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arXiv:quant-ph/0305183

Reappraisal of the causal interpretation of quantum mechanics and of the quantum potential concept

Robert H. Parmenter, Andrew L. DiRienzo

Published May 30, 2003• 2 citations
arXivHTMLPDF

Abstract

The causal interpretation of quantum mechanics, as originally stated by deBroglie and Bohm, had several attractive features. Among these is the possibility that it could address some of the most fundamental questions on quantum phenomena. However, subsequent theoretical conjectures, which have now been included in the orthodox view of the deBroglie Bohm theory, are unphysical and have done much to undermine the original theory's appeal. We, therefore, return to the original theory as our starting point and address one of its perplexing areas: the quantum potential. By avoiding the unphysical conjectures we are led to an understanding of the quantum potential which is distinctly different from that of the orthodox deBroglie Bohm view.

DOI
10.48550/arxiv.quant-ph/0305183

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The causal interpretation of quantum mechanics, as originally stated by deBroglie and Bohm, had several attractive features. Among these is the possibility that it could address some of the most fundamental questions on quantum phenomena. However, subsequent theoretical conjectures, which have now been included in the orthodox view of the deBroglie Bohm theory, are unphysical and have done much to undermine the original theory's appeal. We, therefore, return to the original theory as our starting point and address one of its perplexing areas: the quantum potential. By avoiding the unphysical conjectures we are led to an understanding of the quantum potential which is distinctly different from that of the orthodox deBroglie Bohm view.
This paper introduces and analyses David Bohm's causal interpretation of quantum potential and his viewpoint of nonlocality. As the key of Bohm's causal interpretation of quantum theory, the interpretation of quantum potential has been paid serious attention to by Bohm since 1980's. Bohm reviews quantum potential from the perspective of information and puts forward some new views. Especially, Bohm probes into nonlocality on the basis of the view of quantum potential and active information. This is of great significance in both physics and philosophy.
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 this article, we investigate Bohm's view of quantum theory, especially Bohm's quantum potential, from a new perspective. We develop a quasi-Newtonian approach to Bohmian mechanics. We show that to arrive at Bohmian formulation of quantum mechanics, there is no necessity to start from the Schrödinger equation. We also obtain an equation that restricts the possible forms of quantum potential and determines the functional form of it without appealing to the wave function and the Schrödinger equation. Finally, we discuss about the significance of quantum potential in the conceptual structure of quantum theory.
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.
Schrödinger's original interpretation of the Schrödinger equation had many attractive features lost in later interpretations of the quantum theory. But that interpretation runs into a number of formidable well-known and not so well-known objections. I argue, following the methodological precepts of Paul Feyerabend, that we need not regard any of these objections as fatal, provided we are prepared to opt for a number of bold and rather radical mathematical and theoretical conjectures. These would amount jointly to the conjecture that a fully time-symmetric consistently classically interpreted non-second-quantized analogue of existing quantum field theory would ( pace Jaynes, Tomonaga, Bell, and others) ultimately prove predictively equivalent to orthodox second-quantized theory. Introduction Schrödinger initially proposed his equation as a classical theory of matter waves directly analogous to Maxwell's theory of electromagnetic waves. |ψ| 2 represented a classical charge density functioning in the ordinary classical way as a source of electromagnetic fields, and acted on by these fields via the potential term in the matter–wave equation. This is a theory of coupled classical fields with no probabilities entering into its interpretation, and from a modern point of view it can be thought of in terms of the coupled Dirac and Maxwell fields, without second-quantization and interpreted in a purely classical manner.