Since the nineteenth century, the problem of the arrow of time has been traditionally analyzed in terms of entropy by relating the direction past-to-future to the gradient of the entropy function of the universe. In this paper, we reject this traditional perspective and argue for a global and non-entropic approach to the problem, according to which the arrow of time can be defined in terms of the geometrical properties of spacetime. In particular, we show how the global non-entropic arrow can (...) be transferred to the local level, where it takes the form of a non-spacelike local energy flow that provides the criterion for breaking the symmetry resulting from time-reversal invariant local laws. (shrink)

This inaugural handbook documents the distinctive research field that utilizes history and philosophy in investigation of theoretical, curricular and pedagogical issues in the teaching of science and mathematics. It is contributed to by 130 researchers from 30 countries; it provides a logically structured, fully referenced guide to the ways in which science and mathematics education is, informed by the history and philosophy of these disciplines, as well as by the philosophy of education more generally. The first handbook to cover the (...) field, it lays down a much-needed marker of progress to date and provides a platform for informed and coherent future analysis and research of the subject. -/- The publication comes at a time of heightened worldwide concern over the standard of science and mathematics education, attended by fierce debate over how best to reform curricula and enliven student engagement in the subjects There is a growing recognition among educators and policy makers that the learning of science must dovetail with learning about science; this handbook is uniquely positioned as a locus for the discussion. -/- The handbook features sections on pedagogical, theoretical, national, and biographical research, setting the literature of each tradition in its historical context. Each chapter engages in an assessment of the strengths and weakness of the research addressed, and suggests potentially fruitful avenues of future research. A key element of the handbook’s broader analytical framework is its identification and examination of unnoticed philosophical assumptions in science and mathematics research. It reminds readers at a crucial juncture that there has been a long and rich tradition of historical and philosophical engagements with science and mathematics teaching, and that lessons can be learnt from these engagements for the resolution of current theoretical, curricular and pedagogical questions that face teachers and administrators. (shrink)

The recent discovery of an indeterministic system in classical mechanics, the Norton dome, has shown that answering the question whether classical mechanics is deterministic can be a complicated matter. In this paper I show that indeterministic systems similar to the Norton dome were already known in the nineteenth century: I discuss four nineteenth century authors who wrote about such systems, namely Poisson, Duhamel, Boussinesq and Bertrand. However, I argue that their discussion of such systems was very different from the contemporary (...) discussion about the Norton dome, because physicists in the nineteenth century conceived of determinism in essentially different ways: whereas in the contemporary literature on determinism in classical physics, determinism is usually taken to be a property of the equations of physics, in the nineteenth century determinism was primarily taken to be a presupposition of theories in physics, and as such it was not necessarily affected by the possible existence of systems such as the Norton dome. (shrink)

Zuerst werden die Argumente rekonstruiert, die dafür sprechen, Einsteins Wort, dass Gott nicht würfelt, als Ausdruck eines überholten deterministischen Weltbildes anzusehen. Anschließend werden Forschungsergebnisse der letzten Jahrzehnte benannt, die für eine Neubewertung seiner Position zur dominanten Interpretation der Quantenmechanik sprechen. Den Abschluß bildet die Diskussion der Möglichkeiten einer Reinterpretation seines Satzes vom nicht würfelnden Gott.

Some think that issues to do with scientific method are last century's stale debate; Popper was an advocate of methodology, but Kuhn, Feyerabend, and others are alleged to have brought the debate about its status to an end. The papers in this volume show that issues in methodology are still very much alive. Some of the papers reinvestigate issues in the debate over methodology, while others set out new ways in which the debate has developed in the last decade. The (...) book will be of interest to philosophers and scientists alike in the reassessment it provides of earlier debates about method and current directions of research. (shrink)

Huw Price (1996, 2002, 2003) argues that causal-dynamical theories that aim to explain thermodynamic asymmetry in time are misguided. He points out that in seeking a dynamical factor responsible for the general tendency of entropy to increase, these approaches fail to appreciate the true nature of the problem in the foundations of statistical mechanics (SM). I argue that it is Price who is guilty of misapprehension of the issue at stake. When properly understood, causal-dynamical approaches in the foundations of SM (...) offer a solution for a different problem; a problem that unfortunately receives no attention in Price’s celebrated work. (shrink)

