Geometry of Minkowski Space-Time
This book provides an original introduction to the geometry of Minkowski space-time. A hundred years after the space-time formulation of special relativity by Hermann Minkowski, it is shown that the kinematical consequences of special relativity are merel
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Francesco Catoni Dino Boccaletti Roberto Cannata Vincenzo Catoni Paolo Zampetti •
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Geometry of Minkowski Space–Time
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Francesco Catoni Via Veglia 10 00141 Rome Italy e-mail: [email protected]
Vincenzo Catoni Via Veglia 10 00141 Rome Italy e-mail: [email protected]
Dino Boccaletti Department of Mathematics University of Rome ‘‘La Sapienza’’ Piazzale Aldo Moro 2 00185 Rome Italy e-mail: [email protected]
Paolo Zampetti Casaccia Research Centre ENEA Via Anguillarese 301 00123 Rome Italy e-mail: [email protected]
Roberto Cannata Casaccia Research Centre ENEA Via Anguillarese 301 00123 Rome Italy e-mail: [email protected]
ISSN 2191-5423
e-ISSN 2191-5431
ISBN 978-3-642-17976-1
e-ISBN 978-3-642-17977-8
DOI 10.1007/978-3-642-17977-8 Springer Heidelberg Dordrecht London New York Ó Francesco Catoni 2011 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, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, 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. Cover design: eStudio Calamar, Berlin/Figueres Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
We have written this book with the intention of providing the students (and the teachers) of the first years of university courses with a tool which is easy to be applied and allows the solution of any problem of relativistic kinematics at the same time. The novelty of our presentation consists of the extensive use of hyperbolic numbers for a complete formalization of the kinematics in the Minkowski space– time. In other words, in this book the mathematical relation, stated by special relativity, between space and time is formalized. We recall from Paul Davies book [1], the different significances attributed to ‘‘time’’ over the centuries: For millennia the traditional cultures have given to time an intuitive meaning. Its cyclic nature and biological rhythms predominate over its measure and time and eternity are complementary concepts. Before Galileo and Newton, the time was subjective, not a parameter we have to measure with geometrical precision. Newton encapsulated it in the World description just as a parameter for the mathematical description of the motion: practically the time did nothing. Einstein has given it again its place in the
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