We solve the problem of formulating Brownian motion in a relativistically covariant framework in 3+1 dimensions. We obtain covariant Fokker–Planck equations with (for the isotropic case) a differential operator of invariant d’Alembert form. Treating the spacelike and timelike fluctuations separately in order to maintain the covariance property, we show that it is essential to take into account the analytic continuation of “unphysical” fluctuations.

In this paper, I will develop a nontrivial interpretation of Feyerabend's concept of a hidden anomalous fact. Feyerabend's claim is that some anomalous facts will remain hidden in the absence of alternatives to the theories to be tested. The case of Brownian motion is given by Feyerabend to support this claim. The essential scientific difficulty in this case was the justification of correct and relevant descriptions of Brownian motion. These descriptions could not be simply determined from (...) the available observational data. An examination, however, of this case shows that no alternative theory is or historically was thought to be necessary in order to justify descriptions of Brownian motion that "directly" refute thermodynamics. While Feyerabend's appraisal of this case therefore is incorrect, a sense is developed in which successful alternatives lend inductive support to the correctness of refuting experimental descriptions. Crucial though to the explanation of this support is the notion of arguments that show the possibilities for improving experimental fit. (shrink)

The fluctuation-dissipation theorem is a central theorem in nonequilibrium statistical mechanics by which the evolution of velocity fluctuations of the Brownian particle under a fluctuating environment is intimately related to its dissipative behavior. This can be illuminated in particular by an example of Brownian motion in an ohmic environment where the dissipative effect can be accounted for by the first-order time derivative of the position. Here we explore the dynamics of the Brownian particle coupled to a (...) supraohmic environment by considering the motion of a charged particle interacting with the electromagnetic fluctuations at finite temperature. We also derive particle’s equation of motion, the Langevin equation, by minimizing the corresponding stochastic effective action, which is obtained with the method of Feynman-Vernon influence functional. The fluctuation-dissipation theorem is established from first principles. The backreaction on the charge is known in terms of electromagnetic self-force given by a third-order time derivative of the position, leading to the supraohmic dynamics. This self-force can be argued to be insignificant throughout the evolution when the charge barely moves. The stochastic force arising from the supraohmic environment is found to have both positive and negative correlations, and it drives the charge into a fluctuating motion. Although positive force correlations give rise to the growth of the velocity dispersion initially, its growth slows down when correlation turns negative, and finally halts, thus leading to the saturation of the velocity dispersion. The saturation mechanism in a supraohmic environment is found to be distinctly different from that in an ohmic environment. The comparison is discussed. (shrink)

Can Brownian motion arise from a deterministic system of particles? This paper addresses this question by analysing the derivation of Brownian motion as the limit of a deterministic hard-spheres gas with Lanford’s theorem. In particular, we examine the role of the Boltzmann-Grad limit in the loss of memory of the deterministic system and compare this derivation and the derivation of Brownian motion with the Langevin equation.

Between 1905 and 1913, French physicist Jean Perrin's experiments on Brownian motion ostensibly put a definitive end to the long debate regarding the real existence of molecules, proving the atomic theory of matter. While Perrin's results had a significant impact at the time, later examination of his experiments questioned whether he really gained experimental access to the molecular realm. The experiments were successful in determining the mean kinetic energy of the granules of Brownian motion; however, the (...) values for molecular magnitudes Perrin inferred from them simply presupposed that the granule mean kinetic energy was the same as the mean molecular kinetic energy in the fluid in which the granules move. This stipulation became increasingly questionable in the years between 1908 and 1913, as significantly lower values for these magnitudes were obtained from other experimental results like alpha-particle emissions, ionization, and Planck's blackbody radiation equation. In this case study in the history and philosophy of science, George E. Smith and Raghav Seth here argue that despite doubts, Perrin's measurements were nevertheless exemplars of theory-mediated measurement-the practice of obtaining values for an inaccessible quantity by inferring them from an accessible proxy via theoretical relationships between them. They argue that it was actually Perrin more than any of his contemporaries who championed this approach during the years in question. The practice of theory-mediated measurement in physics had a long history before 1900, but the concerted efforts of Perrin, Rutherford, Millikan, Planck, and their colleagues led to the central role this form of evidence has had in microphysical research ever since. Seth and Smith's study thus replaces an untenable legend with an account that is not only tenable, but more instructive about what the evidence did and did not show. (shrink)

