Thermodynamics and Statistical Mechanics

In 1957, Feyerabend delivered a paper titled ‘On the Quantum-Theory of Measurement’ at the Colston Research Symposium in Bristol to sketch a completion of von Neumann's measurement scheme without collapse, using only unitary quantum dynamics and well-motivated statistical assumptions about macroscopic quantum systems. Feyerabend's paper has been recognised as an early contribution to quantum measurement, anticipating certain aspects of decoherence. Our paper reassesses the physical and philosophical content of Feyerabend's contribution, detailing the technical steps as well as its overall philosophical (...) motivations and consequences. Summarising our results, Feyerabend interpreted collapse as a positivist assumption in quantum mechanics leading to a strict distinction between the uninterpreted formalism of unitary evolution in quantum mechanics and the classically interpreted observational language describing post-measurement outcomes. Thus Feyerabend took the no-collapse completion of the von Neumann measurement scheme to show the dispensability of the positivist assumption, leading the way to a realistic interpretation of quantum theory. We note, however, that there are substantial problems with his account of measurement that bring into question its viability as a legitimate foil to the orthodox view. We further argue that his dissatisfaction with the von Neumann measurement scheme is indicative of early views on theoretical pluralism. (shrink)

The recent use of typicality in statistical mechanics for foundational purposes has stirred an important debate involving both philosophers and physicists. While this debate customarily focuses on technical issues, in this paper I try to approach the problem from an epistemological angle. The discussion is driven by two questions: (1) What does typicality add to the concept of measure? (2) What kind of explanation, if any, does typicality yield? By distinguishing the notions of `typicality-as-vast-majority' and `typicality-as-best-exemplar', I argue that the (...) former goes beyond the concept of measure. Furthermore, I also argue that typicality aims at providing us with a form of causal explanation of equilibrium. (shrink)

The philosophy of superdeterminism is based on a single scientific fact about the universe, namely that cause and effect in physics are not real. In 2020, accomplished Swedish theoretical physicist, Dr. Johan Hansson published a physics proof using Albert Einstein’s Theory of Special Relativity that our universe is superdeterministic meaning a predetermined static block universe without cause and effect in physics. Some argue that Special Relativity is premised on the principle of causality, and therefore, Dr. Hansson’s use of Special Relativity (...) in his proof contradicts his conclusion that cause and effect in physics are not real. However, Special Relativity is not premised on the principle of causality, but rather is consistent with the absence of cause and effect in physics. (shrink)

The fundamental problem on which Ilya Prigogine and the Brussels-Austin Group have focused can be stated briefly as follows. Our observations indicate that there is an arrow of time in our experience of the world (e.g., decay of unstable radioactive atoms like Uranium, or the mixing of cream in coffee). Most of the fundamental equations of physics are time reversible, however, presenting an apparent conflict between our theoretical descriptions and experimental observations. Many have thought that the observed arrow of time (...) was either an artifact of our observations or due to very special initial conditions. An alternative approach, followed by the Brussels-Austin Group, is to consider the observed direction of time to be a basic physical phenomenon and to develop a mathematical formalism that can describe this direction as being due to the dynamics of physical systems. In part I of this essay, I review and assess an attempt to carry out an approach that received much of their attention from the early 1970s to the mid 1980s. In part II, I will discuss their more recent approach using rigged Hilbert spaces. (shrink)

I conduct an empirical analysis of the temporally asymmetric character of our epistemic access to the world by providing an experimental scheme whose results represent the core empirical content of the epistemic asymmetry. I augment this empirical content by formulating a gedanken experiment inspired by a proposal from David Albert. This second experiment cannot be conducted using any technology that is likely to be developed in the foreseeable future, but the expected results help us to state an important constraint on (...) our ability to know the future. Finally, I show that a third experiment concerning precognition, described by Michael Scriven and John Mackie, does not characterize any additional empirical content but does help to illustrate why it is unlikely that any precognition exists. (shrink)

Termodinamica se ocupă cu studiul energiei, a conversiilor sale între diferite forme, cum ar fi căldura, și capacitatea energiei de a produce lucru mecanic. Ea este strâns legată de mecanica statistică, din care pot fi derivate multe relații termodinamice. Se poate argumenta că termodinamica a fost greșit denumită astfel întrucât aceasta nu se referă de fapt la rate de schimbare ca atare și, prin urmare, ar fi fost probabil mai corect ca domeniul să se denumească termostatica. Termodinamica se referă la (...) posibilitatea de declanșare a anumitor reacții chimice, și nu cât de repede au loc acestea. (shrink)

