Quantum mechanics with a fundamental density matrix has been proposed and discussed recently. Moreover, it has been conjectured that the universe is not in a pure state but in a mixed state in this theory. In this paper, I argue that this mixed state conjecture has two main problems: the redundancy problem and the underdetermination problem, which are lacking in quantum mechanics with a definite initial wave function of the universe.

In this short survey article, I discuss Bell’s theorem and some strategies that attempt to avoid the conclusion of non-locality. I focus on two that intersect with the philosophy of probability: (1) quantum probabilities and (2) superdeterminism. The issues they raised not only apply to a wide class of no-go theorems about quantum mechanics but are also of general philosophical interest.

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.

This book argues for two claims: firstly, determinism in science does not infringe upon human free will because it is descriptive, not prescriptive, and secondly, the very formulation, testing and justification of scientific theories presupposes human free will and thereby persons as ontologically primitive. The argument against predetermination is broadly Humean, or more precisely ‘Super-Humean’, whereas that against naturalist reduction is in large Kantian, drawing from Sellars on the scientific and the manifest image. Thus, whilst the book defends scientific realism (...) against the confusion between fact and fake, it also reveals why scientific theories, laws and explanations cannot succeed in imposing norms for our actions upon us, neither on the level of the individual nor on that of society. Esfeld makes a strong case for an ontology of science that is minimally sufficient to explain our scientific and common sense knowledge, not only removing the concern that the laws of nature are incompatible with human freedom, but furthermore showing how our freedom is in fact a very presupposition for science. (shrink)

Explaining the emergence of stochastic irreversible macroscopic dynamics from time-reversible deterministic microscopic dynamics is one of the key problems in philosophy of physics. The Mori-Zwanzig projection operator formalism, which is one of the most important methods of modern nonequilibrium statistical mechanics, allows for a systematic derivation of irreversible transport equations from reversible microdynamics and thus provides a useful framework for understanding this issue. However, discussions of the MZ formalism in philosophy of physics tend to focus on simple variants rather than (...) on the more sophisticated ones used in modern physical research. In this work, I will close this gap by studying the problems of probability and irreversibility using the example of Grabert’s time-dependent projection operator formalism. This allows to better understand how general proposals for understanding probability in statistical mechanics, namely quantum approaches and almost-objective probabilities, can be accomodated in the MZ formalism. Moreover, I will provide a detailed physical analysis, based on the MZ formalism, of various proposals from the philosophical literature, such as Robertson’s theory of justifying coarse-graining via autonomous macrodynamics, Myrvold’s problem of explaining autonomous macrodynamics, and Wallace’s simple dynamical conjecture. (shrink)

The search for the statistical mechanical underpinning of thermodynamic irreversibility has so far focussed on the spontaneous approach to equilibrium. But this is the search for the underpinning of what Brown and Uffink have dubbed the ‘minus first law’ of thermodynamics. In contrast, the second law tells us that certain interventions on equilibrium states render the initial state ‘irrecoverable’. In this article, I discuss the unusual nature of processes in thermodynamics, and the type of irreversibility that the second law embodies. (...) I then search for the microscopic underpinning or statistical mechanical ‘reductive basis’ of the second law of thermodynamics by taking a functionalist strategy. First, I outline the functional role of the thermodynamic entropy: for a thermally isolated system, the thermodynamic entropy is constant in quasi-static processes, but increasing in non-quasi-static processes. I then search for the statistical mechanical quantity that plays this role—rather than the role of the traditional ‘holy grail’ as described by Callender. I argue that in statistical mechanics, the Gibbs entropy plays this role. (shrink)

According to the doctrine of Super-Humeanism, the world’s mosaic consists only of permanent matter points and changing spatial relations, while all the other entities and features figuring in scientific theories are nomological parameters, whose role is merely to build the best law system. In this paper, I develop an argument against Super-Humeanism by pointing out that it is vulnerable to and does not have the resources to solve the well-known problem of immanent comparisons. Firstly, I show that it cannot endorse (...) a fundamentalist solution à la Lewis, since its two pillars—a minimalist ontology and a best system account of lawhood—would generate, together, a tedious problem of internal coherence. Secondly, I consider anti-fundamentalist strategies, proposed within Humeanism, and find them inapplicable to the Super-Humean doctrine. The concern is that, since it is impossible to choose the best law system within Super-Humeanism, this doctrine may be charged with incoherence. (shrink)

One of the most popular arguments in favor of dualism is the zombie-conceivability argument. It is often argued that the possibility of zombies would entail that mental properties are epiphenomenal. This paper attempts to defuse the argument, offering a model of dualist mental causation which can serve as a basis for a modified, interactionist-friendly zombie argument.

