Editors-in-Chief Anne Boutet de Monvel, Université Paris VII Denis Diderot, France Gerald Kaiser, Center for Signals and Waves, Austin, TX, USA - PDF

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Progress in Mathematical Physics Volume 47 Editors-in-Chief Anne Boutet de Monvel, Université Paris VII Denis Diderot, France Gerald Kaiser, Center for Signals and Waves, Austin, TX, USA Editorial Board

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Progress in Mathematical Physics Volume 47 Editors-in-Chief Anne Boutet de Monvel, Université Paris VII Denis Diderot, France Gerald Kaiser, Center for Signals and Waves, Austin, TX, USA Editorial Board Sir M. Berry, University of Bristol, UK C. Berenstein, University of Maryland, College Park, USA P. Blanchard, University of Bielefeld, Germany A.S. Fokas, University of Cambridge, UK D. Sternheimer, Université de Bourgogne, Dijon, France C. Tracy, University of California, Davis, USA Einstein, Poincaré Seminar 2005 Thibault Damour Olivier Darrigol Bertrand Duplantier Vincent Rivasseau Editors Birkhäuser Verlag Basel Boston Berlin Editors: Thibault Damour IHÉS 35, Route de Chartres, Bures-sur-Yvette France Olivier Darrigol Université Denis Diderot (Paris 7) 2, place Jussieu Paris Cedex 05 France Bertrand Duplantier Service de Physique Théorique Orme des Merisiers CEA - Saclay Gif-sur-Yvette Cedex France Vincent Rivasseau Laboratoire de Physique Théorique Université Paris XI Orsay Cedex France Mathematics Subject Classification 83-03, 83A05, 83B05, 83Cxx, 60Hxx A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de . ISBN Birkhäuser Verlag, Basel Boston Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use whatsoever, permission from the copyright owner must be obtained Birkhäuser Verlag, P.O. Box 133, CH-4010 Basel, Switzerland Part of Springer Science+Business Media Printed on acid-free paper produced of chlorine-free pulp. TCF Printed in Germany ISBN-10: ISBN-13: Contents Foreword ix Olivier Darrigol The Genesis of the Theory of Relativity 1 1 Maxwell s theory as it was Flashback: The optics of moving bodies Lorentz s theory Poincaré s criticism The Lorentz invariance Einstein s theory The inertia of energy Conclusions Short bibliography Clifford M. Will Special Relativity: A Centenary Perspective 33 1 Introduction Fundamentals of special relativity Einstein s postulates and insights Time out of joint Spacetime and Lorentz invariance Special relativistic dynamics Classic tests of special relativity The Michelson-Morley experiment Invariance of c Time dilation Lorentz invariance and quantum mechanics Consistency tests of special relativity Special relativity and curved spacetime Einstein s equivalence principle Metric theories of gravity Effective violations of local Lorentz invariance Is gravity Lorentz invariant? vi Contents 6 Tests of local Lorentz invariance at the centenary Frameworks for Lorentz symmetry violations Modern searches for Lorentz symmetry violation Concluding remarks References Jacques Bros and Ugo Moschella The Geometry of Relativistic Spacetime 59 Jacques Bros From Euclid s Geometry to Minkowski s Spacetime 60 Introduction and general survey On the use of geometry in mathematical physics and the concept of spacetime Geometry of description and geometry of representation The use of geometry in more than three dimensions Galilean spacetime as a geometry of representation of motion phenomenons Postulates and construction of Minkowski s spacetime The postulates and the light-cone structure of spacetime Simultaneousness revisited Space-ships flight: the anniversary curve Minkowskian (pseudo-)distance and the inverse triangular inequality: the twin paradox Spatial equidistance and the Lorentz contraction of lengths Lorentz transformations in the Minkowskian plane and two-dimensional Lorentz frames The four-dimensional Minkowski s spacetime; tetrads, Lorentz group and Poincaré group Accelerated motions and curved world-lines Curvilinear distances and the slowing down of clocks Minkowski s description of accelerations A comfortable trip for the Langevin traveler On the visual appearance of rapidly moving objects: Lorentz contraction revisited The Minkowskian energy-momentum space: E = mc 2 and particle physics Toward simple geometries of curved spacetimes References Ugo Moschella The de Sitter and anti-de Sitter Sightseeing Tour 120 Introduction Contents vii 1 An analogy: non-euclidean spaces of constant curvature The de Sitter universe Anti-de Sitter Epilogue References Philippe Grangier Experiments with Single Photons Back to the beginning: Einstein s 1905 and 1909 articles Quantum optics and the photon Using single photons: Quantum Key Distribution Single photon sources Coalescing photons En guise de conclusion : towards entangled photons on demand. 