A brief introduction to the history and philosophy of physical chance.

Scientific realism is the view that our best scientific theories can be regarded as (approximately) true. This is connected with the view that science, physics in particular, and metaphysics could (and should) inform one another: on the one hand, science tells us what the world is like, and on the other hand, metaphysical principles allow us to select between the various possible theories which are underdetermined by the data. Nonetheless, quantum mechanics has always been regarded as, at best, puzzling, if (...) not contradictory. As such, it has been considered for a long time at odds with scientific realism, and thus a naturalized quantum metaphysics was deemed impossible. Luckily, now we have many quantum theories compatible with a realist interpretation. However, scientific realists assumed that the wave-function, regarded as the principal ingredient of quantum theories, had to represent a physical entity, and because of this they struggled with quantum superpositions. In this paper I discuss a particular approach which makes quantum mechanics compatible with scientific realism without doing that. In this approach, the wave-function does not represent matter which is instead represented by some spatio-temporal entity dubbed the primitive ontology: point-particles, continuous matter fields, space-time events. I argue how within this framework one develops a distinctive theory-construction schema, which allows to perform a more informed theory evaluation by analyzing the various ingredients of the approach and their inter-relations. (shrink)

This is an introduction to wave function realism for a compendium on the philosophy of quantum mechanics that will be edited and translated into Portuguese by Raoni Arroyo, entitled Compêndio de Filosofia da Física Quântica. This essay presents the history of wave function realism, its various interpretations, the main arguments that are given for the position, and the main objections that have been raised to it.

It is generally believed that two rival non-relativistic quantum theories, the realist interpretation of quantum mechanics and Bohmian mechanics, are empirically equivalent. In this paper, I use these two quantum theories to show that it is possible to offer a solution to underdetermination in some local cases, by specifying what counts as relevant empirical evidence in empirical equivalence and underdetermination. I argue for a _domain-sensitive_ approach to underdetermination. Domain sensitivity on theories’ predictions plays a role in determining whether two or (...) more theories are empirically equivalent and underdetermined. To support my argument for the denial of the empirical equivalence between Bohmian mechanics and the realist interpretation of quantum mechanics, I argue that they are not empirically equivalent when we consider their predictions for domains outside their application, using the relativistic domain as an example. (shrink)

It is difficult to articulate how we should take a realist attitude towards Bohmian mechanics because there are many versions of it. This paper aims to clarify the realist commitments of Bohmian mechanics and how we can understand it from a general scientific realist perspective. I use the box experiment, a double-slit like experiment conducted by Cardone et al. :1–13, 2004; Int J Mod Phys B 20:1107–1121, 2006), as a working example to argue that a causal realist account that is (...) applicable to Bohmian mechanics, has to be supplemented with the use of Inference to the Best Explanation. The reason is because causal realism on its own does not form a sufficient basis for realism about Bohmian mechanics. In particular, I argue that the existence of the pilot wave explains why we observe an anomalous interference effect in the experiment of Cardone et al. The conclusion to draw is that a complete realist account about Bohmian mechanics rests on explanatory considerations. (shrink)

The primitive ontology approach to quantum mechanics seeks to account for quantum phenomena in terms of a distribution of matter in three-dimensional space and a law of nature that describes its temporal development. This approach to explaining quantum phenomena is compatible with either a Humean or powerist account of laws. In this paper, I offer a powerist ontology in which the law is specified by Bohmian mechanics for a global configuration of particles. Unlike in other powerist ontologies, however, this law (...) is not grounded in a structural power that is instantiated by the global configuration. Instead, I combine the primitive ontology approach with Aristotle’s doctrine of hylomorphism to create a new metaphysical model, in which the cosmos is a hylomorphic substance with an intrinsic power to choreograph the trajectories of the particles. (shrink)

In the recent literature, it has been shown that the wave function in the de Broglie–Bohm theory can be regarded as a new kind of field, i.e., a "multi-field", in three-dimensional space. In this paper, I argue that the natural framework for the multi-field is the original second-order Bohm’s theory. In this context, it is possible: i) to construe the multi-field as a real-valued scalar field; ii) to explain the physical interaction between the multi-field and the Bohmian particles; and iii) (...) to clarify the status of the energy-momentum conservation and the dynamics of the theory. (shrink)