The remarkable connections between gravity and thermodynamics seem to imply that gravity is not fundamental but emergent, and in particular, as Verlinde suggested, gravity is probably an entropic force. In this paper, we will argue that the idea of gravity as an entropic force is debatable. It is shown that there is no convincing analogy between gravity and entropic force in Verlinde’s example. Neither holographic screen nor test particle satisfies all requirements for the existence of entropic force in a thermodynamics (...) system. As a result, there is no entropic force in the gravity system. Furthermore, we show that the entropy increase of the screen is not caused by its statistical tendency to increase entropy as required by the existence of entropic force, but in fact caused by gravity. Therefore, Verlinde’s argument for the entropic origin of gravity is problematic. In addition, we argue that the existence of a minimum size of spacetime, together with the Heisenberg uncertainty principle in quantum theory, may imply the fundamental existence of gravity as a geometric property of spacetime. This provides a further support for the conclusion that gravity is not an entropic force. (shrink)

The Kolmogorov-Sinai entropy is a fairly exotic mathematical concept which has recently aroused some interest on the philosophers’ part. The most salient trait of this concept is its working as a junction between such diverse ambits as statistical mechanics, information theory and algorithm theory. In this paper I argue that, in order to understand this very special feature of the Kolmogorov-Sinai entropy, is essential to reconstruct its genealogy. Somewhat surprisingly, this story takes us as far back as the beginning of (...) celestial mechanics and through some of the most exciting developments of mathematical physics of the 19th century. (shrink)

Many philosophers sympathetic with a Humean understanding of laws of nature have thought that, in the final analysis, the fundamental laws will include not only the traditional dynamical equations, but also two additional principles: the Past Hypothesis and the Statistical Postulate. The former says that the universe began in a particular very-low-entropy macrostate M(0), and the latter posits a uniform probability distribution over the microstates compatible with M(0). Such a view is arguably vindicated by the orthodox Humean Best System Account (...) (BSA). However, I argue here that recent developments of the BSA render the Past Hypothesis otiose. In particular, the trend among Humeans toward a more pragmatic view of laws — according to which the best system is the one that is maximally effective at helping creatures like us amplify our information about the world — does not support the idea that the Past Hypothesis is a law of nature. (shrink)

En esta entrada se mencionan las principales cuestiones en los fundamentos de la mecánica estadı́stica y la termodinámica, y las cuestiones filosóficas en las que repercuten estas áreas de la fı́sica. Al final se añaden lecturas recomendadas, enfatizando las traducidas al español.

I argue that there are two distinct approaches to understanding reduction: the ontology-first approach and the theory-first approach. They concern the relation between ontological reduction and inter-theoretic reduction. Further, I argue for the significance of this distinction by demonstrating that either one or the other approach has been taken as an implicit assumption in, and has in fact shaped, our understanding of what statistical mechanics is. More specifically, I argue that the Boltzmannian framework of statistical mechanics assumes and relies on (...) the ontology-first approach, whereas the Gibbsian framework should assume the theory-first approach. -/- . (shrink)

This report offers a modern perspective on the problem of negative energy, based on a reexamination of the concept of time direction as it arises in a classical and quantum-mechanical context. From this analysis emerges an improved understanding of the general-relativistic stress-energy of matter as being a manifestation of local variations in the energy density of zero-point vacuum fluctuations. Based on those developments, a set of axioms is proposed from which are derived generalized gravitational field equations which actually constitute a (...) simplification of relativity theory in the presence of negative-energy matter and a non-zero cosmological constant. Important clarifications are also achieved regarding the nature of the binary degrees of freedom of matter in the final stages of a gravitational collapse. Those results are then applied to provide original solutions to several long-standing problems in cosmology, including the problem of the nature of dark matter and dark energy, that of the origin of thermodynamic time asymmetry, and several other issues traditionally approached using inflation theory. Finally, we draw on those developments to provide significant new insights into the foundations of quantum theory, regarding, in particular, the problem of quantum non-locality, that of the emergence of time in quantum cosmology, as well as the question of the persistence of quasiclassicality following decoherence. (shrink)

