Time: Its Structure and Role in Physical Theories
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SYNTHESE LIBRARY
STUDIES IN EPISTEMOLOGY, LOGIC, METHODOLOGY, AND PHILOSOPHY OF SCIENCE
Managing Editor: JAAKKO HINTIKKA, Florida State University, Tallahassee
Editors: DONALD DAVIDSON, University of California. Berkeley GABRIEL NUCHELMANS, University of Leyden WESLEY C. SALMON, University of Pittsburgh
VOLUME 179
PETER KROES Department of Philosophy and Social Sciences, Technical University of Eindhoven and Department of Philosophy, Faculty of Science, University of Nijmegen, The Netherlands
TIME: ITS STRUCTURE AND ROLE IN PHYSICAL THEORIES
D. REIDEL PUBLISHING COMPANY A MEMBER OF THE KLUWER "
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library of Congress Cataloging in Publication Data
Kroes, Peter, 1950Time, its structure and role in physical theories. (Synthese library; v. 179) Bibliography: p. Includes indexes. 1. Time. 2. Space and time. QCI73.59.S65K76 1984 ISBN-13: 978-94-009-6524-9 DOL 10.1007/978-94-009-6522-5
I.
Title. 530.1
84-22255
e-ISBN-J3: 978-94-009-6522-5
Pu blished by D. Reidel Pu blishing Company, P.O. Box 17,3300 AA Dordrecht, Holland. Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, 190 Old Derby Street, Hingham, MA 02043, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers Group, P.O. Box 322, 3300 AU Dordrecht, Holland.
All Rights Reserved © 1985 by D. Reidel Publishing Compariy, Dordrecht, Holland
Softcover reprint of the hardcover 1st edition 1985 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner
to Karin
Mark Laura Thomas
TABLE OF CONTENTS
Preface Introduction
xi xiii
I. Physical time and the problem of its structure 1.1 Introduction 1.2 The order structure of time 1.2.1 Partial and total order relations 1.2.2 Newtonian case: total temporal order 1.2.3 Einsteinian case: partial temporal order 1. 2.4 Cosmic time functions 1. 2. 5 causal theories of time 1.3 The topological structure of time 1.3.1 Time and the topology of spacetime 1.3.2 Discrete versus continuous time 1.3.3 Temporal orientability 1.4 The metrical structure of time 1.4.1 Clacks in Newtonian and Einsteinian physics 1.4.2 A geometrical interpretation of the twin paradox 1.4.3 The Unity of Time 1.5 Conclusion tibtes
1 7 7 9 10 14 18 21 21 26 35 39 39 42 48 52 54
II. The geometrical nature of physical time: parameter time and coordinate time 11.1 Introduction 11.2 Parameter and coordinate 11.3 Parameter and coordinate time in Newtonian
58 62
viii
TABLE OF CONTENTS
physics 65 11.3.1 Newtonian space and time: absolute time as parameter 65 II.3.2 Newtonian spacetime: absolute time as parameter and coordinate 69 11.4 Parameter and coordinate time in Einsteinian physics 76 11.4.1 Relativistic space and time: proper time as parameter 77 II.4.2 Relativistic spacetime: proper time and coordinate time