In 1912, Henri Poincaré published an argument which apparently shows that the hypothesis of quanta is both necessary and sufficient for the truth of Planck''s experimentally corroborated law describing the spectral distribution of radiant energy in a black body. In a recent paper, John Norton has reaffirmed the authority of Poincarés argument, setting it up as a paradigm case in which empirical data can be used to definitively rule out theoretical competitors to a given theoretical hypothesis. My goal is to (...) dispute Norton ''s claim that there is no theoretical underdetermination problem arising between classical physics and early quantum theory. The strategy I use in defending my view is to adopt a suggestion made by Jarrett Leplin and Larry Laudan on how to assess the relative merits of competing theoretical alternatives, where each alternative has an equal capacity to save the phenomena. In the course of the paper, I distinguish between two branches of classical physics: classical mechanics and classical electromagnetism. The former is claimed by Norton and Poincaré to be determinately ruled out by the black body evidence; and it is the former that I argue is compatible with this evidence. (shrink)

The history of science has often been presented as a story of the achievements of geniuses: Galileo, Newton, Maxwell, Darwin, Einstein. Recently it has become popular to enrich this story by discussing the social contexts and motivations that may have influenced the work of the genius and its acceptance; or to replace it by accounts of the doings of scientists who have no claim to genius or to discoveries of universal importance but may be typical members of the scientific community (...) at a particular time and place. In this article I consider a different type of story, which further research might reveal to be more common than we now suspect: progress stimulated by gadflies – outspoken critics who challenge the ideas of geniuses, forcing them to revise and improve those ideas, resulting in new knowledge for which the genius gets the credit while the gadfly is forgotten. (shrink)

Sometimes a theory is interpreted realistically--i.e., as literally true--whereas sometimes a theory is interpreted instrumentalistically--i.e., as merely a convenient device for summarizing, systematizing, deducing, etc., a given body of observable facts. This paper is part of a program aimed at determining the basis on which scientists decide on which of these interpretations to accept a theory. I proceed by examining one case: the nineteenth-century debates about the existence of atoms. I argue that there was a gradual transition from an instrumentalist (...) to a realistic acceptance of the atomic theory, because of gradual increases in its predictive power, the "testedness" of its hypotheses, the "determinateness" of its quantities, and because of resolutions of doubts about the acceptability of its basic explanatory concepts. (shrink)

In recent years, an active research program has emerged that aims to develop a Humean best-system account (BSA) of laws of nature that improves on Lewis’s canonical articulation of the view. Its guiding idea is that the laws are cognitive tools tailored to the specific needs and limitations of creatures like us. While current versions of this “pragmatic Humean” research program fare much better than Lewis’s account along many dimensions, I will argue that they have trouble making sense of certain (...) key features of the practice of fundamental physics. Indeed, these features seem to go against the very idea that laws are useful for agents like us. In my view, Humeans can address these issues by paying more attention to the explanatory role of laws. Following this idea, I will propose an account on which what makes a systematization the best is a kind of explanatory power, understood along the lines of the unificationist theory of explanation. The resulting view, I will argue, can make sense of those features of laws that other pragmatic accounts of laws have trouble explaining. (shrink)

