Abstract Lam and Esfeld have argued that, within Bohmian mechanics, the wave function can be interpreted as a physical structure instantiated by the fundamental particles posited by the theory. Further, to characterize the nature of this structure, they appeal to the framework of Ontic Structural Realism (OSR), thereby proposing a structuralist interpretation of Bohmian mechanics. However, I shall point out that OSR denotes a family of distinct views, each of which maintains a different account about the relation between structures and objects, and entails a different kind of ontology. Thus, in this paper I will show how to articulate the structuralist approach to Bohmian Mechanics accordingly to the different standard versions of OSR, and I will evaluate these alternatives. Moreover, I will propose a novel and sui generis kind of structuralist interpretation of Bohmian Mechanics, based on the framework of metaphysical coherentism.
Abstract Lam and Esfeld have argued that, within Bohmian mechanics, the wave function can be interpreted as a physical structure instantiated by the fundamental particles posited by the theory. Further, to characterize the nature of this structure, they appeal to the framework of Ontic Structural Realism (OSR), thereby proposing a structuralist interpretation of Bohmian mechanics. However, I shall point out that OSR denotes a family of distinct views, each of which maintains a different account about the relation between structures and objects, and entails a different kind of ontology. Thus, in this paper I will show how to articulate the structuralist approach to Bohmian Mechanics accordingly to the different standard versions of OSR, and I will evaluate these alternatives. Moreover, I will propose a novel and sui generis kind of structuralist interpretation of Bohmian Mechanics, based on the framework of metaphysical coherentism.
This thesis aims to contribute to the discussion of how to interpret the Bohmian ontology. Bohmian Mechanics is a quantum theory that describes the motion of particles, whose trajectories are determined by the quantum wave-function. This theory faces two key questions. The former concerns the metaphysical characterization of the particles; the latter relates to the ontological status of the wave-function. \nAfter briefly presenting two possible metaphysical characterizations of the particles, I dedicate the bulk of this work to investigating the status of the wave-function. In particular, I analyse the realist view (which regards the wave-function as a multi-dimensional field) and the nomological view (which considers the wave-function as a law-like entity). My investigation touches upon different levels of inquiry. First, I show that these two ontological interpretations depend on contrasting formulations of the law that dictates the particle motion. Second, I argue that both views defend very problematic ontologies that not only violate familiar metaphysical criteria but also fail to provide a satisfactory explanation of the relation between the particles and the wave-function. Third, I spell out the implicit methodologies that underlie the two views, arguing that they conflate three important categories that should rather be kept separate: the informationally-complete representation of the system, the ontologically-complete representation of the system, and the ontology itself. \nFinally, I present and advocate structural realism as the metaphysical framework for investigating and understanding the Bohmian ontology. According to the structuralist interpretation, the wave-function represents a network of modal relations whose relata are the particles. I argue that this third view provides the best account of the Bohmian system for three reasons. First of all, it offers a parsimonious ontology that does not create any issue of metaphysical underdetermination. Secondly, it supplies an explanatorily powerful ontology. Thirdly, it relies on a sound methodological program. I conclude with an interesting insight: this structuralist interpretation can be regarded as reconciling the realist view and the nomological view given that it takes on aspects of both views and is compatible with both formulations of the law of motion for the particles. \n
The aim of this book is to provide a comprehensive guide to the metaphysics of Bohmian mechanics. Bohmian mechanics is a quantum theory that describes the motion of particles following trajectories that are determined by the quantum wave-function. The key question that the theory has to face relates to the ontological interpretation of the quantum wave-function. The main debate has mostly centered around two opposing views, wave-function realism on the one hand, and the nomological view on the other hand. The supporters of the former believe that the wave-function is a physical field living in a high-dimensional space; the supporters of the latter regard the wave-function as just an entity that appears in the laws of nature and lacks physical status. This monograph discusses both views open-mindedly, illuminating their tacit problems and providing new insight into how they can be overcome. Moreover, it discusses the structuralist view, which is often neglected and which can be regarded as a reconciliation of the two main opposing camps.
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.
The nature of the wave function has been a hot topic of debate since the early days of quantum mechanics. The recent PBR theorem proves that the wave function is ontic, representing the ontic state of a physical system or a concrete physical entity. On the other hand, Bohmian mechanics regards the wave function as not ontic but nomological, like a law of nature. This raises an interesting question: does the PBR theorem refute Bohmian mechanics? It seems widely thought that the ontic view and the nomological view are compatible, and thus the PBR theorem has no implications for Bohmian mechanics. In this paper, I argue that this is not the case. First, I point out that the nomological view and the ontic view are two different views of the wave function. This means that the result of the PBR theorem and Bohmian mechanics are incompatible. Next, I argue that the PBR theorem and Bohmian mechanics are nevertheless compatible, and the former does not refute the latter. The reason is that the PBR theorem and Bohmian mechanics are based on different fundamental assumptions, and in particular, Bohmian mechanics rejects one key assumption of the ontological models framework on which the PBR theorem is based. Finally, I argue that the rejection of this assumption will bring to our attention a potential important issue of Bohmian mechanics.
We present a three-dimensional field ontology for Bohmian mechanics in which the single-particle wave functions defined in ordinary physical space are taken as ontological elements alongside particle positions. In this view, each particle is associated with a wave function in three-dimensional space conditioned on the actual positions of the remaining particles. The universal wave function on configuration space is retained within the formalism, but its role is interpreted as nomological: it determines the coupled evolution of the three-dimensional fields without itself being treated as a fundamental physical field. The corresponding evolution equations for the conditioned three-dimensional wave functions follow from the standard Bohmian formalism and, together with the guidance equation, yield dynamics fully equivalent to those of the conventional theory. The empirical and predictive content of Bohmian mechanics is thereby preserved, while its ontological structure is expressed in explicitly three-dimensional terms. Within a ψ-ontic perspective, this proposal makes explicit an ontological organization of Bohmian mechanics in which the dynamical fields are defined on physical space. While fully equivalent to the conventional formulation, expressing the theory in these terms may facilitate interpretation, visualization, and pedagogical presentation.
Abstract Ontic structuralism or ontic structural realism in the philosophy of physics can be broadly considered as an interpretative strategy providing a set of conceptual and metaphysical tools—or, more ambitiously, an ontological framework—in order to account for central features of current fundamental physics. This article aims to review the main structuralist interpretative moves in the context of our two best fundamental physical theories of matter and spacetime, namely, quantum theory (quantum mechanics and quantum field theory) and general relativity. We highlight in particular the structuralist understanding of permutation invariance, entanglement and nonlocality in quantum theory, and of the dynamical features of spacetime, (gauge‐theoretic) diffeomorphism invariance and background independence in general relativity.