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arXiv:2103.00576

A causal and continuous interpretation of the quantum theory: About an original manuscript by David Bohm sent to Louis de Broglie in 1951

Aurélien Drezet, Benjamin Stock

Published Feb 28, 2021• 3 citations
arXivHTMLPDF

Abstract

The aim of this article is reproduce and analyze an original article of David Bohm sent to Louis de Broglie in 1951. This article is the older document of David Bohm about his well known hidden variable theory based on the pilot wave interpretation of Louis de Broglie. We analyse the chronology and the history of this fascinating document.

DOI
10.48550/arxiv.2103.00576

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The aim of this article is reproduce and analyze an original article of David Bohm sent to Louis de Broglie in 1951. This article is the older document of David Bohm about his well known hidden variable theory based on the pilot wave interpretation of Louis de Broglie. We analyse the chronology and the history of this fascinating document.
Abstract David Bohm published his “Suggested Interpretation of Quantum Theory in Terms of Hidden Variables” some twenty five years after Louis de Broglie first presented his similar Pilot Wave theory of quantum mechanics. In the following 30 years what became known as the de Broglie–Bohm approach to quantum theory was to a large extent ignored within the physics community. Even David Bohm himself became somewhat disillusioned with the lack of impact of his interpretation of quantum theory and he directed his interest elsewhere. But some 27 years after Bohm had published his interpretation of quantum theory, interest was rekindled in part by new, detailed calculations that demonstrated clearly and graphically, exactly how his interpretation explained quantum phenomena in terms of well defined individual particle trajectories. These computations encompassed two-slit interference, quantum tunnelling, neutron interferometry, Wheeler’s delayed choice experiment, orbital and intrinsic angular momentum, quantum measurement and Einstein–Podolsky–Rosen nonlocal correlations for orbital angular momentum, intrinsic angular momentum and correlated particle interferometry. Since then, the acceptance of the validity of de Broglie–Bohm theory has steadily grown, as has the interest in the consequences of the approach. For my contribution to the current celebratory volume I was asked to provide a personal review specifically of this novel work within its historical context of the last quarter of the twentieth century.
The de Broglie–Bohm interpretation (Bohmian mechanics, hidden-variables theory, causal interpretation or pilot-wave theory) is one of the interpretations of quantum mechanics which opposes to the claim of standard interpretation on the completeness of description of the state of quantummechanical system, that description in Bohmian mechanics is completed by defining positions of the particles of the system i.e. hidden variables and their dynamics. These facts are the basis of motivation for the introduction of a new theory that can describe dubious axiomatic requirements of standard interpretation. The presented theory is deterministic and explicitly nonlocal. Originators of Bohmian mechanics were L. de Broglie (1927.) and D. Bohm (1952.) who presented mathematically more general and conceptual elaborate formulation. Along with the historical overview, a note is given about the main properties of the theory, such as the issue of nonlocality and hidden variables. The aim of this paper is to present and explain the main ideas and properties of the theory as well as to give a systematic overview of present and historical mathematical construction of the theory and most of all to discuss implications of de Broglie–Bohm theory on the ontology of quantum-mechanical picture, showcasing examples of the equivalency of the description of a free particle as a propagation of the plane wave in space or as the ensemble of the trajectories and of the spreading of the Gaussian wave packet. The main example of the obvious conceptual clashing of the interpretations is presented: the double-slit experiment, with a detailed examination of the Bohmian mechanics’ predictions using presented formalism on the two double-slit experiment. The graphs of trajectories for given examples are obtained.
The Copenhagen interpretation has been the subject of much criticism, notably by De Broglie and Einstein, because it contradicts the principles of causality and realism. The aim of this essay is to study the wave mechanics as an alternative to traditional quantum mechanics, in the continuity of the ideas of Louis de Broglie: the pilot wave theory of De Broglie (where each particle is associated with a wave which guides it), De Broglie-Bohm theory, stochastic electrodynamics (where the stochastic character of particles is caused by the energy field of the fluctuating vacuum), and the analogies between quantum mechanics and hydrodynamics.
Abstract This introductory chapter reviews the main steps in the history of the pilot-wave theory from its inception to the present day, as well as the major philosophical discussions revolving around this theoretical framework. The first part of this essay begins with a discussion of de Broglie’ key ideas leading to the first formulation of the pilot-wave theory in 1924, followed by a detailed analysis of David Bohm’s rediscovery of this framework in 1952 along with the generalizations of his causal interpretation to the Pauli and Dirac theories. Moreover, the second renaissance of the pilot-wave theory is considered. Here I focus on the works of Hiley, Dewdney, Philippidis, Holland and other collaborators of Bohm who provided decisive contributions to the causal interpretation between the late 1970s and the 1980s. This part is concluded taking into account recent developments of the pilot-wave perspective, with particular attention to the approaches of Dürr, Goldstein, Zanghì and Valentini. The second part of the essay discusses in detail some of the main metaphysical debates concerning the ontology of this interpretative framework, as for instance the status of the wave function, the various notions of “particle” employed by various authors, as well as the meaning of quantum operators and contextuality in the de Broglie-Bohm theory. In addition, also the notion of primitive ontology is briefly introduced. Finally, the third part of this introduction illustrates the book chapters, guiding the reader into the various contents of the volume.
Since de Broglie's pilot wave theory was revived by David Bohm in the 1950's, the overwhelming majority of researchers involved in the field have focused on what is nowadays called de Broglie-Bohm dynamics and de Broglie's original double solution program was gradually forgotten. As a result, several of the key concepts in the theory are still rather vague and ill-understood. In the light of the progress achieved over the course of the 90 years that have passed since de Broglie's presentation of his ideas at the Solvay conference of 1927, we reconsider in the present paper the status of the double solution program. More than a somewhat dusty archaeological piece of history of science, we believe it should be considered as a legitimate attempt to reconcile quantum theory with realism.