A simple argument proposes a direct link between realism about quantum mechanics and one kind of metaphysical holism: if elementary quantum theory is at least approximately true, then there are entangled systems with intrinsic whole states for which the intrinsic properties and spatiotemporal arrangements of salient subsystem parts do not suffice. Initially, the proposal is compelling: we can find variations on such reasoning throughout influential discussions of entanglement. Upon further consideration, though, this simple argument proves a bit too simple. To (...) get such metaphysically robust consequences out, we need to put more than minimal realism in. This paper offers a diagnosis: our simple argument seems so compelling thanks to an equivocation. The predictions of textbook quantum theory already resonate with familiar holistic slogans; for realists, then, any underlying reality, conforming to such predictions, also counts as holistic in some sense or other, if only by association. Such associated holism, though, does not establish the sort of specific, robust supervenience failure claimed by our simple argument. While it may be natural to slide to this stronger conclusion, facilitating the slide is not minimal realism per se but an additional explanatory assumption about how and why reality behaves in accordance with our theory: roughly, quantum theory accurately captures patterns in the features and behaviors of physical reality because some underlying metaphysical structure constrains reality to exhibit these patterns. Along with the diagnosis comes a recommendation: we can and should understand one traditional disagreement about the metaphysics of entanglement as another manifestation of a familiar and more general conflict between reductive and non-reductive conceptions of metaphysical theorizing. Such reframing makes clearer what resources reductionists have for resisting the simple argument’s challenge from quantum holism. It also has an important moral for their opponents. Traditional focus on whole-part supervenience failure distracts from a root disagreement about metaphysical structure and its role in our theorizing. Non-reductionists fond of our simple argument would be better off tackling this root directly. (shrink)

Quantum mechanics allegedly supports a holistic metaphysical moral: it is not the case that the intrinsic characters of all entangled wholes supervene on intrinsic properties and spatiotemporal arrangements of proper parts. According to one influential line of reasoning, such holistic supervenience failure follows more or less directly from quantum theory itself. One advertised consequence is the defeat of a natural, broadly reductive worldview commonly linked to Lewis's philosophical doctrine of Humean supervenience. However, the situation is more complicated, in both this (...) and other respects, than it may first appear. This article is an opinionated overview of some especially interesting complications. (shrink)

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, 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. (shrink)

It is generally argued that if the wave-function in the de Broglie–Bohm theory is a physical field, it must be a field in configuration space. Nevertheless, it is possible to interpret the wave-function as a multi-field in three-dimensional space. This approach hasn’t received the attention yet it really deserves. The aim of this paper is threefold: first, we show that the wave-function is naturally and straightforwardly construed as a multi-field; second, we show why this interpretation is superior to other interpretations (...) discussed in the literature; third, we clarify common misconceptions. (shrink)

The ontological models framework distinguishes ψ-ontic from ψ-epistemic wave- functions. It is, in general, quite straightforward to categorize the wave-function of a certain quantum theory. Nevertheless, there has been a debate about the ontological status of the wave-function in the statistical interpretation of quantum mechanics: is it ψ-epistemic and incomplete or ψ-ontic and complete? I will argue that the wave- function in this interpretation is best regarded as ψ-ontic and incomplete.

In this paper, we focus on two related reductive theses in metaphysics—Humean Supervenience and Composition as Identity—and on their status in light of the indications coming from science, in particular quantum mechanics. While defenders of these reductive theses claim that they can be updated so as to resist the quantum evidence, we provide arguments against this contention. We claim that physics gives us reason for thinking that both Humean Supervenience and Composition as Identity are at least contingently false, as the (...) very process of composition determines, at least in some cases, the nature of composed systems. The argument has essentially to do with the fact that denying the reductive theses in question allows one to provide better explanations for the quantum evidence. (shrink)

ABSTRACTA popular strategy for understanding the probabilities that arise in physics is to interpret them via reductionist accounts of chance—indeed, it is sometimes claimed that such accounts are uniquely well-suited to make sense of the probabilities in classical statistical mechanics. Here it is argued that reductionist accounts of chance carry a steep but unappreciated cost: when applied to physical theories of the relevant type, they inevitably distort the relations of probability that they take as input.

