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Journal of Science Education

양자역학의 인과적 해석

조상규, 김명석, 이창열, 최상돈, Jung Ho Kim

Published Jan 1, 1997• 0 citations
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Abstract

We review the Bohm`s interpretation of quantum mechanics. Unlike the Copenhagen interpretation, the Bohm`s interpretation suggests the existence of particle`s trajactories, and consequently explains causality in a natural way. We give several examples, free particle, spinless particle in electromagnetic field, and spin 1/2 particle in electromagnetic field.

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We review the Bohms interpretation of quantum mechanics. Unlike the Copenhagen interpretation, the Bohms interpretation suggests the existence of particle`s trajactories, and consequently explains causality in a natural way. We give several examples, free particle, spinless particle in electromagnetic field, and spin 1/2 particle in electromagnetic field.
In relation to this debate perhaps the greatest significance and contribution of Bohm's causal interpretation of quantum mechanics 3 is that it not only exposes the arbitrary philosophical assumptions underlying the claims of the Copenhagen interpretation but also brings into relief the essentially new content of quantum mechanics, which is reflected in different ways in Bohr's interpretation. Indeed the claim that the quantum formalism itself requires us not only to abandon the quest for explanation of quantum phenomena but also the concepts of causality, continuity and the objective reality of individual micro-objects, is shown to be false. However the existence of the single counter-interpretation proposed by Bohm constitutes sufficient grounds for rejecting the absolute and final necessity of complementary description and indeterminacy, along with the inherent unanalysable and closed nature of quantum phenomena.
A brief account of the world view of classical physics is given first. We then recapitulate as to why the Copenhagen interpretation of the quantum mechanics had to renounce most of the attractive features of the clasical world view such as a causal description, locality, scientific realism and introduce a fundamental distinction between system and apparatus. The crucial role is played in this by the Bohr's insistence on the wavefunction providing the most complete description possible for an even individual system. The alternative of introducing extra dynamical variables, called hidden variables, in addition to the wavefunction of the system so as to be able to retain at least some of the desirable features of classical physics, is then explored. The first such successful attempt was that of Bohm in 1952 who showed that a realistic interpretation of the quantum mechanics can be given which maintains a causal description as well as does not treat systems and measuring appeartus differently. We begin with the construction of the Bohm's theory. He introduces particle positions as the hidden variables. The particle positions play a special role in Bohm theory. The particle trajectories are guided by the wavefunction. The Bohm theory is deterministic. The probability enters through a special assumption, ``quantum equilibrium'' hypothesis, for the initial conditions on the ensemble of particle trajectories. The ``wave or particle'' dilemma is resolved by a ``wave and particle'' resolution. The measurements in Bohm theory can be described without mysticism. Bohm's theory is however nonlocal.
In previous chapters we presented and discussed the standard, generally accepted Copenhagen interpretation of quantum mechanics according to which there exists in nature at the most fundamental level an irreducible and ineliminable indeterminism. Although we saw that what historically constituted the Copenhagen interpretation of quantum mechanics is difficult to specify with precision, three central commitments do characterize it. (1) In general, no particle trajectories can exist in a space–time background. (2) No deterministic description of fundamental physical phenomena is possible. (3) There exists in the laws of the fundamental physical phenomena of nature an essential and ineliminable indeterminism or probability (unlike the probability of classical physics, that there reflects our ignorance of the finer details of complex physical phenomena). A flavor of these features of the Copenhagen interpretation of quantum mechanics can be gotten from the quotations at the beginning of Part VIII ( Some philosophical lessons from quantum mechanics ). On this view, it is in principle impossible to predict, say, the exact future behavior of an electron (that is, to give its position and velocity as functions of the time). According to the Copenhagen school, there can be no causal description of microphenomena in terms of a continuous space–time background (as there is in classical physics). It is generally believed that a causal interpretation of quantum mechanics is impossible, although no proof of this exists.
In this paper we critically review the various attempts that have been made to understand quantum field theory. We focus on Teller's (1990) harmonic oscillator interpretation, and Bohm et al.'s (1987) causal interpretation. The former unabashedly aims to be a purely heuristic account, but we show that it is only interestingly applicable to the free bosonic field. Along the way we suggest alternative models. Bohm's interpretation provides an ontology for the theory—a classical field, with a quantum equation of motion. This too has problems; it is not Lorentz invariant.
Following de Broglie, Bohm, and others, it is assumed that quantum mechanics may be interpreted causally and that the $\ensuremath{\psi}$ function plays the role of a generating function for particle trajectories. By arguing that the $\ensuremath{\psi}$ function should not be interpreted as a probability amplitude, a new method for generating particle trajectories is postulated. The four-momentum of a scalar particle is assumed to be given as the gradient of an unspecified function $F(\ensuremath{\psi})$, where $\ensuremath{\psi}$ is a pure real solution of the Klein-Gordon equation. Since the location of a particle is determined solely by its trajectory, the probability distribution differs from $\ensuremath{\psi}{\ensuremath{\psi}}^{*}$; and therefore, ordinary experimental results differing from the traditional theory may, in principle, be predicted. Particle motion and trajectories are discussed for three examples: a free particle, a particle in a box, and the double slit.
The non-relativistic quantum theory has been interpreted causally by de Broglie, David Bohm, and others, where a quantum entity is viewed as a particle with a definite position and momentum. This interpretation contrasts with the Copenhagen orthodox interpretation, which conveys uncertainty through the commutator relationship between position and momentum operators. This is further exacerbated by the de Broglie-Bohm interpretation, which uses no operators corresponding to these observables. We reconcile these opposing viewpoints by introducing mathematical nonlinear transforms in Bohmian mechanics for the momentum observable. While these nonlinear operator-like transforms cannot be easily represented as matrices in the Hilbert space, we show that they can be utilized in the de Broglie-Bohm interpretations of quantum theory.