It is necessary to distinguish between Boltzmann’s original lecture notes, his extemporaneous lectures, the fair copy of philosophy lectures 3 to 18 by an unknown hand which are mostly on mathematics, and the multi-published versions which only include lectures 1 and 2. There is a difference between his real thought in his notes (or “honne” in Japanese) and what seems to have survived in lectures 1 and 2 for public consumption (“tatamae”). We have stuck with honne, but where it (...) is too abbreviated to make initial sense, we have put it in grammatical and intelligible form as what we think he most probably intended or believed. It was precisely his linguistic philosophy and the relativistic and pragmatic way of presenting it which was largely suppressed or at least toned-down in the fair copy and published versions. Listeners remembered how witty he was when speaking, and the shortened published accounts are also interesting, but his first thoughts, his honne, before prudence set in will interest most readers, though alas as happens with notes there is also some extraneous material. In translating most of the notes for the first three lectures we have ended where mathematics begins to predominate. (shrink)

Some modern cosmological models predict the appearance of Boltzmann Brains: observers who randomly fluctuate out of a thermal bath rather than naturally evolving from a low-entropy Big Bang. A theory in which most observers are of the Boltzmann Brain type is generally thought to be unacceptable, although opinions differ. I argue that such theories are indeed unacceptable: the real problem is with fluctuations into observers who are locally identical to ordinary observers, and their existence cannot be swept under (...) the rug by a choice of probability distributions over observers. The issue is not that the existence of such observers is ruled out by data, but that the theories that predict them are cognitively unstable: they cannot simultaneously be true and justifiably believed. (shrink)

In the last quarter of the nineteenth century, Ludwig Boltzmann explained how irreversible macroscopic laws, in particular the second law of thermodynamics, originate in the time-reversible laws of microscopic physics. Boltzmann’s analysis, the essence of which I shall review here, is basically correct. The most famous criticisms of Boltzmann’s later work on the subject have little merit. Most twentieth century innovations – such as the identification of the state of a physical system with a probability distribution on (...) its phase space, of its thermodynamic entropy with the Gibbs entropy of , and the invocation of the notions of ergodicity and mixing for the justification of the foundations of statistical mechanics – are thoroughly misguided. (shrink)

The book presents the life and personality, the scientific and philosophical work of Ludwig Boltzmann, one of the great scientists who marked the passage from 19th to 20th century physics. His rich and tragic life, ending by suicide at the age of 62, is described in detail. A substantial part of the book is devoted to discussing his scientific and philosophical ideas and placing them in the context of the second half of the 19th century. The fact that (...) class='Hi'>Boltzmann was the man who did most to establish that there is a microscopic, atomic structure underlying macroscopic bodies is documented, as is Boltzmann's influence on modern physics, especially through the work of Planck on light quanta and of Einstein on Brownian motion. Boltzmann was the centre of a scientific revolution, and he has been proved right on many crucial issues. He anticipated Kuhn's theory of scientific revolutions and proposed a theory of knowledge based on Darwin. His basic results, when properly understood, can also be stated as mathematical theorems. Some of these have been proved; others are still at the level of likely but unproven conjectures. The main text of this biography is written almost entirely without equations. Mathematical appendices deepen knowledge of some technical aspects of the subject. (shrink)

Boltzmann’s Bildtheorie, which asserts that scientific theories are ‘mental pictures’ having at best a partial similarity to reality, was a core element of his philosophy of science. The aim of this article is to draw attention to a neglected aspect of it, namely its significance for the issue of scientific explanation and understanding, regarded by Boltzmann as central goals of science. I argue that, in addition to being an epistemological view of the interpretation of scientific theories Boltzmann’s (...) Bildtheorie has implications for the nature of scientific understanding. This aspect has as yet been ignored because discussion of the Bildtheorie has been restricted to the realism-instrumentalism debate. To elucidate my analysis of Boltzmann’s Bildtheorie concrete examples are presented, and the pragmatist and Darwinist roots of Boltzmann’s view are discussed.Moreover, I propose to use Boltzmann’s ideas as a starting-point for developing a novel analysis of the notion of scientific understanding, of which a brief impression is given. It shows that the study of Boltzmann’s philosophy is not only of historical interest but can be relevant also to modern philosophy of science and to the methodology of theoretical physics. (shrink)