While in medicine, comparison of the data supplied by a clinical syndrome with the data supplied by the biological system is used to arrive at the most accurate diagnosis, the same cannot be said of financial economics: the accumulation of statistical results that contradict the Brownian hypothesis used in risk modelling, combined with serious empirical problems in the practical implementation of the Black-Scholes-Merton model, the benchmark theory of mathematical finance founded on the Brownian hypothesis, has failed to change (...) the Brownian representation, which has endured for more than fifty years despite the extent of its invalidation by experience. Without any statistical foundations, one mathematical representation has become the established approach, acting in the minds of practitioners as a “prenotion” in the sense the word is used by Durkheim, i.e. a “schematic, summary representation” which has produced a kind of spontaneous epistemology. The question arises of the persistence of this mathematical representation, which has been the basis for every financial risk modelling approach: how can its long life be explained? How was this spontaneous epistemology formed, and why did it prove to be so persistent? To address this question and offer an answer, I will test the various dynamics of scientific knowledge used with reference to financial modelling. All these dynamics are specific ways of describing the relationship between knowledge of a phenomenon and the phenomenon itself. Observing that it is impossible for the positivist approach to solve the financial puzzle, I turn to the three principal postpositivist dynamics, developed by Kuhn, Lakatos and Quine. I shall try to make to speak these representations of science for financial research, in order to reflect on the dominance of the Brownian representation in finance. We shall see that none of the epistemologies examined can explain why the Brownian representation continues to be used in mathematical finance research. I shall then propose an alternative hypothesis, concerning a significant pervading mental model that has irrigated both academics and practitioners in the financial sector: the “principle of continuity” introduced into economics by Marshall in. I consider that this principle of continuity has become a “persistent idea” in the form of a viral approach to representations, and I give this persistent idea the metaphorical name of the “Brownian virus”. Then, to explain the spread of this Brownian virus through the financial sector, the contamination of financial practices by this mental representation founded on the principle of continuity, I introduce the concept of the “financial Logos”, a discourse that structures practices and organisations, calculations, prudential regulations and accounting standards, leading to a general financialisation of society from the 1980s onwards. (shrink)

In this paper, we examine the pioneering research on electronic noise—the current fluctuations in electronic circuit devices due to their intrinsic physical characteristics rather than their defects—in Germany and the U.S. during the 1910s–1920s. Such research was not just another demonstration of the general randomness of the physical world Einstein’s work on Brownian motion had revealed. In contrast, we stress the importance of a particular engineering context to electronic noise studies: the motivation to design and improve high-gain thermionic-tube (...) amplifiers for radio and wired communications. Engineering scientists’ endeavors to understand electronic noise started in 1918, when Walter Schottky at Siemens formulated a theory of “shot noise,” current fluctuations owing to the random emissions of discrete electrons in a tube. Schottky’s theory was revised and experimentally tested at Siemens, General Electric, and AT&T during the 1920s, leading to the discoveries of several other types of noise and an increasing interest in the thermal fluctuations in electronic circuits. In 1925–1928, J.B. Johnson and Harry Nyquist at Bell Labs developed a theory of thermal noise for any electrical resistor at a non-zero temperature. Although these studies were initiated to chart the fundamental performance limit of electronic technology, they ended up assisting the empirical determination of individual electronic components’ characteristics. (shrink)

The explanation of the phenomenon of Brownian motion, given by Einstein in 1905 and based on the kinetic–molecular conception of matter, is considered one of the fundamental pillars supporting atomism in its victorious struggle against phenomenological physics in the early years of this century. Despite the importance of the subject, there exists no specific study on it of sufficient depth. Generally speaking, most histories of physics repeat the following scheme: the discovery made by Robert Brown in 1827 , (...) of the continuous movement of small particles suspended in a fluid did not arouse interest for a long time. Finally, at the close of the century, Gouy's research brought it to the attention of the physicists. Gouy was convinced that Brownian motion constituted a clear demonstration of the existence of molecules in continuous movement. Nevertheless, he did not work out any mathematized theory that could be subjected to quantitative confirmation. All nineteenth-century research remained at the qualitative level and yet it was able to clarify some general characteristics of the phenomenon: the completely irregular, unceasing, motion of the particles is not produced by external causes. It does not depend on the nature of the particles but only on their size. The first significant measurements, carried out by Felix Exner in 1900, appeared to deny the possibility of reconciling the kinetic theory with Brownian motion. The discovery of the ultra-microscope then allowed Zsigmondy to perceive the presence of movements, which were completely analogous to Brown's, in the particles of the colloids; these movements were rather smaller in size than those invesigated up to then. Thus Zsigmondy aroused interest in the phenomenon. Finally, in 1905, Einstein succeeded in stating the mathematical laws governing the movements of particles on the basis of the principles of the kinetic–molecular theory. The following year Smoluchowski arrived at conclusions which corresponded to Einstein's. These laws received a first, rough confirmation in the years immediately following by the work of The Svedberg, Seddig and, for some historians, Henri. Then in 1908 Jean Perrin gave it a definitive confirmation. (shrink)