The use of statistical methods to model gravitational systems is crucial to physics practice, but the extent to which thermodynamics and statistical mechanics genuinely apply to these systems is a contentious issue. This paper provides new conceptual foundations for gravitational thermodynamics by reconsidering the nature of key concepts like equilibrium and advancing a novel way of understanding thermodynamics. The challenges arise from the peculiar characteristics of the gravitational potential, leading to non-extensive energy and entropy, negative heat capacity, and a lack (...) of standard equilibrium. Hence it has been claimed that only non-equilibrium statistical mechanics is warranted in this domain, whereas thermodynamics is inapplicable. We argue instead that equilibrium statistical mechanics applies to self-gravitating systems at the relevant scale, as they display equilibrium in the form of metastable quasi-equilibrium states. We then develop a minimal framework for thermodynamics that can be applied to these systems and beyond. Thermodynamics applies in the sense that we can devise macroscopic descriptions and explanations of the behaviour of these systems in terms of coarse-grained quantities like energy and temperature within equilibrium statistical mechanics. (shrink)

The use of statistical methods to model gravitational systems is crucial to physics practice, but the extent to which thermodynamics and statistical mechanics genuinely apply to these systems is a contentious issue. This paper provides new conceptual foundations for gravitational thermodynamics by reconsidering the nature of key concepts like equilibrium and advancing a novel way of understanding thermodynamics. The challenges arise from the peculiar characteristics of the gravitational potential, leading to non-extensive energy and entropy, negative heat capacity, and a lack (...) of standard equilibrium. Hence it has been claimed that only non-equilibrium statistical mechanics is warranted in this domain, whereas thermodynamics is inapplicable. We argue instead that equilibrium statistical mechanics applies to self-gravitating systems at the relevant scale, as they display equilibrium in the form of metastable quasi-equilibrium states. We then develop a minimal framework for thermodynamics that can be applied to these systems and beyond. Thermodynamics applies in the sense that we can devise macroscopic descriptions and explanations of the behaviour of these systems in terms of coarse-grained quantities like energy and temperature within equilibrium statistical mechanics. (shrink)

Some physical theories predict that almost all brains in the universe are Boltzmann brains, i.e. short-lived disembodied brains that are accidentally assembled as a result of thermodynamic or quantum fluctuations. Physicists and philosophers of physics widely regard this proliferation as unacceptable, and so take its prediction as a basis for rejecting these theories. But the putatively unacceptable consequences of this prediction follow only given certain philosophical assumptions. This paper develops a strategy for shielding physical theorizing from the threat of Boltzmann (...) brains. The strategy appeals to a form of phenomenal externalism about the physical basis of consciousness. Given that form of phenomenal externalism, the proliferation of Boltzmann brains turns out to be benign. While the strategy faces a psychophysical fine-tuning problem, it both alleviates cosmological fine-tuning concerns that attend physics-based solutions to Boltzmann brain problems and pays explanatory dividends in connection with time’s arrow. (shrink)

If a proposition is typically true, given your evidence, then you should believe that proposition; or so I argue here. In particular, in this paper, I propose and defend a principle of rationality---call it the `Typical Principle'---which links rational belief to facts about what is typical. As I show, this principle avoids several problems that other, seemingly similar principles face. And as I show, in many cases, this principle implies the verdicts of the Principal Principle: so ultimately, the Typical Principle (...) may be the more fundamental of the two. (shrink)

A family of arguments for black hole evaporation relies on conservation laws, defined through symmetries represented by Killing vector fields which exist globally or asymptotically. However, these symmetries often rely on the idealizations of stationarity and asymptotic flatness, respectively. In non-stationary or non-asymptotically-flat spacetimes where realistic black holes evaporate, the requisite Killing fields typically do not exist. Can we ‘de-idealize’ these idealizations, and subsequently the associated arguments for black hole evaporation? Here, I critically examine the strategy of using ‘approximately Killing’ (...) fields to de-idealize black hole spacetimes and approximately extend conservation laws to non-idealized cases. I argue that this approach encounters significant challenges, undermining the use of these idealizations to justify the evaporation of realistic – rather than idealized – black holes, and raising questions about the justified use of such idealizations. (shrink)

