Abstract Realism about quantum theory naturally leads to realism about the quantum state of the universe. It leaves open whether it is a pure state represented by a wave function, or an impure one represented by a density matrix. I characterise and elaborate on Density Matrix Realism, the thesis that the universal quantum state is objective but can be impure. To clarify the thesis, I compare it with Wave Function Realism, explain the conditions under which they are empirically equivalent, consider two generalisations of Density Matrix Realism, and answer some frequently asked questions. I end by highlighting an implication for scientific realism.
Abstract Realism about quantum theory naturally leads to realism about the quantum state of the universe. It leaves open whether it is a pure state represented by a wave function, or an impure one represented by a density matrix. I characterise and elaborate on Density Matrix Realism, the thesis that the universal quantum state is objective but can be impure. To clarify the thesis, I compare it with Wave Function Realism, explain the conditions under which they are empirically equivalent, consider two generalisations of Density Matrix Realism, and answer some frequently asked questions. I end by highlighting an implication for scientific realism.
This article examines the case for preferring density matrix realism over wave function realism, as an approach to the fundamental ontology of our world. To date, there are two arguments that have been used to motivate density matrix realism. One is that we get a simpler and more appealing metaphysics if we move from wave function realism to density matrix realism. The second is that density matrices are more general than wave functions. In both cases, a key purported advantage is that density matrix realists can allow that the universe could be in a mixed state. To be convincing, however, these arguments can’t simply assume that our universe could be in a mixed state, since standard definitions of mixedness seem to preclude such a possibility. Thus, to make density matrix realism plausible, one would need to appeal to some scientifically backed argument that standard definitions of mixedness need revision, that what seemed to be perplexing before represents a genuine way that our world could fundamentally be. Here, Hawking’s model of black hole evaporation seems poised to come to the rescue, and so, we develop a novel argument to this effect. Although we find this way of arguing for density matrix realism to be intriguing and worthy of investigation, we show that there is substantial reason to be cautious. Most physicists, including Hawking, believe that this model will be superseded by a more fundamental theory of quantum gravity. Despite a lack of agreement on the details of such a theory, the guiding principles that do enjoy some consensus point away from an interpretation of black hole evaporation in which the universe as a whole evolves into an (objectively) mixed state. We conclude that there do not seem to be compelling motivations coming from fundamental physics to favour a metaphysics in which the universe is fundamentally a density matrix rather than a wave function.
What is the quantum state of the universe? Although there have been several interesting suggestions, the question remains open. In this paper, I consider a natural choice for the universal quantum state arising from the Past Hypothesis, a boundary condition that accounts for the time-asymmetry of the universe. The natural choice is given not by a wave function (representing a pure state) but by a density matrix (representing a mixed state). I begin by classifying quantum theories into two types: theories with a fundamental wave function and theories with a fundamental density matrix. The Past Hypothesis is compatible with infinitely many initial wave functions, none of which seems to be particularly natural. However, once we turn to density matrices, the Past Hypothesis provides a natural choice---the normalized projection onto the Past Hypothesis subspace in the Hilbert space. Nevertheless, the two types of theories can be empirically equivalent. To provide a concrete understanding of the empirical equivalence, I provide a novel subsystem analysis in the context of Bohmian theories. Given the empirical equivalence, it seems empirically underdetermined whether the universe is in a pure state or a mixed state. Finally, I discuss some theoretical payoffs of the density-matrix theories and present some open problems for future research.
In a quantum universe with a strong arrow of time, we postulate a low-entropy boundary condition (the past hypothesis, PH) to account for the temporal asymmetry. In this article, I show that the PH also contains enough information to simplify the quantum ontology and define a natural initial condition. First, I introduce ‘density-matrix realism’, the thesis that the quantum state of the universe is objective and impure. This stands in sharp contrast to wave-function realism, the thesis that the quantum state of the universe is objective and pure. Second, I suggest that the PH is sufficient to determine a natural density matrix, which is simple and unique. This is achieved by what I call the ‘initial projection hypothesis’: the initial density matrix of the universe is the (normalized) projection onto the PH-subspace (in the Hilbert space). Third, because the initial quantum state is unique and simple, we have a strong case for the nomological thesis: the initial quantum state of the universe is on a par with laws of nature. This new package of ideas has several interesting implications, including on the harmony between statistical mechanics and quantum mechanics, theoretical unity of the universe and the subsystems, and the alleged conflict between Humean supervenience and quantum entanglement.
Abstract What are the ontological implications of quantum theories, that is, what do they tell us about the fundamental objects that make up our world? How should quantum theories make us reevaluate our classical conceptions of the basic constitution of material objects and ourselves? Is there fundamental quantum nonlocality? This book articulates several rival approaches to answering these questions, ultimately defending the wave function realist approach. Wave function realism is a way of interpreting quantum theories so that the central object they describe is the quantum wave function, interpreted as a field in an extremely high-dimensional space. According to this approach, the nonseparability and nonlocality we seem to find in quantum mechanics are ultimately manifestations of a more intuitive, separable, and local picture in higher dimensions.
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.