Quantum paradoxes : quantum theory for the perplexed

302 Pages·2005·2.18 MB·English

by  Yakir Aharonov

Yakir Aharonov and Daniel Rohrlich
Quantum Paradoxes
Quantum Theory for the Perplexed
WILEY-VCH Verlag GmbH & Co. KGaA
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Y.Aharonov and D. Rohrlich
Quantum Paradoxes
Quantum Theory for the Perplexed
TTTTTTTTTThhhhhhhhhhiiiiiiiiiissssssssss PPPPPPPPPPaaaaaaaaaaggggggggggeeeeeeeeee IIIIIIIIIInnnnnnnnnntttttttttteeeeeeeeeennnnnnnnnnttttttttttiiiiiiiiiioooooooooonnnnnnnnnnaaaaaaaaaallllllllllllllllllllyyyyyyyyyy LLLLLLLLLLeeeeeeeeeefffffffffftttttttttt BBBBBBBBBBllllllllllaaaaaaaaaannnnnnnnnnkkkkkkkkkk
Yakir Aharonov and Daniel Rohrlich
Quantum Paradoxes
Quantum Theory for the Perplexed
WILEY-VCH Verlag GmbH & Co. KGaA
Authors All books published by Wiley-VCH are carefully
produced. Nevertheless, authors, editors, and publisher
Prof. Yakir Aharonov do not warrant the information contained in these
School of Physics and Astronomy books, including this book, to be free of errors.
Tel Aviv University Readers are advised to keep in mind that statements,
Ramat Aviv 69978 data, illustrations, procedural details or other items
ISRAEL may inadvertently be inaccurate.
and Library of Congress Card No.:applied for
British Library Cataloging-in-Publication Data:
Department of Physics A catalogue record for this book is available from the
University of South Carolina British Library
Columbia SC 29208
U.S.A. Bibliographic information published by
Die Deutsche Bibliothek
Dr. Daniel Rohrlich Die Deutsche Bibliothek lists this publication in the
Department of Condensed Matter Physics Deutsche Nationalbibliografie; detailed bibliographic
Weizmann Institute of Science data is available in the
Rehovot 76100 Internet at <http://dnb.ddb.de>.
ISRAEL
© 2005 WILEY-VCH Verlag GmbH & Co. KGaA,
Cover Picture Weinheim
© Charles Addams, Courtesy Tee and Charles Addams
Foundation All rights reserved (including those of translation into
other languages). No part of this book may be repro-
duced in any form – nor transmitted or translated into
machine language without written permission from
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used in this book, even when not specifically marked
as such, are not to be considered unprotected by law.
Printed in the Federal Republic of Germany
Printed on acid-free paper
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ISBN-13: 978-3-527-40391-2
ISBN-10: 3-527-40391-4
Preface
Quantum Paradoxes is a series of studies in quantum theory. Each chapter begins with a
paradoxmotivatingthestudy,intherestofthechapter,ofafundamentalaspectofthetheory.
Wehopethatthisstyleinphysics–progressthroughparadox–willruboffonreaders. The
studies,takentogether,setoutanewinterpretationofquantumtheory.
Elementsofthisinterpretationincludetopologicalphases(theAharonov-Bohmeffectand
its generalizations), “modular” variables, nonlocal measurements and relativistic causality,
time-symmetric boundary conditions, measurement of the quantum wave, “weak” measure-
ments and “weak” values, and new axioms for quantum theory. A treatment of “quantum
measurements”,startinginChap.7,playsanimportantroleinthebook. Indeed,measurement
issoimportantthatmanyoftheworkscitedinthebookcanbefoundintheanthologyQuantum
TheoryandMeasurement,editedbyJ.A.WheelerandW.H.Zurek(Princeton: PrincetonU.
Press),1983;thesecitationsincludeanote“reprintedinWZ”withpagenumbers.
Forwhomisthisbookwritten? Itisdesignedforphysicsstudents,physicistsandphiloso-
phersofsciencewithaninterestinfundamentalaspectsofquantumtheory. Thefirsttwochap-
tersofQuantumParadoxesdonotrequirepriorknowledgeofquantumtheory,andChaps.3–4
introduce basic notions of states, observables and quantum phases, so students can use the
bookevenduringafirstcourseinquantummechanics. Itisnot,however,asubstituteforsuch
acourse.
Eachchapterendswithaproblemset. Problemsmarkedwithanasterisk(*)are,ingeneral,
lessstraightforwardthanothers.
Itisapleasuretothankthosewhohavehelpeduswritethisbook. Weareindebtedtocol-
leagues(includingstudents)whoreadpartsofthebookatonestageoranother,mostespecially
PhilipPearleandFritzRohrlich,andtoElisabethWarschawskiformuchencouragementand
technical support. We thank Shula Volk for opening her ceramics studio to us at odd hours
ofthedayandnight,asreportedinSect.2.1. WealsoacknowledgesupportfromtheGiladi
ProgramoftheIsraeliMinistryofAbsorptionandfromtheTichoFund.
YakirAharonov
DanielRohrlich
December2004
QuantumParadoxes:QuantumTheoryforthePerplexed.Y.AharonovandD.Rohrlich
Copyright(cid:1)c 2005Wiley-VCHVerlagGmbH&Co.KGaA,Weinheim
ISBN3-527-40391-4
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Contents
1 TheUsesofParadox 1
1.1 ParadoxinPhysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Gaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Contradictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 OverviewoftheBook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 HowtoWeighaQuantum 11
2.1 WhydoestheColoroftheLightChange? . . . . . . . . . . . . . . . . . . . 11
2.2 Quanta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 UncertaintyRelations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 TheClock-in-the-BoxParadox . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 FromInconsistencytoIncompleteness . . . . . . . . . . . . . . . . . . . . . 21
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 IsQuantumTheoryComplete? 25
3.1 TheEinstein–Podolsky–RosenParadox . . . . . . . . . . . . . . . . . . . . 25
3.2 PolarizedPhotons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3 QuantumStatesandObservables . . . . . . . . . . . . . . . . . . . . . . . . 31
3.4 Bell’sInequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.5 ParadoxandBeyond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4 PhasesandGauges 43
4.1 TwoParadoxicalProcedures . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2 ClassicalandQuantumPhases . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.3 PhaseMeetsGauge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.4 TheAharonov–BohmEffect . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.5 QuantumConsistencyandtheAharonov–BohmEffect . . . . . . . . . . . . 51
4.6 FluxQuantization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.7 Magnetoresistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.8 Non-AbelianPhases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59