Many argue that the standard understanding of the second law of thermodynamics combined with the supposition, backed by recent scientific evidence, that the future is infinite entails that one is, most likely, a momentary Boltzmann brain that will quickly disintegrate into the cosmos. The argument is as follows: (1) Given infinite time, the universe will eventually reach thermodynamic equilibrium; (2) once there, every possible fluctuation away from equilibrium, no matter how improbable, will recur, ad infinitum; (3) those fluctuations that create (...) stable, long-lived creatures, such as we take ourselves to be, will be extremely rare compared to those that create short-lived brains that mistakenly think they are ordinary human beings; hence, by statistical reasoning, (4) one is, with overwhelming probability, just a fleeting instantiation of experience. I argue that this reasoning is invalid since it rests on an error regarding the relationship between infinite sets and their subsets. Once this error is eliminated, the power of the argument fades, and the evidence that we are ordinary human beings becomes decisive. Surprisingly, I find that the best argument for the Boltzmann brain hypothesis requires the assumption that the future is very long but finite. (shrink)

This paper aims to investigate the so-called paradox of deterministic probabilities: in a deterministic world, all probabilities should be subjective; however, they also seem to play important explanatory and predictive roles which suggest they are objective. The problem is then to understand what these deterministic probabilities are. Recent proposed solutions of this paradox are the Mentaculus vision, the range account of probability and a version of frequentism based on typicality. All these approaches aim at defining deterministic objective probabilities as to (...) make them compatible with determinism. In this paper, I argue that one can think of the equivalent of subjective and objective deterministic probabilities in terms of typicality. Also, I show that only what I identify with objective probabilities plays the necessary explanatory and predictive roles, while the subjective components essentially guide beliefs. In this way, the paradox is solved. (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 a world like ours. In this paper, I show that it can be achieved in a simple way and (...) discuss its implications for metaphysics and philosophy of science, including natural properties, free will, explanation, and modality. First, I propose a precise definition of strong determinism. Next, I discuss its philosophical ramifications and a toy example. Finally, I provide a realistic example of a strongly deterministic (and simple) physical theory---the Everettian Wentaculus. A surprising consequence is that whether or not our world is strongly deterministic may be empirically underdetermined. (shrink)

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)

The black hole information loss paradox is a catch-all term for a family of puzzles related to black hole evaporation. For almost 50 years, the quest to elucidate the implications of black hole evaporation has not only sustained momentum, but has also become increasingly populated with proposals that seem to generate more questions than they purport to answer. Scholars often neglect to acknowledge ongoing discussions within black hole thermodynamics and statistical mechanics when analyzing the paradox, including the interpretation of Bekenstein-Hawking (...) entropy, which is far from settled. To remedy the dialectical gridlock, I have formulated an overarching, unified framework, which I call ``Black Hole Paradoxes'', that integrates the debates and taxonomizes the relevant `camps' or philosophical positions. -/- I demonstrate that black hole evaporation within Hawking's semi-classical framework insinuates how late-time Hawking radiation is an entangled global system, a contradiction in terms. The relevant forms of information loss are associated with a decrease in maximal Boltzmann entropy and an increase in global von Neumann entropy respectively, which engender what I've branded the ``paradox of phantom entanglement''. Prospective solutions are then tasked with demonstrating how late-time Hawking radiation is either exclusively an entangled subsystem, in which a black hole remnant lingers as an information safehouse, or exclusively an unentangled global system, in which information is evacuated to the exterior. -/- The disagreement between safehouse and evacuation solutions boils down to the statistical interpretation of thermodynamic black hole entropy, i.e., Bekenstein-Hawking entropy. Safehouse solutions attribute Bekenstein-Hawking entropy to a minority of black hole degrees of freedom, those that are associated with the horizon. Evacuation solutions, in contrast, attribute Bekenstein-Hawking entropy to all black hole degrees of freedom. I argue that the interpretation of Bekenstein-Hawking entropy is the litmus test to vet the overpopulated proposal space. So long as any proposal rejecting Hawking's original calculation independently derives black hole evaporation, globally conserves degrees of freedom and entanglement, preserves a version of semi-classical gravity at sub-Planckian scales, and describes black hole thermodynamics in statistical terms, then it counts as a genuine solution to the paradox. (shrink)

