Basic Relativity An Introductory Essay
This Brief presents a new way of introducing relativity theory, in which perplexing relativistic effects such as time dilation and Lorentz contraction are explained prior to the discussion of Lorentz-transformation. The notion of relativistic mass is show
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Péter Hraskó
Basic Relativity An Introductory Essay
Emeritus Professor at University of Pe´cs, Hungary
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Péter Hraskó University of Pécs H-7633 Pécs Szántó Kovács János u. 1/b Hungary e-mail: [email protected]
ISSN 2191-5423
e-ISSN 2191-5431
ISBN 978-3-642-17809-2
e-ISBN 978-3-642-17810-8
DOI 10.1007/978-3-642-17810-8 Springer Heidelberg Dordrecht London New York Ó Péter Hraskó 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
Traditional presentations of relativity theory start with the introduction of Lorentztransformations from which the peculiar phenomena of the theory (time dilation, Lorentz contraction, the velocity addition formula, etc.) follow. Though this is certainly the most logical approach, it seems rather unfortunate from a pedagogical point of view, since a convincing and conceptually transparent explanation of the Lorentz-transformation itself presents a task of considerable difficulty. Lorentztransformation is based on both the constancy of the light speed and Einstein’s synchronization prescription, and the interrelation between these two constituents is open to the frequent misunderstanding that constancy of the light speed is enforced by the special synchronization of clocks rather than being the law of nature. In order to avoid this pitfall an ad hoc though rigorous presentation of the theory’s perplexing properties in Part 1 precedes the introduction of the Lorentztransformation (and any synchronization procedure). After the introduction of these transformations in Part 2 those same relativistic effects are reconsidered this time in a systematic manner. Part 3 is devoted to the fundamentals of general relativity. The book is based on the lectures given at the post graduate course in physics education at the Eötvös Loránd University (Budapest). Budapest, December 2010
Péter Hraskó
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Contents
Time Dilation to E0 = mc2 . . . . . . . . . . . . . . . . Reference Frames and Inertial Frames . . . . . . . . The Optical Doppler-Effect and Time Dilation . . The Relativity of Simultaneit
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