PHILOSOPHY AND THE FOUNDATIONS OF DYNAMICS

Transcription

1 PHILOSOPHY AND THE FOUNDATIONS OF DYNAMICS Although now replaced by more modern theories, classical mechanics remains a core foundational element of physical theory. From its inception, the theory of dynamics has been riddled with conceptual issues and differing philosophical interpretations, and throughout its long historical development, it has shown subtle conceptual refinement. The interpretive program for the theory has also shown deep evolutionary change over time. discusses crucial issues in the central theory from which contemporary foundational theories are derived, and shows how some core issues (the nature of force, the place of absolute reference frames) have nevertheless remained deep puzzles, despite the increasingly sophisticated understanding of the theory which has been acquired over time. His book will be of great interest to philosophers of science, philosophers in general, and physicists concerned with foundational interpretive issues in their field. lawrence sklar is the Carl G. Hempel and William K. Frankena Distinguished University Professor at the University of Michigan. He is the author of Space, Time and Spacetime (1992), Philosophy of Physics (1992), Physics and Chance (Cambridge, 1995), and Theory and Truth (2000).

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3 PHILOSOPHY AND THE FOUNDATIONS OF DYNAMICS LAWRENCE SKLAR

4 cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Mexico City Cambridge University Press The Edinburgh Building, Cambridge cb2 8ru, UK Published in the United States of America by Cambridge University Press, New York Information on this title: / C 2013 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2013 Printed and bound in the United Kingdom by the MPG Books Group A catalog record for this publication is available from the British Library Library of Congress Cataloging in Publication data Sklar, Lawrence. Philosophy and the foundations of dynamics /. pages cm Includes bibliographical references and index. isbn (hardback) 1. Dynamics. 2. Science Philosophy. I. Title. q d96s dc isbn Hardback isbn Paperback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

5 For Max and Mina

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7 Contents 1 Introduction page The growth of theories 1.2 The formulation and reformulation of theories The structure of this book 8 2 The pre-history of classical dynamics Some Greek knowledge and speculation The growth of mathematical astronomy 2.3 Greek dynamical theory Dynamics in medieval Islam and medieval Latin Europe 22 Suggested reading 23 3 The astronomical revolution Copernicus 3.2 Brahe and Kepler Suggested reading 32 4 Precursors to Newtonian dynamics Galileo 4.2 Descartes Huyghens Other precursors of Newton Suggested reading The Newtonian synthesis Newtonian dynamics Newtonian gravity and Newtonian cosmology 53 Suggested reading 56 6 Philosophical aspects of the Newtonian synthesis The metaphysics of space, time and motion 6.2 Issues concerning explanation Newton s Rules of reasoning in philosophy 69 Suggested reading 74 7 The history of statics 75 Suggested reading 79 vii

8 viii Contents 8 The development of dynamics after Newton From special problems and ad-hoc methods to general theory 8.2 Three developmental streams Philosophical themes in dynamics 87 9 The Newtonian approach after Newton Kinematics, dynamics and constitutive equations The fundamental laws of dynamics 9.3 Philosophical reflections on force Suggested reading From virtual work to Lagrange s equation From virtual work to d Alembert s principle From d Alembert s principle to Lagrange s equation 99 Suggested reading Extremal principles From least time to least action Least action and the issue of explanatory legitimacy 106 Suggested reading Some philosophical reflections on explanation and theory Conservation principles Discovery, controversy and consolidation 13.2 Symmetry and conservation Suggested reading Hamilton s equations The Hamiltonian formalism 14.2 Phase space Suggested reading Canonical transformations, optical analogies and algebraic structures Canonical transformations 15.2 Hamilton Jacobi theory Poisson brackets 142 Suggested reading The search for new foundations A sampler of proposals 16.2 Hertz s neo-cartesianism Mach s relationism Further foundational reflections Suggested reading New directions in the applications of dynamics From celestial mechanics to qualitative dynamics Chaos theory 187

9 Contents 17.3 Statistical mechanics New applications and explanatory projects 194 Suggested reading Spacetime formulations of Newtonian dynamics Relativistic spacetimes Galilean spacetime Curved Galilean spacetime and Newtonian gravity 18.4 Philosophical reflections Suggested reading Formalization: mass and force Informal formalization Formal formalization: mass and force 221 Suggested reading Relationist dynamics Machian dynamics Philosophical questions 239 Suggested reading Modes of explanation The variety of explanatory modes in dynamics Internal issues concerning analytical dynamics Extremal principles and the philosophy of explanation Suggested reading Retrospective and conclusions 261 References 263 Index 266 ix