This book presents the life and personality, the scientific and philosophical work of Ludwig Boltzmann, one of the great scientists who marked the passage from 19th- to 20th-Century physics. His rich and tragic life, ending by suicide at the age of 62, is described in detail. A substantial part of the book is devoted to discussing his scientific and philosophical ideas and placing them in the context of the second half of the 19th century. The fact that Boltzmann (...) was the man who did most to establish that there is a microscopic, atomic structure underlying macroscopic bodies is documented, as is Boltzmann's influence on modern physics, especially through the work of Planck on light quanta and of Einstein on Brownian motion. Boltzmann was the centre of a scientific upheaval, and he has been proved right on many crucial issues. He anticipated Kuhn's theory of scientific revolutions and proposed a theory of knowledge based on Darwin. His basic results, when properly understood, can also be stated as mathematical theorems. Some of these have been proved: others are still at the level of likely but unproven conjectures. The main text of this biography is written almost entirely without equations. Mathematical appendices deepen knowledge of some technical aspects of the subject. (shrink)

The Boltzmann and Gibbs approaches to statistical mechanics have very different definitions of equilibrium and entropy. The problems associated with this are discussed and it is suggested that they can be resolved, to produce a version of statistical mechanics incorporating both approaches, by redefining equilibrium not as a binary property but as a continuous property measured by the Boltzmann entropy and by introducing the idea of thermodynamic-like behaviour for the Boltzmann entropy. The Kac ring model is used (...) as an example to test the proposals. (shrink)

Since the late nineteenth century, physics has been puzzled by the time-asymmetry of thermodynamic phenomena in the light of the apparent T-symmetry of the underlying laws of mechanics. However, a compelling solution to this puzzle has proved elusive. In part, I argue, this can be attributed to a failure to distinguish two conceptions of the problem. According to one, the main focus of our attention is a time-asymmetric lawlike generalisation. According to the other, it is a particular fact about the (...) early universe. This paper aims (i) to distinguish these two different conceptions of the time-asymmetric explanandum in thermodynamics; (ii) to argue in favour of the latter; and (iii) to show that whichever we choose, our rational expectations about the thermodynamic behaviour of the future must depend on what we know about the past: contrary to the common view, statistical arguments alone do not give us good reason to expect that entropy will always continue to increase. (shrink)

The contributions of the great physicist Ludwig Boltzmann to philosophy and biology are not known sufficiently. In philosophy, he was a realist, and much opposed to his colleague's, Mach's, positivism, but also to Berkeley's, Kant's, Hegel's and Schopenhauer's idealisms. In biology, Boltzmann was a passionate Darwinist and tried to explain on the basis of evolution the meaning of photosynthesis as well as the origin of life and of the mind. Boltzmann argued for evolutionary epistemology. Opposing Kant, he (...) derived the fundamental ideas of space, time and causality from the experience of mankind and its ancestors. The laws of thought were acquired in evolution. While they must be broadly true they need not be faultless. Antinomies arise when thought overshoots the mark, i. e. exceeds the limits of the area for which it evolved. As for Boltzmann the experience of the organism in the course of evolution is the only and exclusive source of knowledge, he may be called an absolute Darwinist. A short account of Boltzmann's Darwinian ideas on the origin of morality, on the sense of beauty and on happiness is also given. (shrink)

Emphasis in historiography of science is naturally placed on the discoveries and inventions which scientists make and generally less on new methods of doing science, but sometimes the latter can he an important clue to help us understand the former. For example, while we all acknowledge how great the contributions of Maxwell, Boltzmann, Planck, and Einstein were to physics from roughly 1870 to 1920, we often overlook the significance of a methodological phrase which was popular during that same period, (...) namely, what in German was called “Bildtheorie” or in English “picture theory”. But even before we can properly study its significance we have to know what the theory was, but even this presents problems, since the meaning changed. In fact, this paper is an attempt not only to describe the history of that change from Maxwell to Wittgenstein but to study in particular how Boltzmann’s conception of Bildtheorie seems to have been at least partly incorporated into the approach of Ludwig Wittgenstein. (shrink)