Ludwig Boltzmann is one of the foremost responsible for the development of modern atomism in thermodynamics. His proposition was revolutionary not only because it brought a new vision for Thermodynamics, merging a statistical approach with Newtonian physics, but also because he produced an entirely new perspective on the way of thinking about and describing physical phenomena. Boltzmann dared to flirt with constructivism and realism simultaneously, by hypothesizing the reality of atoms and claiming an inherent probabilistic nature related to many particles (...) systems. Boltzmann faced criticism from the positivists, who rejected the hypothesis of the atom as a matter of principle, and also from physicists, who rejected the idea of a classical bounded system that does not follow deterministic mechanical laws. We consider that Boltzmann thermodynamics has emerged as a systemic theory that deals with macroscopic bodies using collective variables; it was reformulated to a kinetic theory of gases, and subsequently to statistical mechanics. From the theoretical physical point of view, Boltzmann advocates an approach to thermodynamics based on mechanics and was one of the founders of statistical mechanics, together with ideas by Maxwell, Clausius and Gibbs. Subsequently, statistical mechanics has also influenced the development of quantum mechanics and information theory. Using an evolutionary epistemological perspective as a metaphor to describe the physical entities claimed in Boltzmann propositions, we interpret his work as a selected theory that gained attributes of reality and “survived” during a scientific-contextual competition to be more adapted, in the sense that it was able to better explain physical phenomena, and also generated “descendants”. (shrink)

The specific heat of hydrogen gas at low temperatures was first measured in 1912 by Arnold Eucken in Walther Nernst’s laboratory in Berlin, and provided one of the earliest experimental supports for the new quantum theory. Even earlier, Nernst had developed a quantum theory of rotating diatomic gas molecules that figured in the discussions at the first Solvay conference in late 1911. Between 1913 and 1925, Albert Einstein, Paul Ehrenfest, Max Planck, Fritz Reiche, and Erwin Schrödinger, among many others, attempted (...) theoretical descriptions of the rotational specific heat of hydrogen, with only limited success. Quantum theory also was central to the study of molecular spectra, where initially it was more successful. Moreover, the two problems interacted in sometimes surprising ways. Not until 1927, following Werner Heisenberg’s discovery of the behavior of indistinguishable particles in modern quantum mechanics, did American theorist David Dennison find a successful theory of the specific heat of hydrogen. (shrink)

The Pessimistic Induction over the history of science argues that because most past theories considered empirically successful in their time turn out to be not even approximately true, most present ones probably aren’t approximately true either. But why did past scientists accept those incorrect theories? Kyle Stanford’s ‘Problem of Unconceived Alternatives’ is one answer to that question: scientists are bad at exhausting the space of plausible hypotheses to explain the evidence available to them. Here, I offer another answer, which I (...) call the ‘Problem of Misleading Evidence.’ I argue that this proposal is, in important respects, superior to Stanford’s. (shrink)

The corpus of physical theory is a paradigm of knowledge. The evolution of modern physical theory constitutes the clearest exemplar of the growth of knowledge. If the development of physical theory does not constitute an example of progress and growth in what we know about the Universe nothing does. So anyone interested in the theory of knowledge must be interested consequently in the evolution and content of physical theory. Crucial to the conception of physics as a paradigm of knowledge is (...) the way in which physical theory provides explanations of a vast diversity of natural phenomena on the basis of a very few fundamental principles. A central problem for the epistemologist is therefore what is theoretical explanation in physics? Here we can get good insight from what Redhead has said. Indeed one could agree with almost everything Redhead says and simply endorse much of his careful and extensive defence of the covering law account of explanation in the physical sciences at least as an ideal. However I shall, I fear, try the reader's patience by extending some of the considerations he introduced and raising those issues where we disagree, especially in the important area of statistical explanation. (shrink)

It has become something of a dogma in the philosophy of science that modern cosmology has completed Boltzmann's program for explaining the statistical validity of the Second Law of thermodynamics by providing the low entropy initial state needed to ground the asymmetry in entropic behavior that underwrites our inference about the past. This dogma is challenged on several grounds. In particular, it is argued that it is likely that the Boltzmann entropy of the initial state of the universe is an (...) ill-defined or severely hobbled concept. It is also argued that even if the entropy of the initial state of the universe had a well-defined, low value, this would not suffice to explain why thermodynamics works as well as it does for the kinds of systems we care about. Because the role of Boltzmann entropy in our inferences to the past has been vastly overrated, the failure of the Boltzmann program does not pose a serious problem for our knowledge of the past. But it does call a different explanation of why thermodynamics works as well as it does. A suggestion is offered for a different approach. (shrink)

demon thought experiment remains ambiguous even today. One of the most delightful thought It seems that Maxwell originally invoked experiments in the history of physical science is..

