Craig Callender

Co-authored by a mathematical physicist and a philosopher of science, this book is a welcome addition to the growing literature in the foundations of thermodynamics and statistical mechanics. A large and inter-disciplinary book, it contains an impressive range of information about the history, philosophy, and mathematics of thermostatistical physics. Fourteen chapters of physics and history of physics are sandwiched between two more philosophical chapters on the nature of theories and models. Throughout these middle chapters the authors describe, more or less in historical order, a range of topics, including thermodynamics, kinetic theory, probability theory, ergodicity, phase transitions and more. The concentration is on the mathematical models used to describe physical systems. Usually the models are set in their historical context before being described. The necessary mathematical facts are either introduced or relegated to one of the five appendices. References for further reading are copious: there are almost sixty pages of references.

Throughout this century many philosophers and physicists have gone for thc ‘big ki11’ regarding tenses. They have tried to show via McTaggart’s paradox and special relativity that tcnscs arc logically and physically impossible, rcspcctivcly. Ncithcr attempt succccds, though as I argue, both lcavc their mark. In thc iirst two sections of thc paper I introduce some conceptual difficulties for the tensed theory of time. The next section then discusses the standing 0f tenses in light of special relativity, cspccially rcccnt work by Stcin on thc topic. I argue that, Stcin’s possibility thcorcm notwithstanding, special relativity is inconsistent with any philosophicully interesting conception of tense. Finally, I search for help for tenses in the broader context of quantum theory, Lorcntzian interpretations 0f time dilation/length contraction, and gcncral relativistic spacctimcs. I suggest that these avenues d0 not provide tenses the home for which some have hoped.

A persistent question about the deBroglie–Bohm interpretation of quantum mechanics concerns the understanding of Born’s rule in the theory. Where do the quantum mechanical probabilities come from? How are they to be interpreted? These are the problems of emergence and interpretation. In more than 50 years no consensus regarding the answers has been achieved. Indeed, mirroring the foundational disputes in statistical mechanics, the answers to each question are surprisingly diverse. This paper is an opinionated survey of this literature. While acknowledging the pros and cons of various positions, it defends particular answers to how the probabilities emerge from Bohmian mechanics and how they ought to be interpreted.

Must space be a unity? This question, which exercised Aristotle, Descartes and Kant, is a specific instance of a more general one; namely, can the topology of physical space change with time? In this paper we show how the discussion of the unity of space has been altered but survives in contemporary research in theoretical physics. With a pedagogical review of the role played by the Euler characteristic in the mathematics of relativistic spacetimes, we explain how classical general relativity (modulo considerations about energy conditions) allows virtually unrestrained spatial topology change in four dimensions. We also survey the situation in many other dimensions of interest. However, topology change comes with a cost: a famous theorem by Robert Geroch shows that, for many interesting types of such change, transitions of spatial topology imply the existence of closed timelike curves or temporal non-orientability. Ways of living with this theorem and of evading it are discussed.

This paper considers the possibility that nonrelativistic quantum mechanics tells us that Nature cares about time reversal. In a classical world we have a fundamentally reversible world that appears irreversible at higher levels, e.g., the thermodynamic level. But in a quantum world we see, if I am correct, a fundamentally irreversible world that appears reversible at higher levels, e.g., the level of classical mechanics. I consider two related symmetries, time reversal invariance and what I call ‘Wigner reversal invariance.’ Violation of the first is interesting, for not only would it fly in the face of the usual story about temporal symmetry, but it also appears to imply (as I’ll explain) that time is ‘handed’, or as some have misleadingly said in the literature, ‘anisotropic’. Violation of the second is, as I hope to show, even more interesting. The paper also contains a discussion of two mostly neglected topics: what it means to say time is handed and what warrants such an attribution to time.

Are the generalizations of classical equilibrium thermodynamics true of self-gravitating systems? This question has not been addressed from a foundational perspective, but here I tackle it through a study of the “paradoxes” commonly said to afflict such systems. My goals are twofold: (a) to show that the “paradoxes” raise many questions rarely discussed in the philosophical foundations literature, and (b) to counter the idea that these “paradoxes” spell the end for gravitational equilibrium thermodynamics

