Table Of Contentthe frontiers collection
the frontiers collection
SeriesEditors:
D.Dragoman M.Dragoman A.C.Elitzur M.P.Silverman J.Tuszynski H.D.Zeh
Thebooksinthiscollectionaredevotedtochallengingandopenproblemsattheforefront
of modern physics and related disciplines, including philosophical debates. In contrast
totypicalresearchmonographs,however,theystrivetopresenttheirtopicsinamanner
accessiblealsotoscientificallyliteratenon-specialistswishingtogaininsightintothedeeper
implicationsandfascinatingquestionsinvolved.Takenasawhole,theseriesreflectsthe
needforafundamentalandinterdisciplinaryapproachtomodernscience.Itisintendedto
encouragescientistsinallareastoponderoverimportantandperhapscontroversialissues
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
frontiersoftheirownknowledge.
InformationandItsRoleinNature
ByJ.G.Roederer
RelativityandtheNatureofSpacetime
ByV.Petkov
QuoVadisQuantumMechanics?
EditedbyA.C.Elitzur,S.Dolev,N.Kolenda
Life–AsaMatterofFat
TheEmergingScienceofLipidomics
ByO.G.Mouritsen
Quantum–ClassicalAnalogies
ByD.DragomanandM.Dragoman
KnowledgeandtheWorld
ChallengesBeyondtheScienceWars
EditedbyM.Carrier,J.Roggenhofer,G.Ku¨ppers,P.Blanchard
Quantum–ClassicalCorrespondence
ByA.O.Bolivar
Mind,MatterandQuantumMechanics
ByH.Stapp
QuantumMechanicsandGravity
ByM.Sachs
V. Petkov
RELATIVITY
AND THE NATURE
OF SPACETIME
With58Figures
123
Dr.VesselinPetkov
ConcordiaUniversity
LiberalArtsCollege
deMaisonneuveBlvd.West1455
Montreal,QuebecH3G1M8,Canada
E-mail:[email protected]
SeriesEditors:
Prof.DanielaDragoman
UniversityofBucharest,PhysicsFaculty,SolidStateChair,POBoxMG-11,
76900Bucharest,Romania email:[email protected]
Prof.MirceaDragoman
NationalResearchandDevelopmentInstituteinMicrotechnology,POBox38-160,
023573Bucharest,Romania email:[email protected]
Prof.AvshalomC.Elitzur
Bar-IlanUniversity,UnitofInterdisciplinaryStudies,
52900Ramat-Gan,Israel email:[email protected]
Prof.MarkP.Silverman
DepartmentofPhysics,TrinityCollege,
Hartford,CT06106,USA email:[email protected]
Prof.JackTuszynski
UniversityofAlberta,DepartmentofPhysics,Edmonton,AB,
T6G2J1,Canada email:[email protected]
Prof.H.DieterZeh
UniversityofHeidelberg,InstituteofTheoreticalPhysics,Philosophenweg19,
69120Heidelberg,Germany email:[email protected]
Coverfigure:Detailfrom‘VenusBeautyandAnisotropicGeometricDiffusion’byU.Clarenz,U.Diewald,and
M.Rumpf.CourtesyofM.Rumpf
ISSN1612-3018
ISBN-103-540-23889-1SpringerBerlinHeidelbergNewYork
ISBN-13978-3-540-23889-8SpringerBerlinHeidelbergNewYork
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To all who struggle to understand this strange world
Preface
The standard books on relativity do not usually address the questions
of the physical meaning of relativistic effects and the nature of space-
time. This book deals specifically with such conceptual questions. All
kinematic consequences of special relativity are analyzed by explicitly
asking whether the physical objects involved in these effects are three-
dimensional or four-dimensional; this is equivalent to asking whether
those objects exist only at the present moment of their times, as our
commonsensesuggests,oratallmomentsoftheirhistories.Ananswer
tothequestionofthedimensionalityofphysicalobjectswillresolvethe
issue of the nature of spacetime – whether spacetime is just a math-
ematical space (like a seven-dimensional color space, for instance) or
represents a real four-dimensional world.
Thisbookisintendedforphysicists,philosophersofscience,philoso-
phers, physics and philosophy students, and anyone who is interested
in what special relativity is telling us about the world.
Acknowledgements
I would like to express my gratitude to all who contributed to the
appearance of this book. So many people were involved in discussions
on the issues covered here that it is virtually impossible to mention
them all. That is why I would merely like to thank them for their
constructive comments and hope that our discussions have brought us
a little closer to understanding this beautiful but strange world.
I feel I should start the short list of specific acknowledgements by
thankingSpringerandDr.AngelaLaheeforstartingthepublicationof
TheFrontiersCollection.Ithinktheappearanceofsuchaseriesismore
than timely since scientists have already started to lose sight of new
developments in the various scientific fields. I would also like to thank
Stephen Lyle for his excellent technical editing of the manuscript.