The Brownian motion of small particles interacting with a field at a finite temperature is a well-known and well-understood phenomenon. At zero temperature, even though the thermal fluctuations are absent, quantum fields still possess vacuum fluctuations. It is then interesting to ask whether a small particle that is interacting with a quantum field will exhibit Brownian motion when the quantum field is assumed to be in the vacuum state. In this paper, we study the cases of (...) a small charge and an imperfect mirror interacting with a quantum scalar field in (1 + 1) dimensions. Treating the quantum field as a classical stochastic variable, we write down a Langevin equation for the particles. We show that the results we obtain from such an approach agree with the results obtained from the fluctuation-dissipation theorem. Unlike the finite temperature case, there exists no special frame of reference at zero temperature and hence it is essential that the particles do not break Lorentz invariance. We find that that the scalar charge breaks Lorentz invariance, whereas the imperfect mirror does not. We conclude that small particles such as the imperfect mirror will exhibit Brownian motion even in the quantum vacuum, but this effect can be so small that it may prove to be difficult to observe it experimentally. (shrink)

Marian Smoluchowski solved the greatest scientific problem of his time. It was the explanation of the phenomenon of the Brownian motion. In the article, I show that Smoluchowski in fact in this explanation used an ontological interpretation of the causality principle, although in his writings he applied it also in the epistemological interpretation. This is understandable because in the scientific practice some kinds of ontological commitment are required.

In this paper, we examine the history of the idea among physicists that there is a fundamental limit to physical measuring processes and that this limit is set by noise. In contrast to previous studies, that have focused on the realization of the existence of such a limit, we focus on the noise aspect of this history. In his monograph entitled Noise from 1954, the Dutch-American physicist and pioneer of noise Alder van der Ziel described how noise came to be (...) seen as of practical importance for measurements:The study of spontaneous fluctuations was primarily theoretical as recently as 1925. At that time it. (shrink)

We discuss ways in which a typical one-dimensional Brownian motion can be approximated by oscillations which are encoded by finite binary strings of high descriptive complexity. We study the recursive properties of Brownian motions that can be thus obtained.

We discuss ways in which a typical one-dimensional Brownian motion can be approximated by oscillations which are encoded by finite binary strings of high descriptive complexity. We study the recursive properties of Brownian motions that can be thus obtained.

We present the unification of Riemann–Cartan–Weyl (RCW) space-time geometries and random generalized Brownian motions. These are metric compatible connections (albeit the metric can be trivially euclidean) which have a propagating trace-torsion 1-form, whose metric conjugate describes the average motion interaction term. Thus, the universality of torsion fields is proved through the universality of Brownian motions. We extend this approach to give a random symplectic theory on phase-space. We present as a case study of this approach, the invariant (...) Navier–Stokes equations for viscous fluids, and the kinematic dynamo equation of magnetohydrodynamics. We give analytical random representations for these equations. We discuss briefly the relation between them and the Reynolds approach to turbulence. We discuss the role of the Cartan classical development method and the random extension of it as the method to generate these generalized Brownian motions, as well as the key to construct finite-dimensional almost everywhere smooth approximations of the random representations of these equations, the random symplectic theory, and the random Poincaré–Cartan invariants associated to it. We discuss the role of autoparallels of the RCW connections as providing polygonal smooth almost everywhere realizations of the random representations. (shrink)