In the first part of the 19th century, geologists explained volcanoes, earthquakes and mountain-formation on the assumption that the earth has a large molten core underneath a very thin solid crust. This assumption was attacked on astronomical grounds by William Hopkins, who argued that the crust must be at least 800 miles thick, and on physical grounds by William Thomson, who showed that the earth as a whole behaves like a solid with high rigidity. Other participants in the debate insisted (...) that there is evidence for a fluid or plastic layer not far below the crust. It was also suggested that the interior of the earth is a supercritical fluid. By the end of the century many geologists had incorporated the doctrine of a completely solid earth into their theories. Acceptance of a relatively small liquid core, indicated by seismological research, was delayed for another two decades. (shrink)

In several previous papers we have argued for a global and non-entropic approach to the problem of the arrow of time, according to which the “arrow” is only a metaphorical way of expressing the geometrical time-asymmetry of the universe. We have also shown that, under definite conditions, this global time-asymmetry can be transferred to local contexts as an energy flow that points to the same temporal direction all over the spacetime. The aim of this paper is to complete the global (...) and non-entropic program by showing that our approach is able to account for irreversible local phenomena, which have been traditionally considered as the physical origin of the arrow of time. (shrink)

The so-called ergodic hierarchy (EH) is a central part of ergodic theory. It is a hierarchy of properties that dynamical systems can possess. Its five levels are egrodicity, weak mixing, strong mixing, Kolomogorov, and Bernoulli. Although EH is a mathematical theory, its concepts have been widely used in the foundations of statistical physics, accounts of randomness, and discussions about the nature of chaos. We introduce EH and discuss how its applications in these fields.

The modern mathematical theory of dynamical systems proposes a new model of mechanical motion. In this model the deterministic unstable systems can behave in a statistical manner. Both kinds of motion are inseparably connected, they depend on the point of view and researcher's approach to the system. This mathematical fact solves in a new way the old problem of statistical laws in the world which is essentially deterministic. The classical opposition: deterministic‐statistical, disappears in random dynamics. The main thesis of the (...) paper is that the new theory of motion is a revolution in the research programme of classical mechanics. It is the revolution brought about by the development of mathematics. (shrink)

The story of how Perrin’s experimental work established the reality of atoms and molecules has been a staple in (realist) philosophy of science writings (Wesley Salmon, Clark Glymour, Peter Achinstein, Penelope Maddy, …). I’ll argue that how this story is told distorts both what the work was and its significance, and draw morals for the understanding of how theories can be or fail to be empirically grounded.

Roughly speaking, classical statistical physics is the branch of theoretical physics that aims to account for the thermal behaviour of macroscopic bodies in terms of a classical mechanical model of their microscopic constituents, with the help of probabilistic assumptions. In the last century and a half, a fair number of approaches have been developed to meet this aim. This study of their foundations assesses their coherence and analyzes the motivations for their basic assumptions, and the interpretations of their central concepts. (...) The most outstanding foundational problems are the explanation of time-asymmetry in thermal behaviour, the relative autonomy of thermal phenomena from their microscopic underpinning, and the meaning of probability. A more or less historic survey is given of the work of Maxwell, Boltzmann and Gibbs in statistical physics, and the problems and objections to which their work gave rise. Next, we review some modern approaches to (i) equilibrium statistical mechanics, such as ergodic theory and the theory of the thermodynamic limit; and to (ii) non-equilibrium statistical mechanics as provided by Lanford's work on the Boltzmann equation, the so-called Bogolyubov-Born-Green-Kirkwood-Yvon approach, and stochastic approaches such as `coarse-graining' and the `open systems' approach. In all cases, we focus on the subtle interplay between probabilistic assumptions, dynamical assumptions, initial conditions and other ingredients used in these approaches. (shrink)

Central to many issues surrounding reduction in science is the relation between a physical system and its components. In this article we examine how thermodynamic theory relates properties of whole systems to properties of their components. In order to keep the analysis general, we focus our study on universal properties like volume, heat capacity, energy and temperature. In the cases examined we find that scientific explanation requires appeal to properties of components that are spatially as extensive as the whole system. (...) We discuss some implications of our study for the purported paradigmatic reductions of heat and temperature to molecular motion. We conclude that while macro systems reduce ontologically to micro components, epistemologically the reduction of theoretical concepts in general fails. (shrink)

