Recently, proponents of Humean Supervenience have challenged the plausibility of the intuition that the laws of nature ‘govern’, or guide, the evolution of events in the universe. Certain influential thought experiments authored by John Carroll, Michael Tooley, and others, rely strongly on such intuitions. These thought experiments are generally regarded as playing a central role in the lawhood debate, suggesting that the Mill-Ramsey-Lewis view of the laws of nature, and the related doctrine of the Humean Supervenience of laws, are false. (...) In this paper, I take on these recent challenges, arguing that the intuition that the laws govern should be taken seriously. Still, I find the recent discussions insightful, in certain ways. Employing some ideas from one of the critics, I draw some non-standard conclusions about the significance of the thought experiments to the lawhood debate. (shrink)

I argue that none of the usual interpretations of probability provide an adequate interpretation of probabilistic theories in science. Assuming that the aim of such theories is to capture noisy relationships in the world, I suggest that we do not have to give them classical truth-conditional content at all: their probabilities can remain uninterpreted. Indirectly, this account turns out to explain what is right about the frequency interpretation, the best-systems interpretation, and the epistemic interpretation.

I argue that there are such things as nomological probabilities—probabilities that play a certain explanatory role with respect to stable, long-run relative frequencies. Indeed, I argue, we should be willing to accept nomological probabilities even if they turn out to be metaphysically weird or even wholly sui generis entities. I then give an example of one way in which this argument should shape future work on the metaphysics of chance by describing a challenge to a common group of analyses of (...) objective probability—Humean analyses— understood as analyses of nomological probability. (shrink)

In a world awash in statistical patterns, should we conclude that the universe’s evolution or genesis is somehow subject to chance? I draw attention to alternatives that must be acknowledged if we are to have an adequate assessment of what chance the universe might have had.

The conspicuous similarities between interpretive strategies in classical statistical mechanics and in quantum mechanics may be grounded on their employment of common implementations of probability. The objective probabilities which represent the underlying stochasticity of these theories can be naturally associated with three of their common formal features: initial conditions, dynamics, and observables. Various well-known interpretations of the two theories line up with particular choices among these three ways of implementing probability. This perspective has significant application to debates on primitive ontology (...) and to the quantum measurement problem. (shrink)

This paper develops an account of the metaphysics of fundamental laws I call “the Package Deal Account ” that is a descendent of Lewis’ BSA but differs from it in a number of significant ways. It also rejects some elements of the metaphysics in which Lewis develops his BSA. First, Lewis proposed a metaphysical thesis about fundamental properties he calls “Humean Supervenience” according to which all fundamental properties are instantiated by points or point sized individuals and the only fundamental relations (...) are geometrical spatial and temporal relations between these. While the BSA does not require HS Lewis seems to hope that it is true. In contrast, the PDA is not committed to HS or even to the fundamental arena in which fundamental properties are instantiated possessing geometrical structure and thus is able to accommodate relations and structures found in contemporary physics that apparently conflict with HS. Second, although Lewis’ BSA doesn’t require HS his Humeanism does require that fundamental properties are categorical. In contrast, the PDA allows for the possibility that fundamental properties are individuated in terms of laws and so are not categorical. Third, the PDA expands and develops the criteria for what counts in favor of a candidate system with more attention to the criteria employed by physicists in evaluating proposed theories. Fourth and most importantly, unlike Lewis’ BSA, the PDA does not presuppose metaphysically primitive elite properties/quantities that Lewis calls “perfectly natural” properties/quantities or presuppose a metaphysically preferred language whose terms denote such properties/quantities. It replaces Lewis’ account with an account on which natural properties are not metaphysically prior to the laws but are elements of a package that includes a fundamental arena that plays the role of space-time as well as fundamental laws and properties. By doing so it responds to some epistemological and metaphysical issues that have been raised regarding natural properties and their role in the BSA. In sum, the PDA goes further in explicating the notion of laws in terms of the aims and practices of science especially fundamental physics rather than in terms of prior metaphysics. I begin by reviewing Lewis’ account of perfectly natural properties and his Humean BSA of laws. (shrink)