Nonrelativistic quantum mechanics can be derived from real Markov diffusion processes by extending the concept of probability measure to the complex domain. This appears as the only natural way of introducing formally classical probabilistic concepts into quantum mechanics. To every quantum state there is a corresponding complex Fokker-Planck equation. The particle drift is conditioned by an auxiliary equation which is obtained through stochastic energy conservation; the logarithmic transform of this equation is the Schrödinger equation. To every quantum mechanical operator there (...) is a stochastic process; the replacement of operators by processes leads to all the well-known results of quantum mechanics, using stochastic calculus instead of formal quantum rules. Comparison is made with the classical stochastic approaches and the Feynman path integral formulation. (shrink)

We review the relation between spacetime geometries with trace-torsion fields, the so-called Riemann–Cartan–Weyl (RCW) geometries, and their associated Brownian motions. In this setting, the drift vector field is the metric conjugate of the trace-torsion one-form, and the laplacian defined by the RCW connection is the differential generator of the Brownian motions. We extend this to the state-space of non-relativistic quantum mechanics and discuss the relation between a non-canonical quantum RCW geometry in state-space associated with the gradient of the (...) quantum-mechanical expectation value of a self-adjoint operator given by the generalized laplacian operator defined by a RCW geometry. We discuss the reduction of the wave function in terms of a RCW quantum geometry in state-space. We characterize the Schroedinger equation in terms of the RCW geometries and Brownian motions. Thus, in this work, the Schroedinger field is a torsion generating field, both for the linear and non-linear cases. We discuss the problem of the many times variables and the relation with dissipative processes, and the role of time as an active field, following Kozyrev and a recent experiment in non-relativistic quantum systems. We associate the Hodge dual of the drift vector field with a possible angular-momentum source for the phenomenae observed by Kozyrev. (shrink)

The issue of shifting scales between the microscopic and the macroscopic dimensions is a recurrent one in the history of science, and in particular the history of microscopy. But it took on new dimensions in the context of early twentieth-century microscophysics, with the progressive realisation that the physical laws governing the macroscopic world were not always adequate for describing the sub-microscopic one. The paper focuses on the researches of Jean Perrin in the 1900s, in particular his use of Brownian (...) motion to produce evidence of the existence of atoms and in favour of the kinetic theory. His results were described by many contemporaries, and subsequently by historians, as the first direct proof of atomic and molecular reality. The paper examines the different strategies developed by Perrin for bridging the macro and sub-microphysical realms and making the latter accessible to the senses; even though neither atoms nor molecules were ever actually seen, and in fact very few visual representations were shown and published in connection with these experiments. This case provides a good example of how visualizing, representing and convincing could be interwoven in the production of evidence about the sub-microphysical realm circa 1900.Keywords: Jean Perrin; Brownian motion; Ultramicroscope; Evidence; Atom; Atomism. (shrink)

In a recent article, van Fraassen has taken issue with the use to which Perrin’s experiments on Brownian motion have been put by philosophers, especially those defending scientific realism. He defends an alternative position by analysing the details of Perrin’s case in its historical context. In this reply, I argue that van Fraassen has not done the job well enough and I extend and in some respects attempt to correct his claims by close attention to the historical details.

In this paper, I will defend Paul Feyerabend's claim--that there are some scientific theories that cannot be refuted unless one of their rivals is first confirmed--by criticizing Ronald Laymon's well-known attack on Feyerabend's claim. In particular, I will argue both that the Second Law of Thermodynamics was not refuted before the Kinetic Theory's predictions were confirmed, and that it could not have been refuted without the confirmation of the remarkable predictions of some rival theory.