The foundation of statistical mechanics and the explanation of the success of its methods rest on the fact that the theoretical values of physical quantities (phase averages) may be compared with the results of experimental measurements (infinite time averages). In the 1930s, this problem, called the ergodic problem, was dealt with by ergodic theory that tried to resolve the problem by making reference above all to considerations of a dynamic nature. In the present paper, this solution will be analyzed first, (...) highlighting the fact that its very general nature does not duly consider the specificities of the systems of statistical mechanics. Second, Khinchin’s approach will be presented, that starting with more specific assumptions about the nature of systems, achieves an asymptotic version of the result obtained with ergodic theory. Third, the statistical meaning of Khinchin’s approach will be analyzed and a comparison between this and the point of view of ergodic theory is proposed. It will be demonstrated that the difference consists principally of two different perspectives on the ergodic problem: that of ergodic theory puts the state of equilibrium at the center, while Khinchin’s attempts to generalize the result to non-equilibrium states. (shrink)

In his recent book Foundations of Space-Time Theories Michael Friedman argues for a realism about theoretical structure based on specific methodological practices concerning theory unification. Theoretical structures that are essential to the unifying process are to be given a literal realistic interpretation while the remaining ones can be considered as having merely representational status. Friedman’s account of unification involves the notion of a literal reduction or identification of observational properties of entities or objects with their theoretical counterparts. The relationship between (...) these two levels of theory can be construed as that of submodel to model. Once the appropriate reductions are achieved we are then free to conjoin certain theoretical structures with others thereby enabling us, over time, to produce a unified theory encompassing a variety of domains.The alternative to this view Friedman describes as the representationalist approach. Instead of characterizing the relationship between observational and theoretical structures as that of submodel to model the observational properties are simply correlated by way of an embedding (as opposed to an identity) map with their appropriate theoretical counterparts. (shrink)

The atomic hypothesis according to Ludwig Boltzmann. The scientific and philosophical importance of a controversial position at the close of the 19th century. This paper examines Boltzmann’s standpoint in the controversy over the existence of atoms between himself on the one hand and Mach, Ostwald, Helm and to some extent Duhem on the other hand. The latter wanted to develop a physics only constructed with perceptible phenomena. Because of the lack of empirical evidence of the atoms at that time they (...) did not accept them for the construction of physics. In contrast, Boltzmann found the acceptance of atoms to be a fruitful assumption, since for him the construction of physics required going beyond perceptible phenomena. Two different conceptions of nature and of the ways to know nature clashed in this disagreement between Boltzmann and his opponents. Op-posing one-sided positions, Boltzmann supported the hypothetical character of science, in which more than one basic hypothesis can be advanced: he was open to the possibility of fundamental revolutions in science. (shrink)

Relying on the universality of quantum mechanics and on recent results known as the “threshold theorems,” quantum information scientists deem the question of the feasibility of large‐scale, fault‐tolerant, and computationally superior quantum computers as purely technological. Reconstructing this question in statistical mechanical terms, this article suggests otherwise by questioning the physical significance of the threshold theorems. The skepticism it advances is neither too strong (hence is consistent with the universality of quantum mechanics) nor too weak (hence is independent of technological (...) contingencies). *Received June 2009; revised August 2009. †To contact the author, please write to: Department of History and Philosophy of Science, College of Arts and Sciences, Indiana University, Bloomington, IN 47405; e‐mail: [email protected]. (shrink)