For much of this century, philosophers hoped that Einstein’s general theory of relativity would play the role of physician to philosophy. Its development would positively influence the philosophy of methodology and confirmation, and its ontology would answer many traditional philosophical debates—for example, the issue of spacetime substantivalism. In physics, by contrast, the attitude is increasingly that GTR itself needs a physician. The more we learn about GTR the more we discover how odd are the spacetimes that it allows. Not only does GTR permit singularities, naked and clothed, but it allows time travel, topology change, and event and particle horizons, to name but a few of these oddities. Rather than revel in the riches of the theory, however, many physicists seek to rule out one or more of the above “pathologies” on the grounds that they are “physically unreasonable.” Thus contemporary researchers hawk various “cures” for the “illnesses” of GTR: among them, Chronology Protection to ensure against time travel, Cosmic Censorship for naked singularities, Inflation for horizons, and so on. The physics of these illnesses and cures, and the problems they engender, are the source of much controversy in the physics literature. Philosophers have largely neglected it. But clearly the subject needs philosophers of physics to determine whether the patient is genuinely ailing, and if so, to sift the real antidotes from the snake oil.

For much of this century, philosophers hoped that Einstein’s general theory of relativity would play the role of physician to philosophy. Its development would positively influence the philosophy of methodology and confirmation, and its ontology would answer many traditional philosophical debates—for example, the issue of spacetime substantivalism. In physics, by contrast, the attitude is increasingly that GTR itself needs a physician. The more we learn about GTR the more we discover how odd are the spacetimes that it allows. Not only does GTR permit singularities, naked and clothed, but it allows time travel, topology change, and event and particle horizons, to name but a few of these oddities. Rather than revel in the riches of the theory, however, many physicists seek to rule out one or more of the above “pathologies” on the grounds that they are “physically unreasonable.” Thus contemporary researchers hawk various “cures” for the “illnesses” of GTR: among them, Chronology Protection to ensure against time travel, Cosmic Censorship for naked singularities, Inflation for horizons, and so on. The physics of these illnesses and cures, and the problems they engender, are the source of much controversy in the physics literature. Philosophers have largely neglected it. But clearly the subject needs philosophers of physics to determine whether the patient is genuinely ailing, and if so, to sift the real antidotes from the snake oil.

The manifest image is teeming with activity. Objects are booming and buzzing by, changing their locations and properties, vivid perceptions are replaced, and we seem to be inexorably slipping into the future. Time—or at least our experience in time— seems a very turbulent sort of thing. By contrast, time in the scientist image seems very still. The fundamental laws of physics don’t differentiate between past and future, nor do they pick out a present moment that flows. Except for a minus sign in the relativistic metric, there are few differences between the temporal and spatial coordinates in natural science. We seem to have, to echo another debate, an “explanatory gap” between time as we find it in experience and as we find it in science. Reconciling these two images of the world is the principal goal of philosophy of time

Unlike the relativity theory it seeks to replace, causal set theory has been interpreted to leave space for a substantive, though perhaps ‘localized’, form of ‘becoming’. The possibility of fundamental becoming is nourished by the fact that the analogue of Stein’s theorem from special relativity does not hold in causal set theory. Despite this, we find that in many ways, the debate concerning becoming parallels the well-rehearsed lines it follows in the domain of relativity. We present, however, some new twists and challenges. In particular, we show that a novel and exotic notion of becoming is compatible with causal sets. In contrast to the ‘localized’ becoming considered compatible with the dynamics of causal set theory by its advocates, our novel kind of becoming, while not answering to the typical A-theoretic demands, is ‘global’ and objective.

How should one discount utility across time? The conventional wisdom in social science is that one should use an exponential discount function. Such a function is a representation of the axioms that provide a well-defined utility function plus a condition known as stationarity. Yet stationarity doesnt really have much intuitive normative pull on its own. Here I try to cast it in a normative glow by deriving stationarity from two explicitly normative premises, both suggested by the philosophical thesis of temporal neutralism. Putting the argument in this form helps us better understand exponential discounting and challenges to it.

This paper challenges the conventional wisdom dominating the social sciences and philosophy regarding temporal discounting, the practice of discounting the value of future utility when making decisions. Although there are sharp disagreements about temporal discounting, a kind of standard model has arisen, one that begins with a normative standard about how we should make intertemporal comparisons of utility. This standard demands that in so far as one is rational one discounts utilities at future times with an exponential discount function. Tracing the justification for this standard through economics, philosophy and psychology, I’ll make what I believe is the best case one can for it, showing how a non-arbitrariness assumption and a dominance argument together imply that discounting ought to be exponential. Ultimately, however, I don’t find the case compelling. Non-exponential temporal discounting is often rational. If this is correct, Instead of trying to ‘fix’ non-exponential discounting because it is irrational and associated with negative life outcomes, we might instead focus attention on why the conditions obtain that make such discounting rational.