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.

A century after the discovery of quantum mechanics, the meaning of quantum mechanics still remains elusive. This is largely due to the puzzling nature of the wave function, the central object in quantum mechanics. If we are realists about quantum mechanics, how should we understand the wave function? What does it represent? What is its physical meaning? Answering these questions would improve our understanding of what it means to be a realist about quantum mechanics. In this survey article, I review (...) and compare several realist interpretations of the wave function. They fall into three categories: ontological interpretations, nomological interpretations, and the sui generis interpretation. For simplicity, I will focus on non-relativistic quantum mechanics. (shrink)

If there are fundamental laws of nature, can they fail to be exact? In this paper, I consider the possibility that some fundamental laws are vague. I call this phenomenon 'fundamental nomic vagueness.' I characterize fundamental nomic vagueness as the existence of borderline lawful worlds and the presence of several other accompanying features. Under certain assumptions, such vagueness prevents the fundamental physical theory from being completely expressible in the mathematical language. Moreover, I suggest that such vagueness can be regarded as (...) 'vagueness in the world.' For a case study, we turn to the Past Hypothesis, a postulate that (partially) explains the direction of time in our world. We have reasons to take it seriously as a candidate fundamental law of nature. Yet it is vague: it admits borderline (nomologically) possible worlds. An exact version would lead to an untraceable arbitrariness absent in any other fundamental laws. However, the dilemma between fundamental nomic vagueness and untraceable arbitrariness is dissolved in a new quantum theory of time's arrow. (shrink)

Two of the most difficult problems in the foundations of physics are (1) what gives rise to the arrow of time and (2) what the ontology of quantum mechanics is. I propose a unified 'Humean' solution to the two problems. Humeanism allows us to incorporate the Past Hypothesis and the Statistical Postulate into the best system, which we then use to simplify the quantum state of the universe. This enables us to confer the nomological status to the quantum state in (...) a way that adds no significant complexity to the best system and solves the ''supervenient-kind problem'' facing the original version of the Past Hypothesis. We call the resultant theory the Humean unification. It provides a unified explanation of time asymmetry and quantum entanglement. On this theory, what gives rise to time's arrow is also responsible for quantum phenomena. The new theory has a separable mosaic, a best system that is simple and non-vague, less tension between quantum mechanics and special relativity, and a higher degree of theoretical and dynamical unity. The Humean unification leads to new insights that can be useful to Humeans and non-Humeans alike. (shrink)

Physicists are increasingly beginning to take seriously the possibility of laws outside the traditional time-evolution paradigm; yet many popular definitions of determinism are still predicated on a time-evolution picture, making them manifestly unsuited to the diverse range of research programmes in modern physics. In this article, we use a constraint-based framework to set out a generalization of determinism which does not presuppose temporal evolution, distinguishing between strong, weak and delocalised holistic determinism. We discuss some interesting consequences of these generalized notions (...) of determinism, and we show that this approach sheds new light on the long-standing debate surrounding the nature of objective chance. (shrink)

I summarize, in this informal interview, the main approaches to the ‘Past Hypothesis’, the postulation of a low-entropy initial state of the universe. I’ve chosen this as an open problem in the philosophical foundations of physics. I hope that this brief overview helps readers in gaining perspective and in appreciating the diverse range of approaches in this fascinating unresolved debate.

Despite its apparent complexity, our world seems to be governed by simple laws of physics. This volume provides a philosophical introduction to such laws. I explain how they are connected to some of the central issues in philosophy, such as ontology, possibility, explanation, induction, counterfactuals, time, determinism, and fundamentality. I suggest that laws are fundamental facts that govern the world by constraining its physical possibilities. I examine three hallmarks of laws--simplicity, exactness, and objectivity--and discuss whether and how they may be (...) associated with laws of physics. (shrink)

There is a deeply entrenched view in philosophy and physics, the closed systems view, according to which isolated systems are conceived of as fundamental. On this view, when a system is under the influence of its environment this is described in terms of a coupling between it and a separate system which taken together are isolated. We argue against this view, and in favor of the alternative open systems view, for which systems interacting with their environment are conceived of as (...) fundamental, and the environment's influence is represented via the dynamical equations that govern the system's evolution. Taking quantum theories of closed and open systems as our case study, and considering three alternative notions of fundamentality: (i) ontic fundamentality, (ii) epistemic fundamentality, and (iii) explanatory fundamentality, we argue that the open systems view is fundamental, and that this has important implications for the philosophy of physics, the philosophy of science, and for metaphysics. (shrink)