Functional reductionism characterises inter-theoretic reduction as the recovery of the upper-level behaviour described by the reduced theory in terms of the lower-level reducing theory. For instance, finding a statistical mechanical realiser that plays the functional role of thermodynamic entropy allows for establishing a reductive link between thermodynamics and statistical mechanics. This view constitutes a unique approach to reduction that enjoys a number of positive features, but has received limited attention in the philosophy of science. -/- This paper aims to clarify (...) the meaning of functional reductionism in science, with a focus on physics, to define both its place with respect to other approaches to reduction and its connection to ontology. To do so, we develop and explore two alternative frameworks for functional reduction, called Syntactic Functional Reductionism and Semantic Functional Reductionism. They represent two different possible stances on the view that expand and improve the basic functional reductionist approach along different lines, and make clear how the approach works in practice. The former elaborates on David Lewis’ account, is connected with the syntactic view of theories, is committed to a logical characterisation of functional roles, and is embedded within Nagelian reductionism. The latter adopts a semantic view of theories, spells out functional roles mainly in terms of mathematical roles within the models of theories, and is expressed in terms of the related structuralist approach to reduction. The development of these frameworks has the final goal of advancing functional reductionism, to make it a fully-fledged alternative account for reduction in science. (shrink)

Landauer’s principle is, roughly, the principle that logically irreversible operations cannot be performed without dissipation of energy, with a specified lower bound on that dissipation. Although widely accepted in the literature on the thermodynamics of computation, it has been the subject of considerable dispute in the philosophical literature. Proofs of the principle have been questioned on the grounds of insufficient generality and on the grounds of the assumption, used in the proofs, of the availability of reversible processes at the microscale. (...) The relevance of the principle, should it be true, has also been questioned, as it has been argued that microscale fluctuations entail dissipation that always greatly exceeds the Landauer bound. In this article Landauer’s principle is treated within statistical mechanics, and a proof of the principle is given that neither relies on neglect of fluctuations nor assumes the availability of thermodynamically reversible processes. In addition, it is argued that microscale fluctuations are no obstacle to approximating thermodynamic reversibility, in the appropriate sense, as closely as one would like. (shrink)

The epistemic arrow of time is the fact that our knowledge of the past seems to be both of a different kind and more detailed than our knowledge of the future. Just like with the other arrows of time, it has often been speculated that the epistemic arrow arises due to the second law of thermodynamics. In this paper, we investigate the epistemic arrow of time using a fully formal framework. We begin by defining a memory system as any physical (...) system whose present state can provide information about the state of the external world at some time other than the present. We then identify two types of memory systems in our universe, along with an important special case of the first type, which we distinguish as a third type of memory system. We show that two of these types of memory systems are time-symmetric, able to provide knowledge about both the past and the future. However, the third type of memory systems exploits the second law of thermodynamics, at least in all of its instances in our universe that we are aware of. The result is that in our universe, this type of memory system only ever provides information about the past. We also argue that human memory is of this third type, completing the argument. We end by scrutinizing the basis of the second law itself. This uncovers a previously unappreciated formal problem for common arguments that try to derive the second law from the “Past Hypothesis”, i.e., from the claim that the very early universe was in a state of extremely low entropy. Our analysis is indebted to prior work by one of us but expands and improves upon this work in several respects. (shrink)

If the Past Hypothesis underlies the arrows of time, what is the status of the Past Hypothesis? In this paper, I examine the role of the Past Hypothesis in the Boltzmannian account and defend the view that the Past Hypothesis is a candidate fundamental law of nature. Such a view is known to be compatible with Humeanism about laws, but as I argue it is also supported by a minimal non-Humean "governing'' view. Some worries arise from the non-dynamical and time-dependent (...) character of the Past Hypothesis as a boundary condition, the intrinsic vagueness in its specification, and the nature of the initial probability distribution. I show that these worries do not have much force, and in any case they become less relevant in a new quantum framework for analyzing time's arrows---the Wentaculus. Hence, the view that the Past Hypothesis is a candidate fundamental law should be more widely accepted than it is now. (shrink)

