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De Broglie–Bohm Pilot‐Wave Theory: Many Worlds in Denial?

Antony Valentini

Published Jun 24, 2010• 33 citations
Publisher

Abstract

Abstract This chapter replies to claims that the pilot-wave theory of de Broglie and Bohm is really a many-worlds theory with a superfluous configuration appended to one of the worlds. Assuming that pilot-wave theory does contain an ontological pilot wave (a complex-valued field in configuration space), the chapter shows that such claims arise from not interpreting pilot-wave theory on its own terms. Specifically, the theory has its own (‘subquantum’) theory of measurement, and in general describes a ‘non-equilibrium’ state that violates the Born rule. Furthermore, in realistic models of the classical limit, one does not obtain localised pieces of an ontological pilot wave following alternative macroscopic trajectories: from a de Broglie–Bohm viewpoint, alternative trajectories are merely mathematical and not ontological. Thus, from the perspective of pilot-wave theory itself, many worlds is an illusion. It is further argued that, even leaving pilot-wave theory aside, the theory of many worlds is rooted in the intrinsically unlikely assumption that quantum measurements should be modelled on classical measurements, and is therefore unlikely to be true.

DOI
10.1093/acprof:oso/9780199560561.003.0019

Related papers

De Broglie-Bohm Pilot-Wave Theory: Many Worlds in Denial?

Antony Valentini

We reply to claims (by Deutsch, Zeh, Brown and Wallace) that the pilot-wave theory of de Broglie and Bohm is really a many-worlds theory with a superfluous configuration appended to one of the worlds. Assuming that pilot-wave theory does contain an ontological pilot wave (a complex-valued field in configuration space), we show that such claims arise from not interpreting pilot-wave theory on its own terms. Specifically, the theory has its own ('subquantum') theory of measurement, and in general describes a 'nonequilibrium' state that violates the Born rule. Furthermore, in realistic models of the classical limit, one does not obtain localised pieces of an ontological pilot wave following alternative macroscopic trajectories: from a de Broglie-Bohm viewpoint, alternative trajectories are merely mathematical and not ontological. Thus, from the perspective of pilot-wave theory itself, many worlds are an illusion. It is further argued that, even leaving pilot-wave theory aside, the theory of many worlds is rooted in the intrinsically unlikely assumption that quantum measurements should be modelled on classical measurements, and is therefore unlikely to be true.

arXiv:0811.0810•Nov 5, 2008•38 citations

Reply to Valentini, ‘De Broglie–Bohm Pilot‐Wave Theory: Many Worlds in Denial?’

Harvey R. Brown

Abstract The reality of the patterns in the wave-function representing different worlds is not like that of locality and the uncertainty relations, which hold only for the equilibrium distribution. Nor, in the light of the Deutsch–Wallace representation theorem for the Born rule, is the appeal to non-equilibrium probability distributions as the ground for the distinction between pilot-wave theory and many-worlds theory well-motivated. Finally, Valentini's counter-claim, that the latter is motivated by eigenvalue realism, ignores the need to give an account of macroscopic superpositions.

•Jun 24, 2010•7 citations

Comment on Valentini, "De Broglie-Bohm Pilot-Wave Theory: Many Worlds in Denial?"

Harvey R. Brown

Valentini has recently defended the de Broglie-Bohm pilot-wave version of quantum theory from the claim that it is essentially Everett theory encumbered with the redundant postulation of point particles. In this note, Valentini’s central arguments are questioned. 1

•Jan 1, 2009•8 citations

Pilot-Wave Theories as Hidden Markov Models

Jacob A. Barandes

The original version of the de Broglie-Bohm pilot-wave theory, also called Bohmian mechanics, attempted to treat the wave function or pilot wave as a part of the physical ontology of nature. More recent versions of the de Broglie-Bohm theory appearing in the last few decades have tried to regard the pilot wave instead as an aspect of the theory's nomology, or dynamical laws. This paper argues that neither of these views is correct, and that the de Broglie-Bohm pilot wave is best understood as a collection of latent variables in the sense of a hidden Markov model, a construct that was not available when de Broglie and Bohm originally formulated what became their pilot-wave theory. This paper also discusses several other challenges for the ontological view of the pilot wave. One such challenge is due to Foldy-Wouthuysen gauge transformations, which connect up with the Deotto-Ghirardi ambiguity in the de Broglie-Bohm theory. Another challenge arises from the freedom to carry out canonical transformations in the wave function's own notion of phase space, as defined by Strocchi and Heslot.

quant-pharXiv:2602.10569•Feb 12, 2026•0 citations

Comment on Valentini, "De Broglie-Bohm Pilot-Wave Theory: Many Worlds in Denial?" [arXiv:0811.0810]

Harvey R. Brown

Valentini [arXiv:0811.0810] has recently defended the de Broglie-Bohm pilot-wave version of quantum theory from the claim that it is essentially Everett theory encumbered with the redundant postulation of point particles. In this note, Valentini's central arguments are questioned.