Thermodynamics is the science that describes much of the time asymmetric behavior found in the world. This entry's first task, consequently, is to show how thermodynamics treats temporally ‘directed’ behavior. It then concentrates on the following two questions. (1) What is the origin of the thermodynamic asymmetry in time? In a world possibly governed by time symmetric laws, how should we understand the time asymmetric laws of thermodynamics? (2) Does the thermodynamic time asymmetry explain the other temporal asymmetries? Does it (...) account, for instance, for the fact that we know more about the past than the future? The discussion thus divides between thermodynamics being an explanandum or explanans. In the former case the answer will be found in philosophy of physics; in the latter case it will be found in metaphysics, epistemology, and other fields, though in each case there will be blurring between the disciplines. (shrink)

A strongly deterministic theory of physics is one that permits exactly one possible history of the universe. In the words of Penrose (1989), "it is not just a matter of the future being determined by the past; the entire history of the universe is fixed, according to some precise mathematical scheme, for all time.” Such an extraordinary feature may appear unattainable in any realistic and simple theory of physics. In this paper, I propose a definition of strong determinism and contrast (...) it with those of standard determinism and super-determinism. Next, I discuss its consequences for explanation, causation, prediction, fundamental properties, free will, and modality. Finally, I present the first example of a realistic, simple, and strongly deterministic physical theory--the Everettian Wentaculus. As a consequence of physical laws, the history of the Everettian multiverse could not have been different. If the Everettian Wentaculus is empirically equivalent to other quantum theories, we can never empirically find out whether or not our world is strongly deterministic. Even if strong determinism fails to be true, it is closer to the actual world than we have presumed, with implications for some of the central topics in philosophy and foundations of physics. (shrink)

What exists at the fundamental level of reality? On the standard picture, the fundamental reality contains (among other things) fundamental matter, such as particles, fields, or even the quantum state. Non-fundamental facts are explained by facts about fundamental matter, at least in part. In this paper, I introduce a non-standard picture called the "cosmic void” in which the universe is devoid of any fundamental material ontology. Facts about tables and chairs are recovered from a special kind of laws that satisfy (...) strong determinism. All non-fundamental facts are completely explained by nomic facts. I discuss a concrete example of this picture in a strongly deterministic version of the many-worlds theory of quantum mechanics. I discuss some philosophical and scientific challenges to this view, as well as some connections to ontological nihilism. (shrink)

Let ℋ be a finite-dimensional complex Hilbert space and D the set of density matrices on ℋ, i.e., the positive operators with trace 1. Our goal in this note is to identify a probability measure u on D that can be regarded as the uniform distribution over D. We propose a measure on D, argue that it can be so regarded, discuss its properties, and compute the joint distribution of the eigenvalues of a random density matrix distributed according to this (...) measure. (shrink)

In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate---the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate about statistical mechanical probabilities according to which the initial wave function is a ''typical'' choice in the macrostate. Together, they support a probabilistic version of the Second Law of Thermodynamics: typical initial wave functions will increase in entropy. Hence, there are two (...) sources of randomness in such a universe: the quantum-mechanical probabilities of the Born rule and the statistical mechanical probabilities of the Statistical Postulate. I propose a new way to understand time's arrow in a quantum universe. It is based on what I call the Thermodynamic Theories of Quantum Mechanics. According to this perspective, there is a natural choice for the initial quantum state of the universe, which is given by not a wave function but by a density matrix. The density matrix plays a microscopic role: it appears in the fundamental dynamical equations of those theories. The density matrix also plays a macroscopic / thermodynamic role: it is exactly the projection operator onto the Past Hypothesis subspace. Thus, given an initial subspace, we obtain a unique choice of the initial density matrix. I call this property "the conditional uniqueness" of the initial quantum state. The conditional uniqueness provides a new and general strategy to eliminate statistical mechanical probabilities in the fundamental physical theories, by which we can reduce the two sources of randomness to only the quantum mechanical one. I also explore the idea of an absolutely unique initial quantum state, in a way that might realize Penrose's idea of a strongly deterministic universe. (shrink)

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 but by a density matrix. 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. (Bibliographic note: the thesis was submitted for the Master of Science in mathematics at Rutgers University.). (shrink)