We present the Dirac and Laplacian operators on Clifford bundles over space–time, associated to metric compatible linear connections of Cartan–Weyl, with trace-torsion, Q. In the case of nondegenerate metrics, we obtain a theory of generalized Brownian motions whose drift is the metric conjugate of Q. We give the constitutive equations for Q. We find that it contains Maxwell’s equations, characterized by two potentials, an harmonic one which has a zero field (Bohm-Aharonov potential) and a coexact term that generalizes the (...) Hertz potential of Maxwell’s equations in Minkowski space.We develop the theory of the Hertz potential for a general Riemannian manifold. We study the invariant state for the theory, and determine the decomposition of Q in this state which has an invariant Born measure. In addition to the logarithmic potential derivative term, we have the previous Maxwellian potentials normalized by the invariant density. We characterize the time-evolution irreversibility of the Brownian motions generated by the Cartan–Weyl laplacians, in terms of these normalized Maxwell’s potentials. We prove the equivalence of the sourceless Maxwell equation on Minkowski space, and the Dirac-Hestenes equation for a Dirac-Hestenes spinor field written on Minkowski space provided with a Cartan–Weyl connection. If Q is characterized by the invariant state of the diffusion process generated on Euclidean space, then the Maxwell’s potentials appearing in Q can be seen alternatively as derived from the internal rotational degrees of freedom of the Dirac-Hestenes spinor field, yet the equivalence between Maxwell’s equation and Dirac-Hestenes equations is valid if we have that these potentials have only two components corresponding to the spin-plane. We present Lorentz-invariant diffusion representations for the Cartan–Weyl connections that sustain the equivalence of these equations, and furthermore, the diffusion of differential forms along these Brownian motions. We prove that the construction of the relativistic Brownian motion theory for the flat Minkowski metric, follows from the choices of the degenerate Clifford structure and the Oron and Horwitz relativistic Gaussian, instead of the Euclidean structure and the orthogonal invariant Gaussian. We further indicate the random Poincaré–Cartan invariants of phase-space provided with the canonical symplectic structure. We introduce the energy-form of the exact terms of Q and derive the relativistic quantum potential from the groundstate representation. We derive the field equations corresponding to these exact terms from an average on the invariant state Cartan scalar curvature, and find that the quantum potential can be identified with 1 / 12R(g), where R(g) is the metric scalar curvature. We establish a link between an anisotropic noise tensor and the genesis of a gravitational field in terms of the generalized Brownian motions. Thus, when we have a nontrivial curvature, we can identify the quantum nonlocal correlations with the gravitational field. We discuss the relations of this work with the heat kernel approach in quantum gravity. We finally present for the case of Q restricted to this exact term a supersymmetric system, in the classical sense due to E.Witten, and discuss the possible extensions to include the electromagnetic potential terms of Q. (shrink)

The article explores major milestones in reforming higher education in Ukraine, applying the methodology of case studies. It analyzes political and social conditions that influenced the process of reform. The author pays particular attention to the concept of university autonomy, its development and implementation in Ukraine, considering legal and institutional efforts. The impact and experience of some leading institutions like Kyiv-Mohyla Academy is discussed. The author concludes that the task of ensuring comprehensive university autonomy is of a political nature. This (...) is the only reliable instrument for raising of quality of Ukrainian higher education. (shrink)

An extension of the hypothetical experiment of Szilard, which involved the action of a one-molecule gas in an isolated isothermal system, is developed to illustrate how irreversibility may arise out of Brownian motion. As this development requires a consideration of nonmolecular components such as wheels and pistons, the thought-experiment is remodeled in molecular terms and appears to function as a perpetuum mobile.

This chapter focuses on the experimental practices and reasoning strategies employed in nineteenth century investigations on the causal origin of the phenomenon of Brownian movement. It argues that there was an extensive and sophisticated experimental work done on the phenomenon throughout the nineteenth century. Investigators followed as rigorously as possible the methodological standards of their time to make causal claims and advance causal explanations of Brownian movement. Two major methodological strategies were employed. The first was the experimental strategy (...) of varying the circumstances. Suspected causal factors were varied and the resulting effect on Brownian movement was studied. The main goal of this strategy was the identification of difference-making factors, i.e., factors having a causal influence on the phenomenon. The second was the so-called method of hypothesis. Rather than relying exclusively on the ability of experiments to identify difference-making factors, its proponents tried to show how the independently developed tenets of the new kinetic-molecular conception of matter provided a plausible causal explanation of Brownian movement. Each one of these methodological strategies had its distinctive practices and notions of control. None of these strategies could, on its own, establish molecular motion as the cause of Brownian movement. It was only the fruitful combination of the two strategies and of their accompanying practices and notions of control that led, at the end of the nineteenth century, to the recognition of molecular motion as the most probable cause of Brownian movement. (shrink)

The main goal of this paper is to present the Marian Smoluchowski’s work on thermal and primordial fluctuations which are the main cause of Brownian motion and one of the first empirical evidences for molecular structure of matter.