This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a philosophical discussion of randomness in general, I argue that deterministic interpretations of quantum mechanics are strictly speaking incompatible with the Born rule. I also stress the role of outliers, i.e. measurement outcomes that are not 1-random. Although these occur with low probability, their very existence implies that the no-signaling (...) principle used in proofs of randomness of outcomes of quantum-mechanical measurements should be reinterpreted statistically, like the second law of thermodynamics. In three appendices I discuss the Born rule and its status in both single and repeated experiments, review the notion of 1-randomness that in various guises was investigated by Kolmogorov and others and treat Bell’s Theorem and the Free Will Theorem with their implications for randomness. (shrink)

Sober and Huemer have independently argued that simplicity has no place in evaluating philosophical views. In particular, they have argued that the best rationales for scientists to appeal to simplicity in judging between rival theories fail to carry over to philosophers judging between rival philosophical accounts. This paper disagrees with Sober and Huemer. It argues that two rationales for scientific appeals to simplicity equally well underwrite appeals to simplicity when philosophers evaluate rival rational reconstructions of some social normative practice. These (...) two rationales are shown to apply to two philosophical appeals to simplicity: in Quine’s argument against analyticity and in an argument against pluralism in accounts of scientific explanation. Some factors are identified that influence how much weight simplicity should carry in these and other philosophical cases. Simplicity’s legitimate role in evaluating rival rational reconstructions suggests that simplicity will also turn out to be justly relevant to ontological investigations. (shrink)

Abstract: This paper develops and advocates a rule for assigning self-locating credences in quantum branching scenarios, called Indexed Branch-Counting. It is argued that Indexed Branch-Counting can be justified on both accuracy-theoretic grounds and on the grounds that it satisfies a requirement of exchangeability for probability assignments. Since Indexed Branch-Counting diverges from the Born Rule, this poses trouble for Everettian approaches to probability. The paper also addresses a common argument against branch-counting, namely that the rule is incoherent in light of putative (...) vagueness in the number of branches. Finally, the paper addresses a recent proposal from Simon Saunders that aims to reconcile branch-counting with the Born Rule, arguing that the proposal faces challenges. (shrink)

Waiting time is widely used in health and social policy to make resource allocation decisions, yet no general account of the moral significance of waiting time exists. We provide such an account. We argue that waiting time is not intrinsically morally significant, and that the first person in a queue for a resource does not ipso facto have a right to receive that resource first. However, waiting time can and sometimes should play a role in justifying allocation decisions. First, there (...) is a duty of fairness prohibiting line-cutting where a sufficiently just queue exists. Second, waiting time has several morally attractive features that can justify its incorporation into allocation schemes. Where candidates are in relevantly similar circumstances, allocating by waiting time is relatively efficient, maximizes distribution equality relative to other Pareto efficient distributions, and treats candidates fairly. The claim that allocation using waiting time is fair is controversial. Some have claimed that formal lotteries are a fairer way to select among equal beneficiaries. We argue that lotteries are no fairer than allocation based on waiting time when it is equiprobable how a prospective queue will be ordered. In practice, lotteries share many of the disadvantages of queues; which is fairer will depend on contingent features of the allocation scenario. The upshot is that first-come, first-served is in fact a just way to allocate resources in many of the cases where it seems pre-theoretically compelling, and waiting time has unique normative properties which frequently justify its incorporation into resource allocation schemes. (shrink)

Philosophers now seem to agree that frequentism is an untenable strategy to explain the meaning of probabilities. Nevertheless, I want to revive frequentism, and I will do so by grounding probabilities on typicality in the same way as the thermodynamic arrow of time can be grounded on typicality within statistical mechanics. This account, which I will call typicality frequentism, will evade the major criticisms raised against previous forms of frequentism. In this theory, probabilities arise within a physical theory from statistical (...) behavior of almost all initial conditions. The main advantage of typicality frequentism is that it shows which kinds of probabilities (that also have empirical relevance) can be derived from physics. Although one cannot recover all probability talk in this account, this is rather a virtue than a vice, because it shows which types of probabilities can in fact arise from physics and which types need to be explained in different ways, thereby opening the path for a pluralistic account of probabilities. (shrink)

