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Herbert P Ster Markus King the Fundamental Nature and Structure Lecture Notes in Physics 897 Herbert P ster Markus King Inertia and Gravitation The Fundamental Nature and Structure of Space-Time Lecture Notes in Physics Volume 897 Founding Editors W. Beiglböck J. Ehlers K. Hepp H. Weidenmüller Editorial Board B.-G. Englert, Singapore, Singapore P. Hänggi, Augsburg, Germany W. Hillebrandt, Garching, Germany M. Hjorth-Jensen, Oslo, Norway R.A.L. Jones, Sheffield, UK M. Lewenstein, Barcelona, Spain H. von Löhneysen, Karlsruhe, Germany M.S. Longair, Cambridge, UK J.-F. Pinton, Lyon, France J.-M. Raimond, Paris, France A. Rubio, Donostia, San Sebastian, Spain M. Salmhofer, Heidelberg, Germany S. Theisen, Potsdam, Germany D. Vollhardt, Augsburg, Germany J.D. Wells, Geneva, Switzerland The Lecture Notes in Physics The series Lecture Notes in Physics (LNP), founded in 1969, reports new devel- opments in physics research and teaching-quickly and informally, but with a high quality and the explicit aim to summarize and communicate current knowledge in an accessible way. Books published in this series are conceived as bridging material between advanced graduate textbooks and the forefront of research and to serve three purposes: • to be a compact and modern up-to-date source of reference on a well-defined topic • to serve as an accessible introduction to the field to postgraduate students and nonspecialist researchers from related areas • to be a source of advanced teaching material for specialized seminars, courses and schools Both monographs and multi-author volumes will be considered for publication. Edited volumes should, however, consist of a very limited number of contributions only. Proceedings will not be considered for LNP. Volumes published in LNP are disseminated both in print and in electronic for- mats, the electronic archive being available at springerlink.com. The series content is indexed, abstracted and referenced by many abstracting and information services, bibliographic networks, subscription agencies, library networks, and consortia. Proposals should be sent to a member of the Editorial Board, or directly to the managing editor at Springer: Christian Caron Springer Heidelberg Physics Editorial Department I Tiergartenstrasse 17 69121 Heidelberg/Germany [email protected] More information about this series at http://www.springer.com/series/5304 Herbert Pfister • Markus King Inertia and Gravitation The Fundamental Nature and Structure of Space-Time 123 Herbert Pfister Markus King Institut für Theoretische Physik Fakultät Engineering Universität Tübingen Hochschule Albstadt-Sigmaringen Tübingen Albstadt Germany Germany ISSN 0075-8450 ISSN 1616-6361 (electronic) Lecture Notes in Physics ISBN 978-3-319-15035-2 ISBN 978-3-319-15036-9 (eBook) DOI 10.1007/978-3-319-15036-9 Library of Congress Control Number: 2015933272 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com) Preface This is a book on foundational issues of classical (non-quantum) physics. It is not a systematic textbook, and it contains no exercises. Rather, we try to impart some knowledge about the fundamental nature and structure of the physical spacetime in a mostly non-technical, nevertheless hopefully precise and consistent language. (A few more technical details are deferred to two appendices.) Some basic knowledge of general relativity and differential geometry would certainly be helpful, especially for Chap. 2. In some places we also follow the historical evolution of views and ideas, and we enrich the presentation by characteristic, sometimes provocative quotations from the creators of the associated theories and models. An extensive reference list documents the fact that all the claims and theorems formulated here have a secure mathematical and/or observational basis, and it provides the interested and educated reader with the possibility to dig deeper into special topics. In particular, the book aims to provide a (surely personal) selection of relevant literature on the foundations and the nature of spacetime, and one that is not usually found in standard textbooks on classical mechanics or general relativity. Although the book would not properly fall into the category of popular books, undergraduate students should be able to read at least parts of the book (in particular Chap. 1) with understanding and profit. On the other hand, we hope that even professional experts will find some new viewpoints and connections between different topics. The selection of topics treated in detail (and the omission of other items) may be somewhat unusual, but we think it is justified in view of the title of the book. Wherever possible, we emphasize the mutual dependence and interplay between different subjects. As the title of the book promises, a central theme is the phenomenon of inertia, from its historic introduction by Galileo and Newton to the Machian hypothesis of its origin in cosmology, and the (at least partial) observational confirmation of this astonishing fact. It is quite obvious that the first part of the book title is adopted from the book ‘Gravitation and Inertia’ (Ciufolini and Wheeler 1995), but interchanging the words because, presumably more than in any other book, inertia is a dominating theme of the present book. The second part of the title is taken from the brilliant talk by J. Ehlers at the Trieste conference celebrating Dirac’s seventieth birthday (Ehlers v vi Preface 1973). In this way, we would also like to honor the two scientists, J.A. Wheeler and J. Ehlers, who have been the most important mentors for one of the present authors (H.P.) in his struggle with and enthusiasm for general relativity. According to Einstein’s equivalence principle, inertia is intimately connected with gravitation, and on the basis of this principle, through a tedious process, Einstein eventually developed his relativistic theory of gravity, general relativity. This theory turned out to be a complete triumph in every respect, and it stands today unchanged, and without a single conflict with experiment, nearly 100 years after its creation. Chapters 2–4 deal with this theory but, as already stressed above, not in the sense of a systematic and complete, textbook-like presentation, but by focusing on some characteristic and fundamental topics within this immensely rich theory. In Chap. 2, we review the remarkable ‘derivation’ of the (pseudo-)Riemannian spacetime structure from the properties of the elementary objects ‘free particles’ and ‘light rays’, as initiated by H. Weyl, and worked out in detail by J. Ehlers, F. Pirani, A. Schild, and others, nowadays known as EPS axiomatics. Such a physically satisfying deduction of the different levels of geometric structure of our ‘world’ is hardly ever found, even in modern textbook presentations of Einstein’s theory of gravity. Chapter 3 tries to give prominence to the very special structure of general relativity, which manifests itself in the many different routes leading to Einstein’s field equations, in deep mathematical results (Cauchy problem, positive energy theorem, singularity theorems), and in spectacular astrophysical predictions, e.g., the existence of black holes. General relativity also encompasses the whole of classical physics, and therefore Einstein’s field equations are the most involved, but also the richest equations one can think of in this regime. We hope to transmit some of our own astonishment and fascination for the beauty, consistency, and completeness of this theory, something which nobody could foresee at the time of its creation. Chapter 4 returns in a way to the central topic of this book, inertia. In their attempt to find the basic source of this phenomenon, E. Mach, B. and I. Friedlaender, A. Föppl, A. Einstein, and others mainly considered rotating systems, in the tradition of Newton’s rotating bucket. Within general relativity, this led to different models for the so-called dragging of free particles and inertial systems by accelerating, and particularly rotating heavy masses. Taken as a whole, such examples strengthen the hypothesis of E. Mach that inertia is, in a non-causal way, ruled by the overall masses of the universe. Modern precision experiments and observations are in accordance with this view, for which interesting and stimulating, sometimes provocative formulations can be found in modern textbooks and research articles. A particular effect of moving masses in general relativity shows up in a new, non- Newtonian ‘force’, called gravitomagnetism, which has recently been confirmed by intricate satellite experiments, 90 years after its prediction by A. Einstein and H. Thirring. A decisive seed for parts of this book, particularly Chap. 1, and for parts of the research of one of the authors (H.P.), grew out of the following incident. In 1972, as a young lecturer at the University of Tübingen, Germany, he had the duty (or Preface vii rather the privilege) to deliver a major course on theoretical mechanics (4 h a week, over a whole year).
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