I owe a lot to my teacher and friend Anastas Anastassov of Sofia
University. His excellent lectures on general relativity in the 1980s
VIII Preface
and our never-ending discussions prepared the ground for the ideas
developed in this book. My thanks also go to Prof. Tzvetan Bonchev
(at thetimeDean of Sofia University’sFacultyof Physicsand Chair of
the Department of Atomic Physics) and Prof. Ivanka Apostolova (at
the time Chair of Sofia University’s Department of Philosophy). Their
influence is difficult to estimate.
I am grateful to my colleagues from the Department of Philosophy
of Science of the Institute for Philosophical Research at the Bulgarian
Academy of Sciences with whom many of the topics in this book were
discussed in the late 1980s.
Versions of the issues examined in the book have been covered in
different classes I taught – in the philosophy of science classes at Sofia
University in the 1980s and later in the physics and in the philosophy
of science classes at Concordia University. I am grateful to all students
who participated in the class discussions. I also benefited from valu-
able comments from colleagues and students at Concordia University,
McGill University and the University of Montreal, who attended a se-
ries of lectures I gave at a weekly seminar on General Relativity in the
Fall of 1994, held at Concordia University. I would like to express my
sincere thanks to all anonymous referees who made constructive rec-
ommendationsandcommentsondifferentissuesthatarenowincluded
in this book. Most of the results presented here were also reported at
several international conferences and at two inter-university seminars
inMontreal–onopenquestionsinphysicsandonthehistoryandphi-
losophy of science. I am truly grateful to the colleagues and students
who took part in the discussions.
And last, I would like to express my deep gratitude to my wife
Svetoslava and our son Vesselin (Jr) for their understanding, uncondi-
tionalsupport,andencouragement.Thecompletionofthisbookwould
not have been possible without their endless love and faith in me.
Montreal, Vesselin Petkov
12 October 2004
Contents
1 Introduction ........................................ 1
Part I From Galileo to Minkowski
2 On the Impossibility of Detecting Uniform Motion.. 13
2.1 Aristotle’s View on Motion ........................ 14
2.2 Copernicus and Ptolemy’s Arguments
Against the Earth’s Motion........................ 16
2.3 Galileo’s Disproof of Aristotle’s View on Motion ..... 17
2.4 Galileo’s Principle of Relativity .................... 25
3 Exploring the Internal Logic
of Galileo’s Principle of Relativity .................. 29
3.1 On the Physical Meaning
of Galileo’s Principle of Relativity .................. 30
3.2 On the Two Postulates of Special Relativity ......... 48
3.3 A Lesson from a Delayed Discovery................. 51
3.4 Summary ....................................... 53
4 Relativity in Euclidean Space and in Spacetime ..... 55
4.1 Spacetime ....................................... 56
4.2 Derivation of the Lorentz Transformations........... 70
4.3 Four-Dimensional Distance and Three Kinds of Length 78
4.4 Y ‘Dilation’ in Euclidean Space
and Time Dilation in Spacetime.................... 84
4.5 Length Contraction in Euclidean Space
and in Spacetime................................. 91
4.6 The Twin Paradox in Euclidean Space
and in Spacetime................................. 98
4.7 Addition of Velocities............................. 105
4.8 The Metric of Spacetime .......................... 106
X Contents
4.9 On Proper and Coordinate Time ................... 107
4.10 Four-Velocity, Four-Momentum, and Relativistic Mass 111
4.11 Summary ....................................... 116
Part II On the Nature of Spacetime:
Conceptual and Philosophical Issues
5 Relativity and the Dimensionality of the World:
Spacetime Is Real................................... 121
5.1 Has Special Relativity Posed
the Greatest Intellectual Challenge to Humankind? ... 122
5.2 Relativity and Dimensionality of the World.......... 123
5.3 Length Contraction............................... 134
5.4 Time Dilation ................................... 139
5.5 Relativization of Existence and the Twin Paradox .... 142
5.6 Why Is the Issue of the Nature of Spacetime
So Important? ................................... 146
5.6.1 Conventionality of Simultaneity .............. 146
5.6.2 Temporal Becoming......................... 147
5.6.3 Flow of Time and Consciousness ............. 148
5.6.4 Free Will .................................. 152
5.7 Summary ....................................... 153
6 Quantum Mechanics and the Nature of Spacetime .. 155
6.1 Quantum Mechanical Arguments
Against the Reality of Spacetime................... 157
6.2 Is Quantum Mechanical Probability Objective? ...... 158
6.3 The Nature of the Quantum Object
and the Nature of Spacetime....................... 160
6.4 Summary ....................................... 168
7 The Nature of Spacetime
and Validity of Scientific Theories................... 171
7.1 Reliability of Knowledge:
Induction as Hidden Deduction .................... 172
7.2 Correspondence Principle
and Growth of Scientific Knowledge ................ 177
7.3 Can an Accepted Scientific Theory Be Refuted?...... 180
7.4 Is a Final Scientific Theory Possible? ............... 182
7.5 Summary ....................................... 182