What explains the outcomes of chance processes? We claim that their setups do. Chances, we think, mediate these explanations of outcome by setup but do not feature in them. Facts about chances do feature in explanations of a different kind: higher-order explanations, which explain how and why setups explain their outcomes. In this paper, we elucidate this 'mediator view' of chancy explanation and defend it from a series of objections. We then show how it changes the playing field in four (...) metaphysical disputes concerning chance. First, it makes it more plausible that even low chances can have explanatory power. Second, it undercuts a circularity objection against reductionist theories of chance. Third, it redirects the debate about a prominent argument against epistemic theories of chance. Finally, it sheds light on potential chancy explanations of the Universe's origin. (shrink)

In a deterministically evolving world, the usefulness of nontrivial probabilities can seem mysterious. I use the ‘Mentaculus’ machinery developed by David Albert and Barry Loewer to show how all probabilities in such a world can be derived from a single, initial chance event. I go on to argue that this is the only genuine chance event. Perhaps surprisingly, we have good evidence of its existence and nature. I argue that the existence of this chance event justifies our epistemic reliance on (...) nontrivial probabilities. (shrink)

What grounds facts of ground? Some metaphysicians invoke fundamental grounding laws to answer this question. These are general principles that link grounded facts to their grounds. The main business of this paper is to advance the debate about the metaphysics of grounding laws by exploring the prospects of a plausible yet underexplored minimalist account, one which is structurally analogous to a familiar Humean conception of natural laws. In the positive part of this paper, I articulate such a novel view and (...) argue for its merits. The minimalist account shuns essences and takes laws to be unmysterious elite regularities. Therefore, it is a promising alternative for theorists of ground who spurn the acceptance of essentialism about the grounding laws but think that these are needed in our theorizing. In the negative part, I argue that widely accepted principles of ground, coupled with the tenets of minimalism, jeopardize the fundamentality of the grounding laws. I discuss two immediately available and prima facie appealing strategies to evade this threat. However, I show that both have undesirable theoretical costs. I conclude by casting doubts on whether the benefits of a minimalist account of fundamental grounding laws outweigh such costs. (shrink)

I present an account of deterministic chance which builds upon the physico-mathematical approach to theorizing about deterministic chance known as 'the method of arbitrary functions'. This approach promisingly yields deterministic probabilities which align with what we take the chances to be---it tells us that there is approximately a 1/2 probability of a spun roulette wheel stopping on black, and approximately a 1/2 probability of a flipped coin landing heads up---but it requires some probabilistic materials to work with. I contend that (...) the right probabilistic materials are found in reasonable initial credence distributions. I note that, with some normative assumptions, the resulting account entails that deterministic chances obey a variant of Lewis's 'principal principle'. I additionally argue that deterministic chances, so understood, are capable of explaining long-run frequencies. (shrink)

If the laws of nature are as the Humean believes, it is an unexplained cosmic coincidence that the actual Humean mosaic is as extremely regular as it is. This is a strong and well-known objection to the Humean account of laws. Yet, as reasonable as this objection may seem, it is nowadays sometimes dismissed. The reason: its unjustified implicit assignment of equiprobability to each possible Humean mosaic; that is, its assumption of the principle of indifference, which has been attacked on (...) many grounds ever since it was first proposed. In place of equiprobability, recent formal models represent the doxastic state of total ignorance as suspension of judgment. In this paper I revisit the cosmic coincidence objection to Humean laws by assessing which doxastic state we should endorse. By focusing on specific features of our scenario I conclude that suspending judgment results in an unnecessarily weak doxastic state. First, I point out that recent literature in epistemology has provided independent justifications of the principle of indifference. Second, given that the argument is framed within a Humean metaphysics, it turns out that we are warranted to appeal to these justifications and assign a uniform and additive credence distribution among Humean mosaics. This leads us to conclude that, contrary to widespread opinion, we should not dismiss the cosmic coincidence objection to the Humean account of laws. (shrink)