O objetivo deste artigo consiste em expor as idéias, que o físico austríaco Ludwig Boltzmann (1844-1906) sobre o papel que a mecânica clássica desempenha na física. Ele as concebeu numa época em que a mecânica clássica começava a ser considerada como ultrapassada como fundamento para a física. Boltzmann jamais aceitou essa conclusão. Ele a rejeitou ao mesmo tempo em que desenvolvia um pensamento epistemológico sobre a natureza das teorias físicas. Segundo ele, as teorias científicas são apenas representações dos (...) fenômenos naturais. DOI:10.5007/1808-1711.2011v15n2p361. (shrink)

Two arguments have recently been advanced that Maxwell-Boltzmann particles areindistinguishable just like Bose–Einstein and Fermi–Dirac particles. Bringing modalmetaphysics to bear on these arguments shows that ontological indistinguishabilityfor classical (MB) particles does not follow. The first argument, resting on symmetryin the occupation representation for all three cases, fails since peculiar correlationsexist in the quantum (BE and FD) context as harbingers of ontic indistinguishability,while the indistinguishability of classical particles remains purely epistemic. The secondargument, deriving from the classical limits of quantum statistical (...) partition functions,embodies a conceptual confusion. After clarifying the doctrine of haecceitism, a thirdargument is considered that attempts to deflate metaphysical concerns altogether byshowing that the phase-space and distribution-space representations of MB-statisticshave contrary haecceitistic import. Careful analysis shows this argument to fail as well,leaving de re modality unproblematically grounding particle identity in the classicalcontext while genuine puzzlement about the underlying ontology remains for quantumstatistics. (shrink)

Two arguments have recently been advanced that Maxwell-Boltzmann particles areindistinguishable just like Bose–Einstein and Fermi–Dirac particles. Bringing modalmetaphysics to bear on these arguments shows that ontological indistinguishabilityfor classical (MB) particles does not follow. The first argument, resting on symmetryin the occupation representation for all three cases, fails since peculiar correlationsexist in the quantum (BE and FD) context as harbingers of ontic indistinguishability,while the indistinguishability of classical particles remains purely epistemic. The secondargument, deriving from the classical limits of quantum statistical (...) partition functions,embodies a conceptual confusion. After clarifying the doctrine of haecceitism, a thirdargument is considered that attempts to deflate metaphysical concerns altogether byshowing that the phase-space and distribution-space representations of MB-statisticshave contrary haecceitistic import. Careful analysis shows this argument to fail as well,leaving de re modality unproblematically grounding particle identity in the classicalcontext while genuine puzzlement about the underlying ontology remains for quantumstatistics. (shrink)

Charlotte Werndl and Roman Frigg discuss the relationship between the Boltzmannian and Gibbsian framework of statistical mechanics, addressing, in particular, the question when equilibrium values calculated in both frameworks agree. This note points out conceptual confusions that could arise from their discussion, concerning, in particular, the authors’ use of “Boltzmann equilibrium.” It also clarifies the status of the Khinchin condition for the equivalence of Boltzmannian and Gibbsian equilibrium predictions and shows that it follows, under the assumptions proposed by Werndl (...) and Frigg, from standard arguments in probability theory. (shrink)

Boltzmann’s lectures on natural philosophy point out how the principles of mathematics are both an improvement on traditional philosophy and also serve as a necessary foundation of physics or what the English call “Natura Philosophy”, a title which he will retain for his own lectures. We start with lecture #3 and the mathematical contents of his lectures plus a few philosophical comments. Because of the length of the lectures as a whole we can only give the main points of (...) each but organized into a coherent study. Behind his mathematics stands his support of Darwinian evolution interpreted in a partly Lamarckian way. He also supported non-Euclidean geometry. Much of Boltzmann’s analysis of mathematics is an attempt to refute Kant’s static a priori categories and his identification of space with “non-sensuous intuition”. Boltzmann’s strong attention toward discreteness in mathematics can be seen throughout the lectures. Part II of this paper will touch on the historical background of atomism and focus on the discrete way of thinking with which Boltzmann approaches problems in mathematics and beyond. Part III briefly points out how Boltzmann related mathematics and discreteness to music. (shrink)

