experiments, and prefer to avoid difficult questions about the very nature of the measurement process. For instance, one popular point of view is the “correlation interpretation”, which can be considered as a “minimal interpretation” – minimal but sufficient for all practical purposes; it is accepted as a valid rule by a large majority of physicists, even those who prefer to supplement it with other elements in order to reach a more precise interpretation for the whole theory. We will then proceed to discuss various families of interpretations that are less common, including additional variables, modified Schrödinger dynamics, consistent histories, Everett interpretation, etc.
Our purpose in this chapter is to present the key concepts of quantum mechanics in the language of Hilbert spaces. The reader who has not previously met the physical ideas motivating quantum mechanics, and some of the more elementary applications of Schrödinger's equation, is encouraged to read any of a number of excellent texts on the subject such as [1–4]. Otherwise, the statements given here must to a large extent be taken on trust – not an altogether easy thing to do, since the basic assertions of quantum theory are frequently counterintuitive to anyone steeped in the classical view of physics. Quantum mechanics is frequently presented in the form of several postulates, as though it were an axiomatic system such as Euclidean geometry. As often presented, these postulates may not meet the standards of mathematical rigour required for a strictly logical set of axioms, so that little is gained by such an approach. We will do things a little more informally here. For those only interested in the mathematical aspects of quantum mechanics and the role of Hilbert space see [5–8]. Many of the standard applications, such as the hydrogen atom, will be omitted here as they can be found in all standard textbooks, and we leave aside the enormous topic of measurement theory and interpretations of quantum mechanics. This is not to say that we need be totally comfortable with quantum theory as it stands. Undoubtedly, there are some philosophically disquieting features in the theory, often expressed in the form of socalled paradoxes.
In this monograph I present the basic structure of an interpretation of quantum mechanics. Chapter 1 outlines the central ideas behind the interpretation and illustrates them by means of examples: Subsequent chapters fill in the details of the interpretation. But it is important to begin by explaining what I take an interpretation of quantum mechanics to be, and why any further interpretation needs to be offered. After all, quantum mechanics (in some form) is by now both a foundation for much of contemporary physics and a veteran of more than sixty years of intermittent but sometimes intense reflection on its content and meaning. What more can be, or should be, said about the interpretation of this theory? Many physicists believe that no more needs to be said: that there is basically only one way of understanding quantum mechanics, due to Bohr, Heisenberg, Pauli, and others, and that the only remaining interpretative task is that of the physics teacher, who seeks to perfect ways of conveying this understanding to new generations of students. Sir Rudolf Peierls, one of the more lucid and distinguished of these physicists, even objects to the use of the familiar term ‘Copenhagen interpretation’ to refer to the way of understanding quantum mechanics due to Bohr, Heisenberg, Pauli, and others. Because this sounds as if there were several interpretations of quantum mechanics. There is only one. There is only one way in which you can understand quantum mechanics.[…]
Since the purpose of the paper1 in question was to examine the responses to Schrödinger’s cat paradox that are engendered by three particular approaches to quantum mechanics, it is appropriate to comment only on the extent to which the given responses do indeed represent the views of proponents of the various interpretations. For the cases of quantum logic and the many worlds interpretation, I believe that the author has indeed captured the essence of a response that a supporter of that interpretation would give. But I should hope that a supporter of the Copenhagen interpretation would not give the response attributed to him, for it completely misses the point.