B1948 Governing Asia TTTThhhhiiiissss ppppaaaaggggeeee iiiinnnntttteeeennnnttttiiiioooonnnnaaaallllllllyyyy lllleeeefffftttt bbbbllllaaaannnnkkkk BB11994488__11--AAookkii..iinndddd 66 99//2222//22001144 44::2244::5577 PPMM Published by World Scientific Publishing Europe Ltd. 57 Shelton Street, Covent Garden, London WC2H 9HE Head office: 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 Library of Congress Cataloging-in-Publication Data Names: Dragan, Andrzej, author. Title: Unusually special relativity / Andrzej Dragan, University of Warsaw, Poland & National University of Singapore, Singapore. Description: London ; Hackensack, NJ : World Scientific Publishing Europe Ltd., [2022] | Includes bibliographical references and index. Identifiers: LCCN 2021026274 (print) | LCCN 2021026275 (ebook) | ISBN 9781800610804 (hardcover) | ISBN 9781800610880 (paperback) | ISBN 9781800610811 (ebook for institutions) | ISBN 9781800610828 (ebook for individuals) Subjects: LCSH: Special relativity (Physics) Classification: LCC QC173.65 .D726 2022 (print) | LCC QC173.65 (ebook) | DDC 530.11--dc23 LC record available at https://lccn.loc.gov/2021026274 LC ebook record available at https://lccn.loc.gov/2021026275 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Copyright © 2022 by World Scientific Publishing Europe Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. For any available supplementary material, please visit https://www.worldscientific.com/worldscibooks/10.1142/Q0319#t=suppl Desk Editors: Jayanthi Muthuswamy/Michael Beale/Shi Ying Koe Typeset by Stallion Press Email: [email protected] Printed in Singapore JJaayyaanntthhii -- QQ00331199 -- UUnnuussuuaallllyy SSppeecciiaall RReellaattiivviittyy..iinndddd 11 2211//77//22002211 1100::1199::1122 aamm November10,2021 13:35 UnusuallySpecialRelativity 9inx6in b4315-fm pagev Preface (Before Consuming) WhenIwasastudent,Icookedupanearlydraftofthisbook.Iwas starving for a comprehensive and basic course on relativity in my syllabus! Then over the next 20 years I amused my own students (andmyself)bydishingoutsamplesfromtheroughcontentsofthis draft.Aftercountlessinvivotestsandgradualimprovementstothe book’srecipe,dinnerisnowreadytobeservedtoawideraudience. And I trust you will find it to be a tasty meal, as special relativity is not only unexpectedly simple and intuitive, but also incredibly interesting! Tounderstandthisbook,advanced knowledgeofphysicsis not required.Theonly thingyouneedis theability tofocus and recali- brate your common sense, as relativity can be a shock to your perception of “reality”. To ease the mathematical burden I have reduced the tools needed to assimilate and process the material to the bare minimum. As a result, most topics can be grasped with basicunderstandingofhigh-schoolalgebra.Thisisinstarkcontrast totheexistingrelativityliterature,inwhichtheoveruseofcomplex mathematics quickly confuses the reader and clouds the compre- hension.Andwhatwecan’texplaintoourowngrannies,weproba- blyjustdon’tunderstand. A delicious example of this is the phenomenon of the Thomas precession. It is typically skipped in most relativity textbooks for being too technical. And when it is considered, it is often with an intellectual repertoire involving “associative-commutative groupoids”, “gyro-group vector spaces”, “holonomy transforma- tion groups”, “Clifford algebras”, “tetrad formalism” — enough v November10,2021 13:35 UnusuallySpecialRelativity 9inx6in b4315-fm pagevi vi Preface(BeforeConsuming) to turn the most stoic of brains into mush! In my approach, the Thomas precession is derived within three lines using basic, high- schoolvectorcalculus.Beingafanofeducationandnotnecessarily “educationism”,Itrustthatmybookwillserveasanutritiousappe- tisertoanyonebeginningtheirfirstencounterwithrelativity.Those with a hunger for a more formalised, sophisticated, and