One popular approach to statistical mechanics understands statistical mechanical probabilities as measures of rational indifference. Naive formulations of this ``indifference approach'' face reversibility worries - while they yield the right prescriptions regarding future events, they yield the wrong prescriptions regarding past events. This paper begins by showing how the indifference approach can overcome the standard reversibility worries by appealing to the Past Hypothesis. But, the paper argues, positing a Past Hypothesis doesn't free the indifference approach from all reversibility worries. For (...) while appealing to the Past Hypothesis allows it to escape one kind of reversibility worry, it makes it susceptible to another - the Meta-Reversibility Objection. And there is no easy way for the indifference approach to escape the Meta-Reversibility Objection. As a result, reversibility worries pose a steep challenge to the viability of the indifference approach. (shrink)

Taking the formal analogies between black holes and classical thermodynamics seriously seems to first require that classical thermodynamics applies in relativistic regimes. Yet, by scrutinizing how classical temperature is extended into special relativity, I argue that the concept falls apart. I examine four consilient procedures for establishing the classical temperature: the Carnot process, the thermometer, kinetic theory, and black-body radiation. I argue that their relativistic counterparts demonstrate no such consilience in defining the relativistic temperature. As such, classical temperature doesn’t appear (...) to survive a relativistic extension. I suggest two interpretations for this situation: eliminativism akin to simultaneity, or pluralism akin to rotation. (shrink)

For Humeans, many facts—even ones intuitively “about” particular, localized macroscopic parts of the world—turn out to depend on surprisingly global fundamental bases. We investigate some counterintuitive consequences of this picture. Many counterfactuals whose antecedents describe intuitively localized, non-actual states of affairs nevertheless end up involving wide-ranging implications for the global, embedding Humean mosaic. The case of self-undermining chances is a familiar example of this. We examine that example in detail and argue that popular existing strategies such as “holding the laws (...) fixed as laws” or “holding the laws fixed as true” are of no help. Interestingly, we show how a new proposal that draws on the resources of the Mentaculus can yield the right results—but only on the assumption that the Humean can make cross-world identifications. We go on to argue that the Humean cannot make such identifications. We conclude that the root of this trouble is deeper, and its reach broader, than the familiar cases suggest. We think it is very much an open question whether the Humean has sufficient resources to properly conceptualize macroscopic objects or to analyze these “local” counterfactuals. (shrink)

The problem of time's arrow has sparked two distinct metaphysical approaches, each stemming from opposing Humean and non-Humean perspectives on laws of nature. This paper contends that these approaches, despite their differences and inherent challenges, ultimately converge on a common goal: to explain time's arrow, we must comprehend the structure of spacetime during the universe's early stages. The problem of time's arrow has sparked two distinct metaphysical approaches, each stemming from opposing Humean and non-Humean perspectives on laws of nature. This (...) paper contends that these approaches, despite their differences and inherent challenges, ultimately converge on a common goal: to explain time's arrow, we must comprehend the structure of spacetime during the universe's early stages. (shrink)

Causes always seem to come prior to their effects. What might explain this asymmetry? Causation's temporal asymmetry isn't straightforwardly due to a temporal asymmetry in the laws of nature—the laws are, by and large, temporally symmetric. Nor does the asymmetry appear due to an asymmetry in time itself. This Element examines recent empirical attempts to explain the temporal asymmetry of causation: statistical mechanical accounts, agency accounts and fork asymmetry accounts. None of these accounts are complete yet and a full explanation (...) of the temporal asymmetry of causation will likely require contributions from all three programs. (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.

Certain results, most famously in classical statistical mechanics and complex systems, but also in quantum mechanics and high-energy physics, yield a coarse-grained stable statistical pattern in the long run. The explanation of these results shares a common structure: the results hold for a 'typical' dynamics, that is, for most of the underlying dynamics. In this paper I argue that the structure of the explanation of these results might shed some light --a different light-- on philosophical debates on the laws of (...) nature. In the explanation of such patterns, the specific form of the underlying dynamics is almost irrelevant. The conditions required, given a free state-space evolution, suffice to account for the coarse-grained lawful behaviour. An analysis of such conditions might thus provide a different account of how regular behaviour can occur. This paper focuses on drawing attention to this type of explanation, outlining it in the diverse areas of physics in which it appears, and discussing its limitations and significance in the tractable setting of classical statistical mechanics. (shrink)

