Philosophical foundations of interpretations of quantum mechanics

📝 Abstract

It is demonstrated that the reason for the diversity of interpretations of quantum mechanics is that they are not connected by continuity relations with classical physics, and also the reason is the impossibility of operationalist definition of the vector of state. The problem lies in the incompatibility of the philosophical foundations of interpretations, which results in the difficulty of building a unified picture of the world. To solve the problem, we identify general philosophical foundation of interpretations of quantum mechanics and built their classification. We also show that in more general theories, the part of which is quantum mechanics, it is possible to integrate (reconcile) the philosophical foundations of interpretations.

💡 Analysis

It is demonstrated that the reason for the diversity of interpretations of quantum mechanics is that they are not connected by continuity relations with classical physics, and also the reason is the impossibility of operationalist definition of the vector of state. The problem lies in the incompatibility of the philosophical foundations of interpretations, which results in the difficulty of building a unified picture of the world. To solve the problem, we identify general philosophical foundation of interpretations of quantum mechanics and built their classification. We also show that in more general theories, the part of which is quantum mechanics, it is possible to integrate (reconcile) the philosophical foundations of interpretations.

📄 Content

Evgeny Bezlepkin

PHILOSOPHICAL FOUNDATIONS OF INTERPRETATIONS
OF QUANTUM MECHANICS

e-mail: evgeny-bezlepkin@mail.ru

Abstract It is demonstrated that the reason for the diversity of interpretations of quantum mechanics is that they are not connected by continuity relations with classical physics, and also the reason is the impossibility of operationalist definition of the “vector of state”. The problem lies in the incompatibility of the philosophical foundations of interpretations, which results in the difficulty of building a unified picture of the world. To solve the problem, we identify general philosophical foundation of interpretations of quantum mechanics and built their classification. We also show that in more general theories, the part of which is quantum mechanics, it is possible to integrate (reconcile) the philosophical foundations of interpretations.

Keywords Interpretation, formalism, quantum mechanics, ontology, continuity, operationalism.

Introduction

There are many interpretations of quantum mechanics, the foundations of which seem to be inconsistent (for example, deterministic and indeterministic interpretations). In our opinion, it is this incompatibility that is the philosophical problem of the diversity of interpretations. In connection with this, the objective of this article is, first, to identify the cause of plurality of interpretations; second, to distinguish the philosophical foundations for the classification of interpretations and create such a classification; and, third, since the incompatibility of the foundations of interpretations presents a problem for building a unified picture of the world, it is necessary to demonstrate a possibility of minimizing the number of interpretations, if we require their agreement with generalized theories such as, for example, the string theory. A unique ontology (interpretation) of quantum mechanics (QM) cannot be built solely on its own basis. To do this, one should use a holistic approach; i.e., one should reconcile QM with the theories, which are connected with other areas of applicability. Roughly speaking, plurality of interpretations is due to the fact that quantum theory does not “resist” free interpretation of its basic concepts. It is possible that if quantum mechanics existed as a part of another, more general theory, the latter would impose tighter restrictions on the interpretation of the basic concepts of QM. Thus, it seems that it is possible to describe the world in an integral and consistent fashion through a unified theory, to which there will corresponds a unified ontology, whereas the ontology of quantum mechanics will become one of its parts.

The main ideas of quantum mechanics

In order to indicate the source of plurality of interpretations of quantum mechanics, we should clearly identify its basic premises.
For these purposes, we use the theory (formalism) of P. Dirac, because it is the most general one. The initial position of the theory is that to the variety of physical concepts there correspond mathematical concepts (this correspondence is called “parameterization” or “coordinatization”). Thus, the physical objects, which are to be mathematically (quantitatively) studied, should be “parameterized” or “measured”. B. G. Kuznetsov points out that this premise, together with the idea of invariance, is the basis of Dirac’s theory. He writes that in QM there appears “independence of the physical processes from the methods of observation, expressed in the invariance of certain physical quantities with respect to transition from one coordinate parameterization to another” [Kuznetsov 1957, p. 211]. The first thesis of Dirac is the principle of superposition of states, which says that any individual state of a quantum-mechanical system can be expressed in terms of a linear superposition (overlay) of several other states [See: Dirac 1979, p. 24]. The second point is that to the physical concept of “the state of a dynamic system” there corresponds the mathematical concept of “vector” (in an infinite-dimensional Hilbert space) [Ibid. pp. 29-34]. A fundamental quantity in this correspondence is not the “length” of vector, but its “direction” in the vector space, because in this space the Archimedes’ axiom concerning the comparison of lengths does no work; that is, in the space of vectors of quantum mechanics it is impossible to determine which vector is “larger” and which is “smaller”. Dirac gives the vector of state the name “ket-vector”, and, having in mind that to any given collection of vectors one can associate a set of dual vectors, he introduces a concept of “bra-vector”. These vectors describe the state as well as the superposition connections of a quantum-mechanical system. The third thesis. While in classical physics the state of a physical system is described by dynamical variables (coordinate, momentum), in quantum mechanics to the dyna

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