No shield can protect scientific realism from dealing with the quantum measurement problem. One may be able to erect barriers around the observable or classical, preserving a realism about tables, chairs and the like, but there is no safety zone within the quantum realm, the domain of our best physical theory. The upshot is not necessarily that scientific realism is in trouble. That conclusion demands further arguments. The lesson instead may be that scientific realists ought to stake their case on particular interpretations of quantum theory. In any case, the realist can’t ignore the interpretational issues plaguing quantum mechanics.

Two females, Nadine and Fatu, are the sole surviving Northern White Rhinos (NWR). The subspecies is functionally extinct. Hope for NWR now lies in emerging reproductive and genetic technologies, which could potentially produce NWR from induced pluripotent stem cells. What is the rationale for this project? This question raises almost every philosophical issue facing conservation science today. I argue that NWR recovery is hard to justify via many traditional paths (e.g., historical fidelity, ecosystem health, biodiversity), but if we shift focus to white rhinos in general or even mammals then clear benefits emerge.

I show how the two great Humean ways of understanding laws of nature, projectivism and systems theory, have unwittingly reprised developments in metaethics over the past century. This demonstration helps us explain and understand trends in both literatures. It also allows work on laws to “leap- frog” over the birth of many new positions, the nomic counterparts of new theories in metaethics. However, like leap-frogging from agriculture to the internet age, it’s hardly clear that we’ve landed in a good place. My reactionary advice is to return to Hume and work on the central insights that motivated Humeanism about modality in the first place. When updated with contemporary insights, there we will find an attractive naturalistic theory of laws, or so I’ll argue, and along the way we’ll see how projectivism and systems theory both get something right about this overall theory.

This article is an introduction to and advertisement of Erwin Schrödinger’s little-known real-valued wave equation, the first published time dependent Schrödinger equation. I argue that this equation is not merely a historical curiosity. Not only does it show that quantum mechanics need not be viewed as essentially complex-valued, but the real formalism also provides a deep insight into the puzzling nature of time reversal in a quantum world. It is hoped that this observation will stimulate the discovery of other areas where ‘keeping it real’ will prove pedagogically or foundationally useful.

is the thesis that everything supervenes upon the spatiotemporal distribution of local intrinsic qualities. A recent threat to HS, originating in thought experiments by Armstrong and Kripke, claims that the mere possibility of rotating homogeneous discs proves HS false. I argue that the rotating disc argument (RDA) fails. If I am right, Humeans needn't abandon or alter HS to make sense of rotating homogeneous discs. Homogeneous discs, as necessarily understood by RDA, are not the sorts of things in which we should believe. These discs do not belong in our ontology - not because there is a problem with their homogeneity, but (surprisingly) because there is a problem with their rotation. RDA is shown to be a kind of parody of classic arguments for spatial substantivalism.

ABSTRACT Unlike the relativity theory it seeks to replace, causal set theory has been interpreted to leave space for a substantive, though perhaps ‘localized’, form of ‘becoming’. The possibility of fundamental becoming is nourished by the fact that the analogue of Stein’s theorem from special relativity does not hold in CST. Despite this, we find that in many ways, the debate concerning becoming parallels the well-rehearsed lines it follows in the domain of relativity. We present, however, some new twists and challenges. In particular, we show that a novel and exotic notion of becoming is compatible with causal sets. In contrast to the localized becoming considered compatible with the dynamics of CST by its advocates, our novel kind of becoming, while not answering to the typical A-theoretic demands, is global and objective. _1_ Introduction _2_ The Basics of Causal Set Theory _3_ Facing the Same Dilemma? _4_ Taking Growth Seriously _5_ Conclusion

This chapter unfolds a central philosophical problem of statistical mechanics. This problem lies in a clash between the Static Probabilities offered by statistical mechanics and the Dynamic Probabilities provided by classical or quantum mechanics. The chapter looks at the Boltzmann and Gibbs approaches in statistical mechanics and construes some of the great controversies in the field — for instance the Reversibility Paradox — as instances of this conflict. It furthermore argues that a response to this conflict is a critical choice that shapes one's understanding of statistical mechanics itself, namely, whether it is to be conceived as a special or fundamental science. The chapter details some of the pitfalls of the latter ‘globalist’ position and seeks defensible ground for a kind of ‘localist’ alternative.