Reichenbach explains temporally asymmetric phenomena by appeal to entropy and ‘branch structure’. He explains why the entropic gradients of isolated subsystems are oriented towards the future and not the past, and why we have records of the past and not the future, by appeal to the fact that the universe is currently on a long entropic upgrade with subsystems that branch off and become quasi-isolated. Reichenbach’s approach has been criticised for relying too closely on entropy. The more popular approach nowadays (...) is to appeal instead to a particular low-entropy initial state—Albert’s ‘Past Hypothesis’. I’ll argue that this neglect of Reichenbach’s approach is unwarranted. A Reichenbachian account has important advantages over Albert’s: it correctly identifies the minimal temporally asymmetric posit needed to derive key temporally asymmetries and it offers a more adequate account of the record asymmetry. While a Reichenbachian account needs to be supplemented, it provides the right foundations for explaining temporally asymmetric phenomena and what we might ultimately mean by ‘the direction of time’. (shrink)

What's the point of time travel? Not to change the past; no matter how carefully a time traveler plans, all of her attempts to change the past end in failure. Paul Horwich has argued that the implausibility of such failures gives us reason to doubt that there will be frequent time travel to the local past. I defend a modified version of Horwich's argument and show how we might gain evidence about the chance of there being frequent time travel in (...) the future without having any information that explains why that chance value obtains. (shrink)

According to David Lewis’s Principal Principle, our beliefs about the objective chances of outcomes determine our rational credences in those outcomes. Lewis influentially argues that any adequate metaphysics of objective chance must explain why the Principal Principle holds. Since no theory of chance is widely agreed to have met this burden, I suggest we change tack. On the view I develop, a central aspect of the Principal Principle holds not because of what objective chances are but rather because of the (...) explanatory role that objective chances play for the rational agents who believe in them. (shrink)

One of the most difficult problems in the foundations of physics is what gives rise to the arrow of time. Since the fundamental dynamical laws of physics are (essentially) symmetric in time, the explanation for time's arrow must come from elsewhere. A promising explanation introduces a special cosmological initial condition, now called the Past Hypothesis: the universe started in a low-entropy state. Unfortunately, in a universe where there are many copies of us (in the distant ''past'' or the distant ''future''), (...) the Past Hypothesis is not enough; we also need to postulate self-locating (de se) probabilities. However, I show that we can similarly use self-locating probabilities to strengthen its rival---the Fluctuation Hypothesis, leading to in-principle empirical underdetermination and radical epistemological skepticism. The underdetermination is robust in the sense that it is not resolved by the usual appeal to 'empirical coherence' or 'simplicity.' That is a serious problem for the vision of providing a completely scientific explanation of time's arrow. (shrink)

In a quantum universe with a strong arrow of time, we postulate a low-entropy boundary condition to account for the temporal asymmetry. In this paper, I show that the Past Hypothesis also contains enough information to simplify the quantum ontology and define a unique initial condition in such a world. First, I introduce Density Matrix Realism, the thesis that the quantum universe is described by a fundamental density matrix that represents something objective. This stands in sharp contrast to Wave Function (...) Realism, the thesis that the quantum universe is described by a wave function that represents something objective. Second, I suggest that the Past Hypothesis is sufficient to determine a unique and simple density matrix. This is achieved by what I call the Initial Projection Hypothesis: the initial density matrix of the universe is the normalized projection onto the special low-dimensional Hilbert space. Third, because the initial quantum state is unique and simple, we have a strong case for the \emph{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, the dynamic unity of the universe and the subsystems, and the alleged conflict between Humean supervenience and quantum entanglement. (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)

We review the question of whether objective chances are compatible with determinism. We first outline what we mean by chance and what we mean by determinism. We then look at the alleged incompatibility between those concepts. Finally, we look at some ways that one might attempt to overcome the incompatibility.

