Abstract Michael Esfeld’s minimalist ontology is committed to two axioms relating to (1) distance relations that identify simple objects (permanent matter points) while (2) the distances between them change. This article scrutinizes such a conceptual strategy to determine whether it can successfully be applied to all levels of physical reality, as Esfeld contends. To do so, it explores one of his paradigmatic sources, that is, Bohmian mechanics. Two arguments are proposed. First, while Bohm’s original formulation of Bohmian mechanics and the interpretation advocated by Dürr, Goldstein & Zanghì are typically taken as mathematically equivalent, this article argues that Esfeld’s minimalist ontology does not cover the former’s ontological richness. To secure its achievement, the minimalist ontology framework needs to (i) break the equivalence between the two versions via a commitment to the nomological interpretation of the wavefunction (ii) yet attribute some kind of physical efficacy to the wavefunction as a guiding parameter for the evolution of particles living in three-dimensional space. Both requirements will be critically addressed. Second, the article shows that Esfeld’s metaphysical program is not only forced to rely on a theoretically suspicious formulation of quantum mechanics, but that more fundamental, under-development approaches in theoretical physics are way less reconcilable with its axioms, thus questioning its alleged universality.
Abstract Michael Esfeld’s minimalist ontology is committed to two axioms relating to (1) distance relations that identify simple objects (permanent matter points) while (2) the distances between them change. This article scrutinizes such a conceptual strategy to determine whether it can successfully be applied to all levels of physical reality, as Esfeld contends. To do so, it explores one of his paradigmatic sources, that is, Bohmian mechanics. Two arguments are proposed. First, while Bohm’s original formulation of Bohmian mechanics and the interpretation advocated by Dürr, Goldstein & Zanghì are typically taken as mathematically equivalent, this article argues that Esfeld’s minimalist ontology does not cover the former’s ontological richness. To secure its achievement, the minimalist ontology framework needs to (i) break the equivalence between the two versions via a commitment to the nomological interpretation of the wavefunction (ii) yet attribute some kind of physical efficacy to the wavefunction as a guiding parameter for the evolution of particles living in three-dimensional space. Both requirements will be critically addressed. Second, the article shows that Esfeld’s metaphysical program is not only forced to rely on a theoretically suspicious formulation of quantum mechanics, but that more fundamental, under-development approaches in theoretical physics are way less reconcilable with its axioms, thus questioning its alleged universality.
It is argued that in Bohmian mechanics the effective wave function of a subsystem of the universe does not encode the influences of other par-ticles on the subsystem. This suggests that the ontology of Bohmian mechanics does not consist only in Bohmian particles and their posi-tions. It is nonetheless pointed out that since the wave function in configuration space may represent the state of ergodic motion of non-Bohmian particles in three-dimensional space, the ontology of Bohmian mechanics may still consist only in particles. Bohmian mechanics, which is also called the de Broglie-Bohm theory, is a realistic alternative to standard quantum mechanics initially proposed by de Broglie (1928) and later developed by Bohm (1952). According to the theory, a complete realistic description of a quantum system is provided by the configuration defined by the positions of its particles together with its wave function. It has been a hot topic of debate how to interpret the wave function in the theory. Recently Esfeld et al (2013) further developed the nomological interpretation of the wave function, as suggested by Dürr, Goldstein and Zangh̀ı (1997), Goldstein and Teufel (2001) and Goldstein and Zangh̀ı (2012). They argued that the ontology of Bohmian mechanics consists only in Bohmian particles and their positions, and in particular, the effective wave function of a subsystem of the universe encodes the influences of other particles in the universe on the subsystem. In this note, we will argue that this interesting view may be problematic. The Bohmian law of motion is expressed by two equations, a guiding equation for the configuration of particles in three-dimensional space and the Schrödinger equation, describing the time evolution of the wave function, which enters the guiding equation. The law can be formulated as follows: dQ(t) dt = vΨ(t)(Q(t)). (1)
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
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 It has been argued that in the context of Bohm’s approach to quantum mechanics, the postulation of a three-dimensional ontology (as opposed to a high-dimensional one) is presumed to be the only interpretation that may reliably support object-oriented realism by virtue of the fact that this ontology is approximately preserved through scientific change, at least in the classical–quantum transition. Based on an interpretative analysis of the Bohmian formulation, I shall critically evaluate the tenability of this argument. In so doing, I shall argue that this formulation admits the postulation of an alternative ontology that is properly defined in a high-dimensional space, and is approximately preserved among this transition. As a result, both the three-dimensional and the high-dimensional worldviews shall form the basis of an equally reliable endorsement of object-oriented realism in the context of the Bohmian framework. I shall conclude that this argument becomes a problem of metaphysical underdetermination between a three and a high-dimensional Bohmian interpretation.
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.
The article points out that the modern formulation of Bohm’s quantum theory, known as Bohmian mechanics, is committed only to particles’ positions and a law of motion. We explain how this view can avoid the open questions that the traditional view faces, according to which Bohm’s theory is committed to a wave-function that is a physical entity over and above the particles, although it is defined on configuration space instead of three-dimensional space. We then enquire into the status of the law of motion, elaborating on how the main philosophical options to ground a law of motion, namely Humeanism and dispositionalism, can be applied to Bohmian mechanics. In conclusion, we sketch out how these options apply to primitive ontology approaches to quantum mechanics in general. 1 Introduction2 What is the Ontological Status of the Wave-Function?3 Humeanism about Laws4 Laws Grounded in Dispositions5 Advantages of Dispositionalism6 Conclusion