arXiv:0901.1278•Jan 9, 2009•7 citations

Guiding Waves in Quantum Mechanics

Abstract The pilot-wave theory of de Broglie and Bohm has a special place in the history of contemporary physics, being it the very first alternative formulation of quantum mechanics. As is well-known, such a framework established itself as a leading interpretation of the quantum formalism in virtue of the solutions provided to the major technical and conceptual challenges affecting the orthodox view. The de Broglie-Bohm theory in fact not only solves the famous measurement problem, one of the most cogent issues faced by standard quantum mechanics, but also it clarifies the formal structure of the latter theory as a consequence of a consistent set of principles and an precise, unambiguous ontology. This volume aims to provide the reader with a discussion of the pilot-wave perspective which is as informative, comprehensive and accessible as possible, while at the same time clarifying confusions and misunderstandings that are unfortunately still common in literature despite the long history of this theoretical framework. The book features chapters about the various perspectives on the pilot-wave theory, its extensions to relativity and quantum field theory, and its experimental applications to various branches of physics, as for instance quantum electrodynamics, quantum chemistry, and quantum engineering. Moreover, the volume includes essays on the history and philosophy of de Broglie-Bohm theory in order to delineate its developments and the vicissitudes of its pioneers, as well as to understand the scientific image of the universe it provides.

•Apr 1, 2025•1 citation
Abstract This chapter replies to claims that the pilot-wave theory of de Broglie and Bohm is really a many-worlds theory with a superfluous configuration appended to one of the worlds. Assuming that pilot-wave theory does contain an ontological pilot wave (a complex-valued field in configuration space), the chapter shows that such claims arise from not interpreting pilot-wave theory on its own terms. Specifically, the theory has its own (‘subquantum’) theory of measurement, and in general describes a ‘non-equilibrium’ state that violates the Born rule. Furthermore, in realistic models of the classical limit, one does not obtain localised pieces of an ontological pilot wave following alternative macroscopic trajectories: from a de Broglie–Bohm viewpoint, alternative trajectories are merely mathematical and not ontological. Thus, from the perspective of pilot-wave theory itself, many worlds is an illusion. It is further argued that, even leaving pilot-wave theory aside, the theory of many worlds is rooted in the intrinsically unlikely assumption that quantum measurements should be modelled on classical measurements, and is therefore unlikely to be true.
We reply to claims (by Deutsch, Zeh, Brown and Wallace) that the pilot-wave theory of de Broglie and Bohm is really a many-worlds theory with a superfluous configuration appended to one of the worlds. Assuming that pilot-wave theory does contain an ontological pilot wave (a complex-valued field in configuration space), we show that such claims arise from not interpreting pilot-wave theory on its own terms. Specifically, the theory has its own ('subquantum') theory of measurement, and in general describes a 'nonequilibrium' state that violates the Born rule. Furthermore, in realistic models of the classical limit, one does not obtain localised pieces of an ontological pilot wave following alternative macroscopic trajectories: from a de Broglie-Bohm viewpoint, alternative trajectories are merely mathematical and not ontological. Thus, from the perspective of pilot-wave theory itself, many worlds are an illusion. It is further argued that, even leaving pilot-wave theory aside, the theory of many worlds is rooted in the intrinsically unlikely assumption that quantum measurements should be modelled on classical measurements, and is therefore unlikely to be true.
Abstract The reality of the patterns in the wave-function representing different worlds is not like that of locality and the uncertainty relations, which hold only for the equilibrium distribution. Nor, in the light of the Deutsch–Wallace representation theorem for the Born rule, is the appeal to non-equilibrium probability distributions as the ground for the distinction between pilot-wave theory and many-worlds theory well-motivated. Finally, Valentini's counter-claim, that the latter is motivated by eigenvalue realism, ignores the need to give an account of macroscopic superpositions.
The original version of the de Broglie-Bohm pilot-wave theory, also called Bohmian mechanics, attempted to treat the wave function or pilot wave as a part of the physical ontology of nature. More recent versions of the de Broglie-Bohm theory appearing in the last few decades have tried to regard the pilot wave instead as an aspect of the theory's nomology, or dynamical laws. This paper argues that neither of these views is correct, and that the de Broglie-Bohm pilot wave is best understood as a collection of latent variables in the sense of a hidden Markov model, a construct that was not available when de Broglie and Bohm originally formulated what became their pilot-wave theory. This paper also discusses several other challenges for the ontological view of the pilot wave. One such challenge is due to Foldy-Wouthuysen gauge transformations, which connect up with the Deotto-Ghirardi ambiguity in the de Broglie-Bohm theory. Another challenge arises from the freedom to carry out canonical transformations in the wave function's own notion of phase space, as defined by Strocchi and Heslot.
Abstract The pilot-wave theory of de Broglie and Bohm has a special place in the history of contemporary physics, being it the very first alternative formulation of quantum mechanics. As is well-known, such a framework established itself as a leading interpretation of the quantum formalism in virtue of the solutions provided to the major technical and conceptual challenges affecting the orthodox view. The de Broglie-Bohm theory in fact not only solves the famous measurement problem, one of the most cogent issues faced by standard quantum mechanics, but also it clarifies the formal structure of the latter theory as a consequence of a consistent set of principles and an precise, unambiguous ontology. This volume aims to provide the reader with a discussion of the pilot-wave perspective which is as informative, comprehensive and accessible as possible, while at the same time clarifying confusions and misunderstandings that are unfortunately still common in literature despite the long history of this theoretical framework. The book features chapters about the various perspectives on the pilot-wave theory, its extensions to relativity and quantum field theory, and its experimental applications to various branches of physics, as for instance quantum electrodynamics, quantum chemistry, and quantum engineering. Moreover, the volume includes essays on the history and philosophy of de Broglie-Bohm theory in order to delineate its developments and the vicissitudes of its pioneers, as well as to understand the scientific image of the universe it provides.