In recent years, the philosophy of Ludwig Boltzmann has become a point of interest within the field of history of philosophy of science. Attention has centred around Boltzmann’s philosophical considerations connected to his defense of atomism in physics. In analysing these considerations, several scholars have attributed a pragmatist stance to Boltzmann. In this paper, I want to argue that, whatever pragmatist traits may be found in Boltzmann’s diverse writings, his defense of atomism in physics can not (...) be analysed this way. In other words, I wish to show that he did not defend atomism as “preferable for its practical virtues”, as has been alleged.1 On the contrary, Boltzmann considered the atomist picture to be indispensable — more precisely, an indispensable prerequisite for making the application of continuous differential equations an understandable enterprise. (shrink)

We consider the relativistic statistical mechanics of an ensemble of N events with motion in space-time parametrized by an invariant “historical time” τ. We generalize the approach of Yang and Yao, based on the Wigner distribution functions and the Bogoliubov hypotheses to find approximate dynamical equations for the kinetic state of any nonequilibrium system, to the relativistic case, and obtain a manifestly covariant Boltzmann- type equation which is a relativistic generalization of the Boltzmann-Uehling-Uhlenbeck (BUU) equation for indistinguishable particles. (...) This equation is then used to prove the H-theorem for evolution in τ. In the equilibrium limit, the covariant forms of the standard statistical mechanical distributions are obtained. We introduce two-body interactions by means of the direct action potential V(q), where q is an invariant distance in the Minkowski space-time. The two- body correlations are taken to have the support in a relative O(2, 1)-invariant subregion of the full spacelike region. The expressions for the energy density and pressure are obtained and shown to have the same forms (in terms of an invariant distance parameter) as those of the nonrelativistic theory and to provide the correct nonrelativistic limit. (shrink)

A comparison is made of the traditional Loschmidt and Zermelo objections to Boltzmann's H-theorem, and its simplified variant in the Ehrenfests' 1912 wind-tree model. The little-cited 1896 objection of Zermelo is also analysed. Significant differences between the objections are highlighted, and several old and modern misconceptions concerning both them and the H-theorem are clarified. We give particular emphasis to the radical nature of Poincare's and Zermelo's attack, and the importance of the shift in Boltzmann's thinking in response to (...) the objections as a whole. (shrink)

ABSTRACT. Two arguments have recently been advanced that Maxwell-Boltzmann particles are indistinguishable just like Bose-Einstein and Fermi-Dirac particles. Bringing modal metaphysics to bear on these arguments shows that ontological indistinguishability for classical (MB) particles does not follow. The first argument, resting on symmetry in the occupation representation for all three cases, fails since peculiar correlations exist in the quantum (BE and FD) context as harbingers of ontic indistinguishability, while the indistinguishability of classical particles remains purely epistemic. The second argument, (...) deriving from the classical limits of quantum statistical partition functions, embodies a conceptual confusion. After clarifying the doctrine of haecceitism, a third argument is considered that attempts to deflate metaphysical concerns altogether by showing that the phase-space and distribution-space representations of MB-statistics have contrary haecceitistic import. Careful analysis shows this argument to fail as well, leaving de re modality unproblematically grounding particle identity in the classical context while genuine puzzlement about the underlying ontology remains for quantum statistics. (shrink)

Many commentators agree that Wittgenstein took the idea that propositions are Bilder, or at least the terminology of Bilder, from Heinrich Hertz, or from Hertz and Ludwig Boltzmann. Boltzmann, the great Viennese theoretical physicist, was the founder of statistical thermodynamics, the modern theory of heat. The context within which Hertz and Boltzmann worked was one in which many prominent theoretical physicists accepted the Kantian restriction that our thought cannot access 'things in themselves', but works only with representations. (...) Wittgenstein may have found what Hertz said attractive, but even if he did develop a theory of representation or a picture theory of meaning, neither was something that he just took over from Hertz, fully formed, and his main concerns were puzzles about intentionality, not science. Hertz and Boltzmann did influence various aspects of the Tractatus. Their greatest and most lasting influence on Wittgenstein, though, was on his conception of philosophy itself: its aim, and its method. (shrink)