Certain results, most famously in classical statistical mechanics and complex systems, but also in quantum mechanics and high-energy physics, yield a coarse-grained stable statistical pattern in the long run. The explanation of these results shares a common structure: the results hold for a ‘typical’ dynamics, that is, for most of the underlying dynamics. In this paper I argue that the structure of the explanation of these results might shed some light—a different light—on philosophical debates on the laws of nature. In (...) the explanation of such patterns, the specific form of the underlying dynamics is almost irrelevant. The constraints required, given a free state-space evolution, suffice to account for the coarse-grained lawful behaviour. An analysis of such constraints might thus provide a different account of how regular behaviour can occur. This paper focuses on drawing attention to this type of explanation, outlining it in the diverse areas of physics in which it appears, and discussing its limitations and significance in the tractable setting of classical statistical mechanics. (shrink)

We argue that the asymmetry between diverging and converging electromagnetic waves is just one of many asymmetries in observed phenomena that can be explained by a past hypothesis and statistical postulate (together assigning probabilities to different states of matter and field in the early universe). The arrow of electromagnetic radiation is thus absorbed into a broader account of temporal asymmetries in nature. We give an accessible introduction to the problem of explaining the arrow of radiation and compare our preferred strategy (...) for explaining the arrow to three alternatives: (i) modifying the laws of electromagnetism by adding a radiation condition requiring that electromagnetic fields always be attributable to past sources, (ii) removing electromagnetic fields and having particles interact directly with one another through retarded action-at-a-distance, (iii) adopting the Wheeler-Feynman approach and having particles interact directly through half-retarded half-advanced action-at-a-distance. In addition to the asymmetry between diverging and converging waves, we also consider the related asymmetry of radiation reaction. (shrink)

A collection of newly commissioned papers on themes from David Albert's Time and Chance (HUP, 2000), with replies by Albert. Introduction [Barry Loewer, Brad Weslake, and Eric Winsberg] I. Overview of Time and Chance 1. The Mentaculus: A Probability Map of the Universe [Barry Loewer] II. Philosophical Foundations 2. The Metaphysical Foundations of Statistical Mechanics: On the Status of PROB and PH [Eric Winsberg] 3. The Logic of the Past Hypothesis [David Wallace] 4. In What Sense Is the Early Universe (...) Fine-Tuned? [Sean M. Carroll] 5. The Meta-Reversibility Objection [Christopher J. G. Meacham] 6. Typicality versus Humean Probabilities as the Foundation of Statistical Mechanics [Dustin Lazarovici] 7. The Past Hypothesis and the Nature of Physical Laws [Eddy Keming Chen] 8. On the Albertian Demon [Tim Maudlin] III. Underwriting the Asymmetries of Knowledge and Intervention 9. Reading the Past in the Present [Nick Huggett] 10. Causes, Randomness, and the Past Hypothesis [Mathias Frisch] 11. Time, Flies, and Why We Can’t Control the Past [Alison Fernandes] 12. The Concept of Intervention in Time and Chance [Sidney Felder] Conclusion [David Albert]. (shrink)

Norton’s and Myrvold’s recent analyses of fluctuations and Landauer’s principle are compatible.

A gas in a box is perhaps the most important model system studied in thermodynamics and statistical mechanics. Usually, studies focus on the gas, whereas the box merely serves as an idealized confinement. The present article focuses on the box as the central object and develops a thermodynamic theory by treating the geometric degrees of freedom of the box as the degrees of freedom of a thermodynamic system. Applying standard mathematical methods to the thermody- namics of an empty box allows (...) equations with the same structure as those of cosmology and classical and quantum mechanics to be derived. The simple model system of an empty box is shown to have interesting connections to classical mechanics, special relativity, and quantum field theory. (shrink)

I attempt to get as clear as possible on the chain of reasoning by which irreversible macrodynamics is derivable from time-reversible microphysics, and in particular to clarify just what kinds of assumptions about the initial state of the universe, and about the nature of the microdynamics, are needed in these derivations. I conclude that while a “Past Hypothesis” about the early Universe does seem necessary to carry out such derivations, that Hypothesis is not correctly understood as a constraint on the (...) early Universe’s entropy. (shrink)

This paper aims to investigate the so-called paradox of deterministic probabilities: in a deterministic world, all probabilities should be subjective; however, they also seem to play important explanatory and predictive roles which suggest they are objective. The problem is then to understand what these deterministic probabilities are. Recent proposed solutions of this paradox are the Mentaculus vision, the range account of probability, and a version of frequentism based on typicality. All these approaches aim at defining deterministic objective probabilities as to (...) make them compatible with determinism. In this paper I argue that one can think of the equivalent of subjective and objective deterministic probabilities in terms of typicality. Also, I show that only what I identify with objective probabilities play the necessary explanatory and predictive roles, while the subjective components essentially guide beliefs. In this way, the paradox is solved. (shrink)