147 References Thibault Damour Einstein : His Approach to Physics On Einstein s Epistemology Einstein and Philosophy Hume, Kant, Mach and Poincaré Scientific Philosophy and Einstein s Conceptual Innovation Einstein and the Theories of Relativity Einstein and the Kantian Quantum A Crucial Conversation Waves Over Here, Quanta Over There! Einstein s Ghost Field, Born s Probability Amplitude, and Heisenberg s Uncertainty Relations A Watershed Moment Adventurers in Entangled Reality The Mouse and the Universe The Multiple World The Kantian Quantum References Albert Einstein On Boltzmann s Principle and Some Immediate Consequences Thereof Translation by Bertrand Duplantier and Emily Parks from the original German text into French and English 183 Bertrand Duplantier Commentary 194 General potential Moments of any order viii Contents Bertrand Duplantier Brownian Motion, Diverse and Undulating A brief history of Brownian motion Robert Brown and his precursors The period before Einstein William Sutherland, Albert Einstein, Marian von Smoluchowski Louis Bachelier Paul Langevin Jean Perrin s experiments Measurements by Brownian fluctuations Micromanipulation of DNA molecules Measurement of force by Brownian fluctuations Theory Potential theory and Brownian motion Introduction Newtonian potential Harmonic functions and the Theorem of the Mean The Dirichlet problem Relation between potential theory and Brownian motion Recurrence properties of Brownian motion The fine geometry of the planar Brownian curve The Brownian boundary Potential theory in a neighborhood of a Brownian curve Multifractality Generalized multifractality Foreword This book is the fourth in a series of lectures of the Séminaire Poincaré, whichis directed towards a large audience of physicists and of mathematicians. The goal of this seminar is to provide up-to-date information about general topics of great interest in physics. Both the theoretical and experimental aspects are covered, with some historical background. Inspired by the Bourbaki seminar in mathematics in its organization, hence nicknamed Bourbaphi, the Poincaré Seminar is held twice a year at the Institut Henri Poincaré in Paris, with contributions prepared in advance. Particular care is devoted to the pedagogical nature of the presentations so as to fulfill the goal of being readable by a large audience of scientists. This volume contains the seventh such Seminar, held in It is devoted to Einstein s 1905 papers and their legacy. After a presentation of Einstein s epistemological approach to physics, and the genesis of special relativity, a centenary perspective is offered. The geometry of relativistic spacetime is explained in detail. Single photon experiments are presented, as a spectacular realization of Einstein s light quanta hypothesis. A previously unpublished lecture by Einstein, which presents an illuminating point of view on statistical physics in 1910, at the dawn of quantum mechanics, is reproduced. The volume ends with an essay on the historical, physical and mathematical aspects of Brownian motion. We hope that the publication of this series will serve the community of physicists and mathematicians at the graduate student or professional level. We thank the Commissariat àl Énergie Atomique (Division des Sciences de la Matière), the Centre National de la Recherche Scientifique (Sciences Physique et Mathématiques), and the Daniel Iagolnitzer Foundation for sponsoring the Seminar. Special thanks are due to Chantal Delongeas for the preparation of the manuscript. Thibault Damour Olivier Darrigol Bertrand Duplantier Vincent Rivasseau
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