Wavefunction collapse models modify Schrödinger's equation so that it describes the rapid evolution of a superposition of macroscopically distinguishable states to one of them. This provides a phenomenological basis for a physical resolution to the so-called “measurement problem.” Such models have experimentally testable differences from standard quantum theory. The most well developed such model at present is the Continuous Spontaneous Localization (CSL) model in which a universal fluctuating classical field interacts with particles to cause collapse. One “side effect” of this (...) interaction is that the field imparts energy to the particles: experimental evidence on this has led to restrictions on the parameters of the model, suggesting that the coupling of the classical field to the particles must be mass-proportional. Another “side effect” is that the field imparts momentum to particles, causing a small blob of matter to undergo random walk. Here we explore this in order to supply predictions which could be experimentally tested. We examine the translational diffusion of a sphere and a disc, and the rotational diffusion of a disc, according to CSL. For example, we find that the rms distance an isolated 10−5 cm radius sphere diffuses is ≈(its diameter, 5 cm) in (20 sec, a day), and that a disc of radius 2 ⋅ 10−5 cm and thickness 0.5 ⋅ 10−5 cm diffuses through 2πrad in about 70 sec (this assumes the “standard” CSL parameter values). The comparable rms diffusions of standard quantum theory are smaller than these by a factor 10−3±1. It is shown that the CSL diffusion in air at STP is much reduced and, indeed, is swamped by the ordinary Brownian motion. It is also shown that the sphere's diffusion in a thermal radiation bath at room temperature is comparable to the CSL diffusion, but is utterly negligible at liquid He temperature. Thus, in order to observe CSL diffusion, the pressure and temperature must be low. At the low reported pressure of 5 ⋅ 10−17 Torr, achieved at 4.2°K, the mean time between air molecule collisions with the (sphere, disc) is ≈(80, 45)min. This is ample time for observation of the putative CSL diffusion with the standard parameters and, it is pointed out, with any parameters in the range over which the theory may be considered viable. This encourages consideration of how such an experiment may actually be performed, and the paper closes with some thoughts on this subject. (shrink)

Gödel’s incompleteness applies to any system with recursively enumerable axioms and rules of inference. Chaitin’s approach to Gödel’s incompleteness relates the incompleteness to the amount of information contained in the axioms. Zurek’s quantum Darwinism attempts the physical description of the universe using information as one of its major components. The capacity of quantum Darwinism to describe quantum measurement in great detail without requiring ad-hoc non-unitary evolution makes it a good candidate for describing the transition from quantum to classical. A baby-universe (...) diffusion model of cosmic inflation is analyzed using quantum Darwinism. In this model cosmic inflation can be approximated as Brownian motion of a quantum field, and quantum Darwinism implies that molecular interaction during Brownian motion will make the quantum field decohere. The quantum Darwinism approach to decoherence in the baby-universe cosmic-inflation model yields the decoherence times of the baby-universes. The result is the equation relating the baby-universe’s decoherence time with the Hubble parameter, and that the decoherence time is considerably shorter than the cosmic inflation period. (shrink)

Under certain conditions private information can be a source of trade. Arbitrage for instance can occur as a result of the existence of private information. In this paper we want to explicitly model information. To do so we define an ‘information function’. This information function is a mathematical object, also known as a so called ‘wave function’. We use the definition of wave function as it is used in quantum mechanics and we attempt to show the usefulness of this wave (...) function in an economic context. We attempt to answer the following questions. How does the information function relate to private information? How can we use the information function to define the ‘quantity’ of information? How can we use the information function in arbitrage-based option pricing? How can the information function be used in the formulation of a so called Universal Brownian motion? (shrink)

Autonomy -- Hydrodynamics -- Brownian motion -- From Brownian motion to bending beams -- An engineering approach -- The right variables and natural kinds.

Secretion systems enable bacteria to import and secrete large macromolecules including DNA and proteins. While most components of these systems have been identified, the molecular mechanisms of macromolecular transport remain poorly understood. Recent findings suggest that various bacterial secretion systems make use of the translocation ratchet mechanism for transporting polymers across the cell envelope. Translocation ratchets are powered by chemical potential differences generated by concentration gradients of ions or molecules that are specific to the respective secretion systems. Bacteria employ these (...) potential differences for biasing Brownian motion of the macromolecules within the conduits of the secretion systems. Candidates for this mechanism include DNA import by the type II secretion/type IV pilus system, DNA export by the type IV secretion system, and protein export by the type I secretion system. Here, we propose that these three secretion systems employ different molecular implementations of the translocation ratchet mechanism. Brownian ratchets are often discussed in the context of directed molecular movement. Bacterial secretion systems transport molecules through membranes in a directed fashion. Here, we focus on recent experiments supporting a role of translocation ratchets in the secretion and import of proteins and DNA. (shrink)

In this note, we consider a Merton model for default risk, where the firm’s value is driven by a Brownian motion and a compound Poisson process.