A dual form of the general relativistic and covariant generalization of the first vorticity theorem of Helmholtz is proven. This dual form is the generalization of Boltzmann's formulation of the Helmholtz theorem.

Summary Boltzmann's principle is part of classical physics, and one of the corner-stones of Planck's quantum theory. It is shown, why Planck's theory of radiation can be derived from this principle without abandoning classical physics, if due regard is taken of atomism. Finally, there is given an outline of a quantum theory completely based on statistical axioms without any appeal to nonclassical physical principles.

Boltzmann's principle is part of classical physics, and one of the corner-stones of Planck's quantum theory. It is shown, why Planck's theory of radiation can be derived from this principle without abandoning classical physics, if due regard is taken of atomism. Finally, there is given an outline of a quantum theory completely based on statistical axioms without any appeal to nonclassical physical principles.

This paper is an attempt to clarify why Ludwig Boltzmann from about 1895 to 1905 seemed to adopt a series of extreme epistemological positions, ranging from phenomenalism to pragmatism, while emphatically rejecting what he called ‘metaphysics’ (by which he meant all traditional philosophy). He concluded that all philosophical differences were merely linguistic and most were ultimately meaningless. But at about the time that young Ludwig Wittgenstein began absorbing these desperate ideas (1905), Boltzmann himself under the influence of Franz (...) Brentano seemed to assume a type of representationalism about the external physical world, while in his own mind adopting it for pragmatic reasons. Why? Because “it worked”. He seems to have defended his non-representationalist Bildtheorie on similar grounds, but his suicide followed shortly (1906). (shrink)

Using computer simulations, we investigate the time evolution of the (Boltzmann) entropy of a dense fluid not in local equilibrium. The macrovariables M describing the system are the (empirical) particle density f = {f(x,v)} and the total energy E. We find that S(ft,E) is a monotone increasing in time even when its kinetic part is decreasing. We argue that for isolated Hamiltonian systems monotonicity of S(Mt) = S(MXt) should hold generally for ‘‘typical’’ (the overwhelming majority of) initial microstates (phase (...) points) X0 belonging to the initial macrostate M0, satisfying MX0 = M0. This is a consequence of Liouville's theorem when Mt evolves according to an autonomous deterministic law. (shrink)

O objectivo do presente artigo é apresentar as ideias que o físico teórico austríaco Ludwig Boltzmann (1844-1906) desenvolveu acerca da natureza e do papel das leis do pensamento. Muito influenciado por Charles Darwin, Boltzmann recusou-se a compreender as leis do pensamento segundo a filosofia de Kant. Em particular, Boltzmann defendeu uma concepção evolutiva das leis do pensamento. O artigo mostra de que forma a concepção das leis do pensamento aceite por Boltzmann impôs uma transformação da sua (...) ideia sobre aquilo que seria o próprio da filosofia. /// Aim of this article is to show some of the epistemological ideas developed by Ludwig Bolzmann (1844-1906). The author of the article considers in particular Bolzmann's view on the nature and role of the laws of reason in the construction of scientific theories. Moreover, he also analyses the influence of Charles Darwin on the Austrian theoretical physicist and how this influence can be viewed as the turning point for the definition of Boltzmann's conception of philosophy. (shrink)

The purpose of the article is to present the ideas that the Austrian physicist Ludwig Boltzmann developed on the role of classical mechanics in physics. He had elaborated them at a time when classical mechanics began to be considered as not being any more the ground for all other physical theories. Boltzmann never accepted this conclusion. He rejected it, developing at the same time some ideas on the epistemological nature of scientific theories. According to him, scientific theories are (...) representations of natural phenomena. (shrink)