Acceptance of the quantization of the elementary electrical charge was preceded by a bitter dispute between Robert Millikan and Felix Ehrenhaft, which lasted for many years. Both Millikan and Ehrenhaft obtained very similar experimental results and yet Millikan was led to formulate the elementary electrical charge and Ehrenhaft to fractional charges. There have been four major attempts to reconstruct the historical events that led to the controversy: Holton ; Franklin ; Barnes et al. ; Goodstein. So we have the controversy (...) not only among the original protagonists but also among those who have interpreted the experiment. The objective of this study is a critical appraisal of the four interpretations and an attempt to provide closure to the controversy. It is plausible to suggest that Ehrenhaft's methodology approximated the traditional scientific method, which did not allow him to discard anomalous data. Millikan, on the other hand, in his publications espoused the scientific method but in private was fully aware of the dilemma faced and was forced to select data to uphold his presuppositions. A closure to the controversy is possible if we recognize that Millikan's data selection procedure depended primarily on his commitment to his presuppositions. Franklin's finding that the selection of the drops did not change the value of e but only its statistical error carries little weight as Millikan did not perform Franklin-style analyses that could have justified the exclusion of drops. It is plausible to suggest that had Millikan performed such analyses, he would have included them in his publication in order to provide support for his data selection procedures. In the absence of his presuppositions, Millikan could not tell which was the ‘expected correct’ value of e and the degree of statistical error. Finally, if we try to understand Millikan's handling of data with no reference to his presuppositions, then some degree of ‘misconduct’ can be perceived. Introduction An appraisal of Holton's interpretation An appraisal of Franklin's interpretation An appraisal of Barnes, Bloor and Henry's interpretation An appraisal of Goodstein's interpretation A crucial test: the second drop of 15 March 1912 Conclusion: Is closure possible? (shrink)

: Testing the claims that scientists make is extremely difficult. Testing the claims that philosophers of science make about science is even more difficult, difficult but not impossible. I discuss three efforts at testing the sorts of claims that philosophers of science make about science: the influence of scientists' age on the alacrity with which they accept new views, the effect of birth order on the sorts of contributions that scientists make, and the role of novel predictions in the acceptance (...) of new scientific views. Without attempting to test philosophical claims, it is difficult to know what they mean. (shrink)

A longstanding criticism of Ernest Nagel's model of reduction is that it fails to take theory change into account. This criticism builds on the received view that Nagelian reductions are incompatible with theory change. This article challenges the received view by showing that Nagel's model can easily accommodate theory change. Indeed, Nagel's model is essentially static as it only gives unchanging formal and nonformal conditions for reduction; in contrast, theory change belongs to the dynamic history of science; as a result, (...) the application of Nagel's model to scientific knowledge from different historical periods yields a series of Nagelian reductions of different degrees of reductive success. This Nagelian treatment of theory change is illustrated by considering the enterprise of reducing thermodynamics to statistical mechanics in the late nineteenth century. It is also contended that, in handling theory change Nagel's model has greater merits than subsequent models (exemplified by Kenneth Schaffner's general reduction-replacement model). This article concludes by suggesting that Nagel's model of reduction deals with theory change exactly in the same way as logical empiricism does with historicism. (shrink)

This paper examines Boltzmann’s responses to the Loschmidt reversibility objection to the H-theorem, as presented in his Lectures on Gas Theory. I describe and evaluate two distinct conceptions of the assumption of molecular disorder found in this work, and contrast these notions with the Stosszahlansatz, as well as with the predominant contemporary conception of molecular disorder. Both these conceptions are assessed with respect to the reversibility objection. Finally, I interpret Boltzmann as claiming that a state of molecular disorder serves as (...) a necessary condition for the application of probabilistic arguments. This in turn offers a way to bridge the conceptual gap between the H-theorem and his combinatorial argument. (shrink)

Or better: time asymmetry in thermodynamics. Better still: time asymmetry in thermodynamic phenomena. “Time in thermodynamics” misleadingly suggests that thermodynamics will tell us about the fundamental nature of time. But we don’t think that thermodynamics is a fundamental theory. It is a theory of macroscopic behavior, often called a “phenomenological science.” And to the extent that physics can tell us about the fundamental features of the world, including such things as the nature of time, we generally think that only fundamental (...) physics can. On its own, a science like thermodynamics won’t be able to tell us about time per se. But the theory will have much to say about everyday processes that occur in time; and in particular, the apparent asymmetry of those processes. The pressing question of time in the context of thermodynamics is about the asymmetry of things in time, not the asymmetry of time, to paraphrase Price ( , ). I use the title anyway, to underscore what is, to my mind, the centrality of thermodynamics to any discussion of the nature of time and our experience in it. The two issues—the temporal features of processes in time, and the intrinsic structure of time itself—are related. Indeed, it is in part this relation that makes the question of time asymmetry in thermodynamics so interesting. This, plus the fact that thermodynamics describes a surprisingly wide range of our ordinary experience. We’ll return to this. First, we need to get the question of time asymmetry in thermodynamics out on the table. (shrink)