A classic source for understanding the connections between information theory and physics, this text was written by one of the giants of 20th-century physics and is appropriate for upper-level undergraduates and graduate students. Topics include the principles of coding, coding problems and solutions, the analysis of signals, a summary of thermodynamics, thermal agitation and Brownian motion, and thermal noise in an electric circuit. A discussion of the negentropy principle of information introduces the author's renowned examination of Maxwell's demon. (...) Concluding chapters explore the associations between information theory, the uncertainty principle, and physical limits of observation, in addition to problems related to computing, organizing information, and inevitable errors. 1962 ed. 81 figures. 14 tables. (shrink)

This paper aims to cast light on the reasons that explain the shift of opinion—from scepticism to realism—concerning the reality of atoms and molecules in the beginning of the twentieth century, in light of Jean Perrin’s theoretical and experimental work on the Brownian movement. The story told has some rather interesting repercussions for the rationality of accepting the reality of explanatory posits. Section 2 presents the key philosophical debate concerning the role and status of explanatory hypotheses c. 1900, focusing (...) on the work of Duhem, Stallo, Ostwald, Poincaré and Boltzmann. Section 3 examines in detail Perrin’s theoretical account of the molecular origins of Brownian motion, reconstructs the structure and explains the strength of Perrin’s argument for the reality of molecules. Section 4 draws three important lessons for the current debate over scientific realism. (shrink)

This issue ofScience in Contextis dedicated to the question of whether there was a “cinematographic turn” in the sciences around the beginning of the twentieth century. In 1895, the Lumière brothers presented their projection apparatus to the Parisian public for the first time. In 1897, the Scottish medical doctor John McIntyre filmed the movement of a frog's leg; in Vienna, in 1898, Ludwig Braun made film recordings of the contractions of a living dog's heart (cf. Cartwright 1992); in 1904, Lucien (...) Bull filmed in slow motion a bullet entering a soap bubble. In 1907 and 1908, respectively, Max Seddig and Victor Henri recorded Brownian motion with the help of a cinematograph (Curtis 2005). In 1909, the Swiss Julius Ries was one of the first to film fertilization and cell division in sea urchins (Ries 1909). In that same year in Paris, Louise Chevroton and Frédéric Vlès used a film camera to observe cell division in the same object (Chevroton and Vlès 1909). As early as 1898, the Parisian surgeon Eugène-Louis Doyen began filming several of his operations, among them the spectacular separation of the Siamese twins Doodica and Radica (Bonah and Laukötter 2009). And in England, the scientist and zoologist Francis Martin Duncan produced an array of popular-scientific films for Charles Urban: “The unseen world: A series of microscopic studies” was presented to the public in the Alhambra Theatre in London for the first time in 1903 (see Gaycken in this issue). (shrink)

In this chapter, one considers finance at its very foundations, namely, at the place where assumptions are being made about the ways to measure the two key ingredients of finance: risk and return. It is well known that returns for a large class of assets display a number of stylized facts that cannot be squared with the traditional views of 1960s financial economics (normality and continuity assumptions, i.e. Brownian representation of market dynamics). Despite the empirical counterevidence, normality and continuity (...) assumptions were part and parcel of financial theory and practice, embedded in all financial practices and beliefs. Our aim is to build on this puzzle for extracting some clues revealing the use of one research strategy in academic community, model tinkering defined as a particular research habit. We choose to focus on one specific moment of the scientific controversies in academic finance: the ‘leptokurtic crisis’ opened by Mandelbrot in 1962. The profoundness of the crisis came from the angle of the Mandelbrot’s attack: not only he emphasized an empirical inadequacy of the Brownian representation, but also he argued for an inadequate grounding of this representation. We give some insights in this crisis and display the model tinkering strategies of the financial academic community in the 1970s and the 1980s. (shrink)