Why do we value higher-level scientific explanations if, ultimately, the world is physical? An attractive answer is that physical explanations often cite facts that don’t make a difference to the event in question. I claim that to properly develop this view we need to commit to a type of deterministic chance. And in doing so, we see the theoretical utility of deterministic chance, giving us reason to accept a package of views including deterministic chance.

Fine-tuning in physics and cosmology is often used as evidence that a theory is incomplete. For example, the parameters of the standard model of particle physics are “unnaturally” small, which has driven much of the search for physics beyond the standard model. Of particular interest is the fine-tuning of the universe for life, which suggests that our universe’s ability to create physical life forms is improbable and in need of explanation, perhaps by a multiverse. This claim has been challenged on (...) the grounds that the relevant probability measure cannot be justified because it cannot be normalized, and so small probabilities cannot be inferred. We show how fine-tuning can be formulated within the context of Bayesian theory testing in the physical sciences. The normalizability problem is seen to be a general problem for testing any theory with free parameters, and not a unique problem for fine-tuning. Physical theories in fact avoid such problems in one of two ways. Dimensional parameters are bounded by the Planck scale, avoiding troublesome infinities, and we are not compelled to assume that dimensionless parameters are distributed uniformly, which avoids non-normalizability. (shrink)

According to Humean theories of objective chance, the chances reduce to patterns in the history of occurrent events, such as frequencies. According to non-Humean accounts, the chances are metaphysically fundamental, existing independently of the "Humean Mosaic" of actually-occurring events. It is therefore possible, by the lights of non-Humeanism, for the chances and the frequencies to diverge wildly. Humeans often allege that this undermines the ability of non-Humean accounts of chance to rationalize adherence to David Lewis' Principal Principle (PP), which states (...) that an agent's degrees of belief should match what they take to be the objective chances. In this paper, I propose two approaches to justifying (PP) for non-Humean chance, hence defusing the Humean objection. The first approach justifies (PP) via the role it plays in informing outright beliefs about long-run frequencies. The second approach justifies (PP) by showing that adherence to (PP), even for non-Humean chance, maximizes expected epistemic utility according to the actual objective chance function. I then address an objection to this approach, concerning the alleged circularity of the derivations. (shrink)

How should we give accounts of scientific modal relations? According to the Humean, we should do so by considering the role of such relations in our lives and scientific theorizing. For example, to give a Humean account of chance, we need to identity a non-modal relation that can play the ‘role’ of chance—typically that of guiding credences and scientifically explaining events. Defenders of Humean accounts claim to be uniquely well placed to meet this aim. Humean chances are objective, and so (...) suitable for explaining. Humean chances reduce to patterns in actual events in a way that limits the possible divergence between relative frequencies and chances. So, they argue, Humean chances can uniquely be shown to satisfy chance−credence principles. I’ll argue that Humeans have no special advantage. When used in scientific contexts, Humean chances must be allowed to diverge from the relative frequencies. So, when considering the scientific question of whether agents who align their credences to the chances will do well, it is merely probable that they will. This scientific use of chance undercuts the Humean’s claimed advantage over their rivals. This undercutting also points to a deeper tension in Humeanism: Humeans must either give up the aim of recovering scientific practice, or live with a disunity between science and metaphysics. While a focus on function is laudable, the motivation for being Humean must come from elsewhere. (shrink)

In this paper, I defend an empiricist account of modality that keeps a substantive account of modal commitment, but throws out the metaphysics. I suggest that if we pair a deflationary attitude toward representation with a substantive account of how scientific models are constructed and put to use, the result is an account that deflates the metaphysics of modal commitment without deflating the content of modal claims.

In a recent article, Gordon Belot uses the so-called undermining phenomenon to try to raise a new difficulty for reductive accounts of objective probability, such as Humean Best System accounts. In this paper I will give a critical discussion of Belot’s paper and argue that, in fact, there is no new difficulty here for chance reductionists to address.