The violation of Bell’s inequality has shown that quantum theory and relativity are in tension: reality is nonlocal. Nonetheless, many have argued that GRW-type theories are to be preferred to pilot-wave theories as they are more compatible with relativity: while relativistic pilot-wave theories require a preferred slicing of space-time, foliation-free relativistic GRW-type theories have been proposed. In this paper I discuss various meanings of ‘relativistic invariance,’ and I show how GRW-type theories, while being more relativistic in one sense, are less (...) relativistic in another. If so, the initial claim that GRW-type theories have a greater compatibility with relativity is unwarranted: both type of theories violate relativity, one way or another. (shrink)

In this paper I present a new perspective for interpreting the wavefunction as a non-material, non-epistemic, non-representational entity. I endorse a functional view according to which the wavefunction is defined by its roles in the theory. I argue that this approach shares some similarities with the nomological account of the wave function as well as with the pragmatist and epistemic approaches to quantum theory, while avoiding the major objections of these alternatives.

In this paper I present a new perspective for interpreting the wavefunction as a non-material, nonepistemic, non-representational entity. I endorse a functional view according to which the wavefunction is defined by its roles in the theory. I argue that this approach shares some similarities with the nomological account of the wave function as well as with the pragmatist and epistemic approaches to quantum theory, while avoiding the major objections of these alternatives.

Against what is commonly accepted in many contexts, it has been recently suggested that both deterministic and indeterministic quantum theories are not time‐reversal invariant, and thus time is handed in a quantum world. In this paper, I analyze these arguments and evaluate possible reactions to them. In the context of deterministic theories, first I show that this conclusion depends on the controversial assumption that the wave‐function is a physically real scalar field in configuration space. Then I argue that answers which (...) restore invariance by assuming the wave‐function is a ray in Hilbert space fall short. Instead, I propose that one should deny that the wave‐function represents physical systems, along the lines proposed by the so‐called primitive ontology approach. Moreover, in the context of indeterministic theories, I argue that time‐reversal invariance can be restored suitably redefining its meaning. (shrink)

Many agree that the pilot-wave theory is to be understood as a first-order theory, in which the law constrains the velocity of the particles. However, while Dürr, Goldstein and Zanghì maintain that the pilot-wave theory is Galilei invariant, Valentini argues that such a symmetry is mathematical but it has no physical significance. Moreover, some wavefunction realists insist that the pilot-wave theory is not Galilei invariant in any sense. It has been maintained by some that this disagreement originates in the disagreement (...) about ontology, as Valentini, contrary to Dürr, Goldstein and Zanghì, has been taken to endorse wavefunction realism. In this paper I argue that Valentini’s argument is independent of the choice of the ontology of matter: it is based of the notion of natural kinematics for a theory, and the idea that the kinematics should match the dynamics. If so, I also argue that there are several reasons to dispute Valentini’s claim that the kinematical symmetries should constrain dynamical ones. (shrink)

A salient feature of de Broglie-Bohm quantum theory is that particles have determinate positions at all times and in all physical contexts. Hence, the trajectory of a particle is a well-defined concept. One then may expect that the closely related notion of inertial trajectory is also unproblematically defined. I show that this expectation is not met. I provide a framework that deploys six different ways in which dBB theory can be interpreted, and I state that only in the canonical interpretation (...) the concept of inertial trajectory is the customary one. However, in this interpretation the description of the dynamical interaction between the pilot-wave and the particles, which is crucial to distinguish inertial from non-inertial trajectories, is affected by serious difficulties, so other readings of the theory intend to avoid them. I show that in the alternative interpretations the concept at issue gets either drastically altered, or plainly undefined. I also spell out further conceptual difficulties that are associated to the redefinitions of inertial trajectories, or to the absence of the concept. (shrink)