The year 1905 has been called Einstein's annus mirabilis in virtue of three ground-breaking works completed over the span of a few months --- the light quantum paper (Einstein, 1905a), the Brownian motion paper (Einstein, 1905c), and the paper on the electrodynamics of moving bodies introducing the special theory of relativity (Einstein, 1905d). There are prima facie reasons for thinking that the origins of these papers cannot be understood in isolation from one another. Due to space limitations, we (...) concentrate primarily on the light quantum paper, since, in key respects, it marks the turning point for the annus mirabilis. The task is to probe, not just how the idea of the light quantum might have occurred to Einstein, but, more importantly, what convinced him that the idea was not just a quixotic hypothesis, but an unavoidable and demonstrable feature of radiation. The crucial development, we suggest, arose from comparing the energy fluctuations that following rigorously from the Stefan-Boltmann law, as well as from Wien's distribution formula for blackbody radiation, with what it is reasonable to expect from Maxwell's electromagnetic theory of light. A special case of this is addressed in (Einstein, 1904). The outcome for the general case leads naturally to the central theoretical argument of the light quantum paper, the expectation of Brownian-like motion, and several of the key results for the electrodynamics of moving bodies. (shrink)

After 1905, Einstein's miraculous year, physics would never be the same again. In those twelve months, Einstein shattered many cherished scientific beliefs with five extraordinary papers that would establish him as the world's leading physicist. This book brings those papers together in an accessible format. The best-known papers are the two that founded special relativity: On the Electrodynamics of Moving Bodies and Does the Inertia of a Body Depend on Its Energy Content? In the former, Einstein showed that absolute time (...) had to be replaced by a new absolute: the speed of light. In the second, he asserted the equivalence of mass and energy, which would lead to the famous formula E = mc 2 . The book also includes On a Heuristic Point of View Concerning the Production and Transformation of Light , in which Einstein challenged the wave theory of light, suggesting that light could also be regarded as a collection of particles. This helped to open the door to a whole new world--that of quantum physics. For ideas in this paper, he won the Nobel Prize in 1921. The fourth paper also led to a Nobel Prize, although for another scientist, Jean Perrin. On the Movement of Small Particles Suspended in Stationary Liquids Required by the Molecular-Kinetic Theory of Heat concerns the Brownian motion of such particles. With profound insight, Einstein blended ideas from kinetic theory and classical hydrodynamics to derive an equation for the mean free path of such particles as a function of the time, which Perrin confirmed experimentally. The fifth paper, A New Determination of Molecular Dimensions , was Einstein's doctoral dissertation, and remains among his most cited articles. It shows how to calculate Avogadro's number and the size of molecules. These papers, presented in a modern English translation, are essential reading for any physicist, mathematician, or astrophysicist. Far more than just a collection of scientific articles, this book presents work that is among the high points of human achievement and marks a watershed in the history of science. Coinciding with the 100th anniversary of the miraculous year, this new paperback edition includes an introduction by John Stachel, which focuses on the personal aspects of Einstein's youth that facilitated and led up to the miraculous year. (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 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)

I argue that scientific realism, insofar as it is only committed to those scientific posits of which we have causal knowledge, is immune to Kyle Stanford’s argument from unconceived alternatives. This causal strategy is shown not to repeat the shortcomings of previous realist responses to Stanford’s argument. Furthermore, I show that the notion of causal knowledge underlying it can be made sufficiently precise by means of conceptual tools recently introduced into the debate on scientific realism. Finally, I apply this strategy (...) to the case of Jean Perrin’s experimental work on the atomic hypothesis, disputing Stanford’s claim that the problem of unconceived alternatives invalidates a realist interpretation of this historical episode. 1 Stanford’s Argument from Unconceived Alternatives2 Previous Attempts to Undermine the Problem of Unconceived Alternatives2.1 The plausibility of unconceived alternatives2.2 The distinctness of unconceived alternatives2.3 The induction from past to present3 Causal Knowledge as a Criterion for the Realist3.1 How Chakravartty’s proposal differs from earlier causal strategies3.2 Causal realism and the detection/auxiliary distinction4 Causal Realism, Unconceived Alternatives, and the Atomic Hypothesis4.1 Perrin and the philosophers: some initial observations4.2 Roush and Stanford on Perrin4.3 From Brownian motion to the reality of atoms4.4 What we know about atoms5 Conclusion. (shrink)