Relativity and the Nature of Spacetime

The most important question that is addressed in this book is "what is the nature (the ontological status) of spacetime?" or, equivalently, "what is the dimensionality of the world at the macroscopic level?" The answer to this question is developed via a

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the frontiers collection Series Editors: D. Dragoman M. Dragoman A.C. Elitzur M.P. Silverman J. Tuszynski H.D. Zeh The books in this collection are devoted to challenging and open problems at the forefront of modern physics and related disciplines, including philosophical debates. In contrast to typical research monographs, however, they strive to present their topics in a manner accessible also to scientifically literate non-specialists wishing to gain insight into the deeper implications and fascinating questions involved. Taken as a whole, the series reflects the need for a fundamental and interdisciplinary approach to modern science. It is intended to encourage scientists in all areas to ponder over important and perhaps controversial issues beyond their own speciality. Extending from quantum physics and relativity to entropy, time and consciousness – the Frontiers Collection will inspire readers to push back the frontiers of their own knowledge.

Information and Its Role in Nature By J.G. Roederer Relativity and the Nature of Spacetime By V. Petkov Quo Vadis Quantum Mechanics? Edited by A. C. Elitzur, S. Dolev, N. Kolenda Life – As a Matter of Fat The Emerging Science of Lipidomics By O.G. Mouritsen Quantum–Classical Analogies By D. Dragoman and M. Dragoman Knowledge and the World Challenges Beyond the Science Wars Edited by M. Carrier, J. Roggenhofer, G. K¨uppers, P. Blanchard Quantum–Classical Correspondence By A.O. Bolivar Mind, Matter and Quantum Mechanics By H. Stapp Quantum Mechanics and Gravity By M. Sachs

V. Petkov

RELATIVITY AND THE NATURE OF SPACETIME With 58 Figures

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Dr. Vesselin Petkov Concordia University Liberal Arts College de Maisonneuve Blvd. West 1455 Montreal, Quebec H3G 1M8, Canada E-mail: [email protected]

Series Editors: Prof. Daniela Dragoman University of Bucharest, Physics Faculty, Solid State Chair, PO Box MG-11, 76900 Bucharest, Romania email: [email protected]

Prof. Mircea Dragoman National Research and Development Institute in Microtechnology, PO Box 38-160, 023573 Bucharest, Romania email: [email protected]

Prof. Avshalom C. Elitzur Bar-Ilan University, Unit of Interdisciplinary Studies, 52900 Ramat-Gan, Israel email: [email protected]

Prof. Mark P. Silverman Department of Physics, Trinity College, Hartford, CT 06106, USA email: [email protected]

Prof. Jack Tuszynski University of Alberta, Department of Physics, Edmonton, AB, T6G 2J1, Canada email: [email protected]

Prof. H. Dieter Zeh University of Heidelberg, Institute of Theoretical Physics, Philosophenweg 19, 69120 Heidelberg, Germany email: [email protected] Cover figure: Detail from ‘Venus Beauty and Anisotropic Geometric Diffusion’ by U. Clarenz, U. Diewald, and M. Rumpf. Courtesy of M. Rumpf

ISSN 1612-3018 ISBN-10 3-540-23889-1 Springer Berlin Heidelberg New York ISBN-13 978-3-540-23889-8 Springer Berlin Heidelberg New York Library of Congress Control Number: 2005924256 This work is subject to copyright. All rights are reserved, whether the whole or part of th