In this work celebrating the centenary of quantum mechanics, we review the principles of the de Broglie-Bohm theory (dBB), also known as pilot-wave theory. We assess the most common reading of it (the Nomological interpretation based on the notion of primitive ontology in tridimensional space) and defend instead a more causal and pluralistic approach, drawing on classical analogies with optics and hydrodynamics. Within this framework, we review some of the approaches exploiting mechanical analogies to overcome the limitations of the current dBB theory and perhaps quantum mechanics itself.
In this work celebrating the centenary of quantum mechanics, we review the principles of the de Broglie-Bohm theory (dBB), also known as pilot-wave theory. We assess the most common reading of it (the Nomological interpretation based on the notion of primitive ontology in tridimensional space) and defend instead a more causal and pluralistic approach, drawing on classical analogies with optics and hydrodynamics. Within this framework, we review some of the approaches exploiting mechanical analogies to overcome the limitations of the current dBB theory and perhaps quantum mechanics itself.
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.
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.
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.
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.
We define the de Broglie-Bohm (dBB) weak interpretation as the dBB interpretation restricted to particles in unbound states whose wave function is defined in the three-dimensional physical space, and the dBB strong interpretation as the usual dBB interpretation applied to all wave functions, in particular to particles in bound states whose wave function is defined in a 3N-dimensional configuration space in which N is the number of particules. We show that the current criticisms of the dBB interpretation do not apply to this weak interpretation and that, furthermore, there are theoritical and experimental reasons to justify the weak dBB interpretation. Theoretically, the main reason concern the continuity existing for such particles between quantum mechanics and classical mechanics: we demonstrate in fact that the density and the phase of the wave function of a single-particle (or a set of identical particles without interaction), when the Planck constant tends to 0, converges to the density and the action of a set of unrecognizable prepared classical particles that satisfy the statistical Hamilton-Jacobi equations. As the Hamilton-Jacobi action pilots the particle in classical mechanics, this continuity naturally concurs with the weak dBB interpretation. Experimentally, we show that the measurement results of the main quantum experiments (Young's slits experiment, Stern and Gerlach, EPR-B) are compatible with the de Broglie-Bohm weak interpretation and everything takes place as if these unbounded particles had trajectories. In addition, we propose two potential solutions to complete the dBB weak interpretation.
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.