mathe- matised approach are welcome to satiate themselves by turning to anotherbookfromtherichrepertoireonthetopic. We will derive Lorentz transformations using three completely differentmethods.Wewilldiscussindetailallknownandunknown apparent paradoxes and riddles of special relativity, providing insights into these problems from many opposing angles and enablingadeeperunderstandingofthesubject.Withinthisbookwe will go well beyond the basics, eventually touching on topics typi- cally considered to be “more advanced”, such as non-inertial acce- lerated reference frames, static black holes, and even white holes. We will step into what it means to be quantum and how that is connected to relativity. All of this is presented as simply and com- prehensibly as possible, without skipping the essence. There will beorthodoxversesandtherewillbesuperluminalapocrypha.And for the inevitable errors that slipped in unnoticed, may the Devil carrymebarebackkickingandscreamingintotheabyssofdisgrace. Smacznego!a Bigthanksto SamAkina, MatthewHalsteadand Jules Jonesfor theirinvaluable help! aBonappe´tit! November10,2021 13:35 UnusuallySpecialRelativity 9inx6in b4315-fm pagevii About the Author Andrzej Dragan is a professor of physics at University of Warsaw and a visiting profes- sorat NationalUniversityofSingapore,where he is leading a research group on relativistic quantum information. A former research fel- lowatImperialCollegeLondonandUniversity of Nottingham, Professor Dragan is also the recipient of multiple awards and scholarships, includingonesfromEuropeanScienceFounda- Photographer: tion, State Committee for Scientific Research, PawełFabjan´ski Award for the Young Scholars from the Foun- dation for Polish Science, and the Minister of Education Award for OutstandingScholars.HeisalsoaformerScientificSecretaryanda longtimememberoftheHeadCommitteeofthePhysicsOlympiad. Also known for the photographic “Dragan effect”, Professor DraganwasnamedPhotographeroftheYearbytheDigitalCamera Magazine UK, nominated to the Golden Lion award at the Cannes advertisingfestival,awardedBestinShowfromtheCreativeReview UK and declared winner of the London Fashion Film Festival, to name just a few, for his short films. He has never tasted coffee. ScantheQRcodetoaccesstheauthor’scollection of Youtube videos that explain the fundamen- tal concepts of physics described in Unusually SpecialRelativity. vii B1948 Governing Asia TTTThhhhiiiissss ppppaaaaggggeeee iiiinnnntttteeeennnnttttiiiioooonnnnaaaallllllllyyyy lllleeeefffftttt bbbbllllaaaannnnkkkk BB11994488__11--AAookkii..iinndddd 66 99//2222//22001144 44::2244::5577 PPMM November10,2021 13:35 UnusuallySpecialRelativity 9inx6in b4315-fm pageix Contents Preface(BeforeConsuming) v AbouttheAuthor vii 1. LetThereBe(TheSpeedof)Light 1 1.1 LorentzTransformationa` laMinkowski . . . . . . . 1 1.2 MotionasaHyperbolicRotationofSpacetime. . . . 6 1.3 CanAnythingMoveFasterthanLight? . . . . . . . . 8 1.4 SpacetimeIntervalandtheCausalOrder . . . . . . . 9 1.5 Questions . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 13 2. ConsequencesofTimeDilationandLorentzContraction 15 2.1 RelativityofSimultaneity . . . . . . . . . . . . . . . . 15 2.2 TimeDilationandLorentzContraction . . . . . . . . 16 2.3 ParadoxofaTruckInsideaTunnel . . . . . . . . . . 19 2.4 IsLorentzContractionReal? . . . . . . . . . . . . . . 20 2.5 TheParadoxthatStartedItAll . . . . . . . . . . . . . 22 2.6 TheTwinParadox . . . . . . . . . . . . . . . . . . . . 26 2.7 TheUnbearableLoopinessofBeing? . . . . . . . . . 29 2.8 ElvisLives! . . . . . . . . . . . . . . . . . . . . . . . . 30 2.9 TheSpeedWalkerParadox . . . . . . . . . . . . . . . 32 2.10 VelocityTransformationinWonderland . . . . . . . 34 2.11 Questions . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.12 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 38 ix