468 research outputs found

    Decoherence, the measurement problem, and interpretations of quantum mechanics

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    Environment-induced decoherence and superselection have been a subject of intensive research over the past two decades, yet their implications for the foundational problems of quantum mechanics, most notably the quantum measurement problem, have remained a matter of great controversy. This paper is intended to clarify key features of the decoherence program, including its more recent results, and to investigate their application and consequences in the context of the main interpretive approaches of quantum mechanics.Comment: 41 pages. Final published versio

    Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory

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    Bohmian mechnaics is the most naively obvious embedding imaginable of Schr\"odingers's equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at first appear to have little to do with the spectrum of predictions of quantum mechanics. It turns out, however, that as a consequence of the defining dynamical equations of Bohmian mechanics, when a system has wave function ψ\psi its configuration is typically random, with probability density ρ\rho given by âˆŁÏˆâˆŁ2|\psi|^2, the quantum equilibrium distribution. It also turns out that the entire quantum formalism, operators as observables and all the rest, naturally emerges in Bohmian mechanics from the analysis of ``measurements.'' This analysis reveals the status of operators as observables in the description of quantum phenomena, and facilitates a clear view of the range of applicability of the usual quantum mechanical formulas.Comment: 77 page

    Towards a classification of continuity and on the emergence of generality

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    This dissertation has for its primary task the investigation, articulation, and comparison of a variety of concepts of continuity, as developed throughout the history of philosophy and a part of mathematics. It also motivates and aims to better understand some of the conceptual and historical connections between characterizations of the continuous, on the one hand, and ideas and commitments about what makes for generality (and universality), on the other. Many thinkers of the past have acknowledged the need for advanced science and philosophy to pass through the “labyrinth of the continuum” and to develop a sufficiently rich and precise model or description of the continuous; but it has been far less widely appreciated how the resulting description informs our ideas and commitments regarding how (and whether) things become general (or how we think about universality). The introduction provides some motivation for the project and gives some overview of the chapters. The first two chapters are devoted to Aristotle, as Aristotle’s Physics is arguably the foundational book on continuity. The first two chapters show that Aristotle\u27s efforts to understand and formulate a rich and demanding concept of the continuous reached across many of his investigations; in particular, these two chapters aim to better situate certain structural similarities and conceptual overlaps between his Posterior Analytics and his Physics, further revealing connections between the structure of demonstration or proof (the subject of logic and the sciences) and the structure of bodies in motion (the subject of physics and study of nature). This chapter also contributes to the larger narrative about continuity, where Aristotle emerges as one of the more articulate and influential early proponents of an account that aligns continuity with closeness or relations of nearness. Chapter 3 is devoted to Duns Scotus and Nicolas Oresme, and more generally, to the Medieval debate surrounding the “latitude of forms” or the “intension and remission of forms,” in which concerted efforts were made to re-focus attention onto the type of continuous motions mostly ignored by the tradition that followed in the wake of Aristotelian physics. In this context, the traditional appropriation of Aristotle’s thoughts on unity, contrariety, genera, forms, quantity and quality, and continuity is challenged in a number of important ways, reclaiming some of the largely overlooked insights of Aristotle into the intimate connections between continua and genera. By realizing certain of Scotus’s ideas concerning the intension and remission of qualities, Oresme initiates a radical transformation in the concept of continuity, and this chapter argues that Oresme’s efforts are best understood as an early attempt at freeing the concept of continuity from its ancient connection to closeness. Chapters 4 and 5 are devoted to unpacking and re-interpreting Spinoza’s powerful theory of what makes for the ‘oneness’ of a body in general and how ‘ones’ can compose to form ever more composite ‘ones’ (all the way up to Nature as a whole). Much of Spinoza reads like an elaboration on Oresme’s new model of continuity; however, the legacy of the Cartesian emphasis on local motion makes it difficult for Spinoza to give up on closeness altogether. Chapter 4 is dedicated to a closer look at some subtleties and arguments surrounding Descartes’ definition of local motion and ‘one body’, and Chapter 5 builds on this to develop Spinoza’s ideas about how the concept of ‘one body’ scales, in which context a number of far-reaching connections between continuity and generality are also unpacked. Chapter 6 leaves the realm of philosophy and is dedicated to the contributions to the continuitygenerality connection from one field of contemporary mathematics: sheaf theory (and, more generally, category theory). The aim of this chapter is to present something like a “tour” of the main philosophical contributions made by the idea of a sheaf to the specification of the concept of continuity (with particular regard for its connections to universality). The concluding chapter steps back and discusses a number of distinct characterizations of continuity in more abstract and synthetic terms, while touching on some of the corresponding representations of generality to which each such model gives rise. This chapter ends with a brief discussion of some of the arguments that have been deployed in the past to claim that continuity (or discreteness) is “better.

    Facets and Levels of Mathematical Abstraction

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    International audienceMathematical abstraction is the process of considering and manipulating operations, rules, methods and concepts divested from their reference to real world phenomena and circumstances, and also deprived from the content connected to particular applications. There is no one single way of performing mathematical abstraction. The term "abstraction" does not name a unique procedure but a general process, which goes many ways that are mostly simultaneous and intertwined ; in particular, the process does not amount only to logical subsumption. I will consider comparatively how philosophers consider abstraction and how mathematicians perform it, with the aim to bring to light the fundamental thinking processes at play, and to illustrate by significant examples how much intricate and multi-leveled may be the combination of typical mathematical techniques which include axiomatic method, invarianceprinciples, equivalence relations and functional correspondences.L'abstraction mathĂ©matique consiste en la considĂ©ration et la manipulation d'opĂ©rations, rĂšgles et concepts indĂ©pendamment du contenu dont les nantissent des applications particuliĂšres et du rapport qu'ils peuvent avoir avec les phĂ©nomĂšnes et les circonstances du monde rĂ©el. L'abstraction mathĂ©matique emprunte diverses voies. Le terme " abstraction " ne dĂ©signe pasune procĂ©dure unique, mais un processus gĂ©nĂ©ral oĂč s'entrecroisent divers procĂ©dĂ©s employĂ©s successivement ou simultanĂ©ment. En particulier, l'abstraction mathĂ©matique ne se rĂ©duit pas Ă  la subsomption logique. Je vais Ă©tudier comparativement en quels termes les philosophes expliquent l'abstraction et par quels moyens les mathĂ©maticiens la mettent en oeuvre. Je voudrais parlĂ  mettre en lumiĂšre les principaux processus de pensĂ©e en jeu et illustrer par des exemples divers niveaux d'intrication de techniques mathĂ©matiques rĂ©currentes, qui incluent notamment la mĂ©thode axiomatique, les principes d'invariance, les relations d'Ă©quivalence et les correspondances fonctionnelles

    Into their land and labours : a comparative and global analysis of trajectories of peasant transformation

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    The fate of rural societies in the past and today cannot be understood in a singular manner. Peasantries across the world have followed different trajectories of change and have developed divergent repertoires of accommodation, adaptation and resistance. Understanding these multiple trajectories requires new historical knowledge about the role of peasantries within long-term and worldwide economic and social transformations. This paper aims to make sense of this diversity from a comparative, integrated, and systemic approach. The paper is structured around the notions of peasant work, peasant frontiers, peasant communities and peasant regimes. These concepts figure as key analytical tools in an innovative research framework to analyze the paths of peasant transformation in modern world history beyond idealization and teleologization

    Cyber-Security Challenges with SMEs in Developing Economies: Issues of Confidentiality, Integrity & Availability (CIA)

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