In this paper I aim to demonstrate that Rudolf Carnap's analysis of the application of information theory within physics, an intellectual-historical precedent of current philosophical criticisms toward this tendency, is justified. First, Carnap and Bar-Hillel (1952) underlined the unjustified ‘semantification’ of Shannon entropy Furthermore, Carnap criticized the ‘physicalization’ of Shannon entropy, but that criticism was not accepted by the physics community of the 1950s (Köhler 2001). Finally, in the posthumously published "Two Essays on Entropy" Carnap (1977) developed a critical assessment (...) of entropy concepts that showed some deep conceptual and interpretative deficiencies in Jaynes (1957a) and Brillouin’s (1956) informational approaches to thermophysics. (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)

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)

[Accepted for publication in Lakatos's Undone Work: The Practical Turn and the Division of Philosophy of Mathematics and Philosophy of Science, special issue of Kriterion: Journal of Philosophy. Edited by S. Nagler, H. Pilin, and D. Sarikaya.] Lakatos’s analysis of progress and degeneration in the Methodology of Scientific Research Programmes is well-known. Less known, however, are his thoughts on degeneration in Proofs and Refutations. I propose and motivate two new criteria for degeneration based on the discussion in Proofs and Refutations (...) – superfluity and authoritarianism. I show how these criteria augment the account in Methodology of Scientific Research Programmes, providing a generalized Lakatosian account of progress and degeneration. I then apply this generalized account to a key transition point in the history of entropy – the transition to an information-theoretic interpretation of entropy – by assessing Jaynes’s 1957 paper on information theory and statistical mechanics. (shrink)

Thermodynamic macro variables, such as the temperature or volume macro variable, can take on a continuum of allowable values, called thermodynamic macro values. Although referring to the same macro phenomena, the macro variables of Boltzmannian Statistical Mechanics (BSM) differ from thermodynamic macro variables in an important respect: within the framework of BSM the evolution of macro values of systems with finite available phase space is invariably modelled as discontinuous, due to the method of partitioning phase space into macro regions with (...) sharp, fixed boundaries. Conceptually, this is at odds with the continuous evolution of macro values as described by thermodynamics, as well as with the continuous evolution of the micro state assumed in BSM. This discrepancy I call the discontinuity problem. I show how it arises from BSM’s framework and demonstrate its consequences, in particular for the foundational project of reducing thermodynamics to BSM: thermodynamic macro values are shown to not supervene on the corresponding BSM macro values. With supervenience being a conditio sine qua non for the kind of reduction envisaged by the foundational project, the latter is in jeopardy. (shrink)

It is often said that the world is explained by laws of nature together with initial conditions. But does that mean initial conditions don’t require further explanation? And does the explanatory role played by initial conditions entail or require that time has a preferred direction? This chapter looks at the use of the ‘initialness defence’ in physics, the idea that initial conditions are intrinsically special in that they don’t require further explanation, unlike the state of the world at other times. (...) Such defences commonly assume a primitive directionality of time to distinguish between initial and final conditions. Using the case study of the time-asymmetry of thermodynamics and the so-called ‘past hypothesis’ — the hypothesis that the early universe was in a state of very low entropy —, I outline and support a deflationary account of the initialness defence that does not pre- suppose a basic directionality of time, and argue that there is a relevant explanatory asymmetry between initial conditions and the state of systems at other times only if certain causal conditions are satisfied. Hence, the initialness defence is available to those who reject a fundamental direction of time. (shrink)

In what sense is the direction of time a matter of convention? In 'The Direction of Time', Hans Reichenbach makes brief reference to parallels between his views about the status of time’s direction and his conventionalism about geometry. In this article, I: (1) provide a conventionalist account of time direction motivated by a number of Reichenbach’s claims in the book; (2) show how forwards and backwards time can give equivalent descriptions of the world despite the former being the ‘natural’ direction (...) of time; and (3) argue that this offers an important middle-ground position between existing realist and antirealist accounts of the direction of time. (shrink)