This thesis develops a detailed account of the emergence of for all practical purposes continuous, quasi-classical world histories from the discontinuous, stochastic micro dynamics of Minimal Bohmian Mechanics (MBM). MBM is a non-relativistic quantum theory. It results from excising the guiding equation from standard Bohmian Mechanics (BM) and reinterpreting the quantum equilibrium hypothesis as a stochastic guidance law for the random actualization of configurations of Bohmian particles. On MBM, there are no continuous trajectories linking up individual configurations. Instead, individual configurations (...) are actualized independently of each other, carving out the decoherence-induced branching structure of the universal wave function. Yet, by contrast to the Everett interpretation, branches of the universal wave function are not actualized in parallel, i.e. all at the same time. Rather, world branches, on MBM, are actualized sequentially. -/- For an introduction to MBM, the transition from BM to MBM is described, and their empirical equivalence is established. I present the conditions under which MBM can be classified as a primitive ontology (PO) theory, regarded as crucial for the acceptance of a theory as Bohmian by many proponents of BM. While rendering MBM compatible with the PO approach, it must not fall prey to the problem of communication, arising from the two-space reading of BM. -/- The issue of temporal solipsism, identified by Bell as a serious problem for his “Everett (?) theory” – the historic predecessor of MBM – is discussed. I argue that Barbour’s time capsule approach does not provide a satisfactory solution. In particular, his adopting a more than minimal psychophysical parallelism between brain processes and experience of macroscopic change is argued to be reasonable in light of our current best neuroscience, yet problematic for theories relying solely on time capsules, understood as highly structured, individual, internally static configurations. As a solution, I introduce worlds, and world histories, as key concepts in providing a link between MBM’s micro dynamics and macroscopic phenomena. Worlds, other than time capsules, are coarse-grained regions in phase- or configuration space, defined as sets of possible micro states satisfying a relation of sufficient similarity from a macroscopic perspective, with respect to a given micro state. Hence, worlds may overlap. -/- I argue that worlds thus construed are a reasonable option for replacing the disjoint macro regions of phase space, resulting from the usual way of partitioning phase space in the standard framework of Boltzmannian statistical mechanics. This move solves the issue of discontinuous change of macro variables upon the micro state crossing the boundary between different macro regions. -/- I adapt this move for MBM’s discontinuous micro dynamics in configuration space. Issues revolving around the microscopic-macroscopic distinction, particle identity, impenetrability and haecceity in light of the desideratum of particle number conservation, etc., are discussed. I provide a detailed explanation of how overlapping worlds in MBM form world histories, thereby linking up macroscopically distinct worlds. Thus, the problem of temporal solipsism is resolved in a way that is compatible with a more than minimal psychophysical parallelism. (shrink)

Although contemporary metaphysics has recently undergone a neo-Aristotelian revival wherein dispositions, or capacities are now commonplace in empirically grounded ontologies, being routinely utilised in theories of causality and modality, a central Aristotelian concept has yet to be given serious attention – the doctrine of hylomorphism. The reason for this is clear: while the Aristotelian ontological distinction between actuality and potentiality has proven to be a fruitful conceptual framework with which to model the operation of the natural world, the distinction between (...) form and matter has yet to similarly earn its keep. In this chapter, I offer a first step toward showing that the hylomorphic framework is up to that task. To do so, I return to the birthplace of that doctrine - the biological realm. Utilising recent advances in developmental biology, I argue that the hylomorphic framework is an empirically adequate and conceptually rich explanatory schema with which to model the nature of organisms. (shrink)

The paper retraces the development from the measurement problem to the primitive ontology programme. It assesses the contribution of the GRW theory to this programme and discusses the pros and cons of the GRWm matter density ontology and the GRWf flash ontology in comparison to the Bohmian particle ontology. It thereby pursues the evaluation of the proposals for a primitive ontology of quantum physics.

We critically examine the role and status probabilities, as they enter via the Quantum Equilibrium Hypothesis, play in the standard, deterministic interpretation of deBroglie’s and Bohm’s Pilot Wave Theory (dBBT), by considering interpretations of probabilities in terms of ignorance, typicality and Humean Best Systems, respectively. We argue that there is an inherent conflict between dBBT and probabilities, thus construed. The conflict originates in dBBT’s deterministic nature, rooted in the Guidance Equation. Inquiring into the latter’s role within dBBT, we find it (...) explanatorily redundant (in particular for dBBT’s solution of the Measurement Problem, which only requires that the corpuscles possess definite positions), and subject to a number of difficulties. Following a suggestion from Bell, we propose to abandon the Guidance Equation, whilst retaining dBBT’s point particle-based Primitive Ontology, with positions as local beables. The resultant theory, which we identify as a stochastic, minimally deBroglie-Bohmian theory, describes a random walk through configuration space. Its probabilities, we propose, are best understood as dispositions of possible corpuscle configurations to manifest themselves. We subsequently evaluate the merits of sdBBT vis-à-vis dBBT, such as the justification of the Symmetrisation Postulate and the violation of the Action-Reaction Principle. Not only is sdBBT an attractive Bohmian theory that, whilst retaining dBBT's virtues, overcomes many of its shortcomings; it also sparks off a number of exciting follow-up questions, such as a comparison between sdBBT and other stochastic hidden-variable theories, e.g. Nelson Stochastics, or between sdBBT and the Everett interpretation. (shrink)