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 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.
Bohmian Mechanics (Dürr et al. 1992) and the Pilot Wave theory (Valentini 1991) provide two opposite understandings of what guides the particles. On one hand there is a universal nomological wave-function (Dürr et al. 1997), which dictates the motion of the particles (the primitive ontology), on the other hand there is universal Ψ-field, which acts causally on the particle configuration. Both views have to face many challenges. Among them, the nomological interpretation has to account for how the law – the wave-function - is grounded in the primitive ontology (Esfeld 2013), while the causal interpretation has to solve the problem of how an entity in configuration space can be the cause of a motion in physical space (Esfeld et al. 2013). Considering now the problem of the nomological interpretation, the anchorage of the lawlike wave-function to the primitive ontology was provided by Esfeld, who recently proposed to ground the wave-function in a dispositional property instantiated by all the particles taken as a whole (Esfeld et al. 2013). However, two challenges come here: the first concerns the tension in deciding whether or not the dispositional property should be part of the primitive ontology, and the second concerns the weak explanatory power that the dispositionalist account can provide. The debate has led to an interesting structuralist account (Esfeld et al. 2015, Lam 2015), which is to regard the wave-function as a modal structure, which relates all the particles of the universe in a non-local fashion, hence explaining the dynamics of the particles. Regarding the problems of the causal interpretation, Valentini thinks of the Ψ- field not as concrete and as physical as an electromagnetic field, but as a ‘more abstract field’ (Valentini 1991): in fact, it lives in configuration space and for this reason it does not admit test particles. Moreover, he does not regard it as an efficient cause of the particle configuration, but as a formal cause, in an Aristotelian-Thomistic sense, in such a way that it should be considered as a guiding form. According to his Aristotelian view of formal cause, the motion is the fulfilling of what exists potentially, which is represented by the Ψ-field (Valentini 1991). The reason why the Ψ-field should be regarded as a real ‘guiding form’ is twofold: on one hand it is its form that determines the trajectories of the particles, on the other hand, its role is to storage formal information between the particles. After having analyzed both representations of the ‘Ψ’, as a modal structure in the first scenario, and as a formal cause in the second, I will claim that, if we hold Esfeld’s account of the universal wave-function in Bohmian Mechanics and the characterization by Valentini of the pilot wave, then the two views do not differ as much as it is normally thought, because in both the wave-function is regarded as a dynamical structure. This reconciliation is especially achieved if we consider that, being all the particles identical, both theories may be reformulated in a reduced-configuration space.
In this thesis we study the de Broglie-Bohm pilot-wave interpretation of quantum theory. We consider the domain of non-relativistic quantum theory, relativistic quantum theory and quantum field theory, and in each domain we consider the possibility of formulating a pilot-wave interpretation. For non-relativistic quantum theory a pilot-wave interpretation in terms of particle beables can readily be formulated. But this interpretation can in general not straightforwardly be generalized to relativistic wave equations. The problems which prevent us from devising a pilot-wave interpretation for relativistic wave equations also plague the standard quantum mechanical interpretation, where these problems led to the conception of quantum field theory. Therefore most of our attention is focussed on the construction of a pilot-wave interpretation for quantum field theory. We thereby favour the field beable approach, developed amongst others by Bohm, Hiley, Holland, Kaloyerou and Valentini. Although the field beable approach can be successfully applied to bosonic quantum field theory, it seems not straightforward to do so for fermionic quantum field theory.
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 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.
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.