Towards the end of the 19th century there were those who wished to see the kinetic theory abandoned. This paper attempts to show that this reaction was primarily due to philosophical objections rather than the result of scientific difficulties encountered by the kinetic theory. First the relevant philosophical background is examined as well as the relation between the kinetic theory and thermodynamics. Next the scientific difficulty known as the specific heats ratio anomaly is discussed and finally Boltzmann's philosophy of science (...) is examined. (shrink)

This article examines the role of philosophy in the development of the kinetic theory of gases. Two opposing accounts of this role, by Peter Clark and John Nyhof, are discussed and criticized. Contrary to both accounts, it is argued that philosophical views of scientists can fundamentally influence the results of their scientific work. This claim is supported by a detailed analysis of the philosophical views of Maxwell and Boltzmann, and of their work on the kinetic theory, especially concerning the so-called (...) specific heat anomaly. It leads to the conclusion that the scientific development of the kinetic theory cannot be understood without taking into account the role of philosophy. (shrink)

This paper is concerned with the introduction of statistical concepts in the molecular theory of heat. In particular, we analyse the arguments invoked by Clausius between 1857 and 1862, and the motivation presented by Maxwell in 1860 to introduce his distribution of velocities. We first show that Maxwell's great insight seems to have been the recognition that the dynamical laws of molecular collision and thermal equilibrium could be made compatible only if the theory of heat became statistical. As for Clausius, (...) historians of science have observed that in 1857 he used probabilities to bring regularity to the theory, but have not satisfactorily analysed important features of his use of probabilities in the context of the theory of heat. We show that only in 1862, in order to answer a criticism to his paper of 1858, Clausius gave a meaning to random motion, along the lines proposed by Maxwell, in his paper of 1860. (shrink)

This is an extensive review of recent work on the foundations of statistical mechanics.

An intricate, long, and occasionally heated debate surrounds Boltzmann’s H-theorem (1872) and his combinatorial interpretation of the second law (1877). After almost a century of devoted and knowledgeable scholarship, there is still no agreement as to whether Boltzmann changed his view of the second law after Loschmidt’s 1876 reversibility argument or whether he had already been holding a probabilistic conception for some years at that point. In this paper, I argue that there was no abrupt statistical turn. In the first (...) part, I discuss the development of Boltzmann’s research from 1868 to the formulation of the H-theorem. This reconstruction shows that Boltzmann adopted a pluralistic strategy based on the interplay between a kinetic and a combinatorial approach. Moreover, it shows that the extensive use of asymptotic conditions allowed Boltzmann to bracket the problem of exceptions. In the second part I suggest that both Loschmidt’s challenge and Boltzmann’s response to it did not concern the H-theorem. The close relation between the theorem and the reversibility argument is a consequence of later investigations on the subject. (shrink)

La física durante la segunda mitad del siglo XIX experimentó una silenciosa pero profunda revisión de sus fundamentos. A pesar de su importancia para los desarrollos posteriores de la física, los estudios históricos y filosóficos sobre dicho periodo son escasos comparados con aquellos de principios del siglo XX. Este trabajo reconstruye algunos aspectos de la física de este periodo usando dos herramientas conceptuales: espacios controversiales de Oscar Nudler y estilo de razonamiento científico de Ian Hacking. El objetivo es mostrar los (...) elementos que produjeron el desbloqueo conceptual de la controversia sobre el determinismo durante la segunda mitad del siglo XIX y principios del siglo XX. (shrink)