The main objective of this dissertation is to philosophically assess how the use of informational concepts in the field of classical thermostatistical physics has historically evolved from the late 1940s to the present day. I will first analyze in depth the main notions that form the conceptual basis on which 'informational physics' historically unfolded, encompassing (i) different entropy, probability and information notions, (ii) their multiple interpretative variations, and (iii) the formal, numerical and semantic-interpretative relationships among them. In the following, I (...) will assess the history of informational thermophysics during the second half of the twentieth century. Firstly, I analyse the intellectual factors that gave rise to this current in the late forties (i.e., popularization of Shannon's theory, interest in a naturalized epistemology of science, etc.), then study its consolidation in the Brillouinian and Jaynesian programs, and finally claim how Carnap (1977) and his disciples tried to criticize this tendency within the scientific community. Then, I evaluate how informational physics became a predominant intellectual current in the scientific community in the nineties, made possible by the convergence of Jaynesianism and Brillouinism in proposals such as that of Tribus and McIrvine (1971) or Bekenstein (1973) and the application of algorithmic information theory into the thermophysical domain. As a sign of its radicality at this historical stage, I explore the main proposals to include information as part of our physical reality, such as Wheeler’s (1990), Stonier’s (1990) or Landauer’s (1991), detailing the main philosophical arguments (e.g., Timpson, 2013; Lombardi et al. 2016a) against those inflationary attitudes towards information. Following this historical assessment, I systematically analyze whether the descriptive exploitation of informational concepts has historically contributed to providing us with knowledge of thermophysical reality via (i) explaining thermal processes such as equilibrium approximation, (ii) advantageously predicting thermal phenomena, or (iii) enabling understanding of thermal property such as thermodynamic entropy. I argue that these epistemic shortcomings would make it impossible to draw ontological conclusions in a justified way about the physical nature of information. In conclusion, I will argue that the historical exploitation of informational concepts has not contributed significantly to the epistemic progress of thermophysics. This would lead to characterize informational proposals as 'degenerate science' (à la Lakatos 1978a) regarding classical thermostatistical physics or as theoretically underdeveloped regarding the study of the cognitive dynamics of scientists in this physical domain. (shrink)

What is the proper metaphysics of quantum mechanics? In this dissertation, I approach the question from three different but related angles. First, I suggest that the quantum state can be understood intrinsically as relations holding among regions in ordinary space-time, from which we can recover the wave function uniquely up to an equivalence class (by representation and uniqueness theorems). The intrinsic account eliminates certain conventional elements (e.g. overall phase) in the representation of the quantum state. It also dispenses with first-order (...) quantification over mathematical objects, which goes some way towards making the quantum world safe for a nominalistic metaphysics suggested in Field (1980, 2016). Second, I argue that the fundamental space of the quantum world is the low-dimensional physical space and not the high-dimensional space isomorphic to the ``configuration space.'' My arguments are based on considerations about dynamics, empirical adequacy, and symmetries of the quantum mechanics. Third, I show that, when we consider quantum mechanics in a time-asymmetric universe (with a large entropy gradient), we obtain new theoretical and conceptual possibilities. In such a model, we can use the low-entropy boundary condition known as the Past Hypothesis (Albert, 2000) to pin down a natural initial quantum state of the universe. However, the universal quantum state is not a pure state but a mixed state, represented by a density matrix that is the normalized projection onto the Past Hypothesis subspace. This particular choice has interesting consequences for Humean supervenience, statistical mechanical probabilities, and theoretical unity. (shrink)

The paper uses the concept of typicality to spell out an argument against Humean supervenience and the best system account of laws. It proves that, in a very general and robust sense, almost all possible Humean worlds have no Humean laws. They are worlds of irreducible complexity that do not allow for any systematization. After explaining typicality reasoning in general, the implications of this result for the metaphysics of laws are discussed in detail.

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)