Table Of ContentPractical Relativity
Practical Relativity
From First Principles to the Theory of Gravity
RICHARD N. HENRIKSEN
Queen’s University, Kingston, Ontario
A John Wiley and Sons, Ltd., Publication
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LibraryofCongressCataloguing-in-PublicationData
Henriksen,R.N.
Practicalrelativity: fromfirstprinciplestothetheoryofgravity/RichardN.Henriksen.
p. cm.
Includesbibliographicalreferencesandindex.
ISBN978-0-470-74142-9(cloth)–ISBN978-0-470-74141-2(pbk.) 1. Relativity(Physics)I.Title.
QC173.58.H362010
530.11–dc22
2010023306
AcataloguerecordforthisbookisavailablefromtheBritishLibrary
ISBN:978-0-470-74142-9(H/B)978-0-470-74141-2(P/B)
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Coverimages: DiceimagefromSightsThatEinsteinCouldNotYetSee–visualizationofrelativisticeffects. UteKraus,
HannsRuder,DanielWeiskopf,CorvinZahn. LatticeworkandClocksfromSpacetimePhysics,2ebyE.FTaylorandJ.A.
Wheeler(cid:1)c 1992byEdwinTaylorandJohnArchibaldWheeler,usedwithpermission.
To the memory of Gertrude and Norman, Emma and Halter;
and to Judith who is life’s force incarnate.
Contents
Preface ix
Acknowledgements xi
Introduction xiii
Part I: The World Without Gravity 1
1. Non-Relativity for Relativists 3
1.1 Vectors and Reference Frames 3
1.1.1 Reference Frames 4
1.1.2 Inertial Reference Frames 25
2. Invariance of Physical Law Under Change of Inertial Frame of
Reference 45
2.1 Prologue 45
2.2 The Theory of Light or Electromagnetic Waves 48
2.2.1 Wave Propagation Speed 48
2.3 Measurement Theory and the Lorentz Transformations 62
3. Implications: Using and Understanding the Lorentz Transformations 79
3.1 Prologue 79
3.2 Kinematic Applications 80
3.2.1 Time 80
3.2.2 Time and Rotation 91
3.2.3 Time and the Lorentz Transformation 93
3.2.4 Space 94
3.2.5 Space and Time 99
3.3 Kinematic Acceleration 101
3.3.1 Thomas Precession 104
3.4 Geometrical Optics 108
3.4.1 Pictures of Moving Objects 111
3.4.2 Light Echoes 118
4. The Measure of Space-Time 123
4.1 Prologue 123
4.2 Metric Space-Time 124
4.2.1 Two Metric Derivations of the Lorentz Transformation 133
viii Contents
4.3 Four-Vector Dynamics 136
4.3.1 Lagrangian Dynamics Without Fundamental Forces 140
4.3.2 Collisions Between Free Particles 152
5. Electromagnetic Theory in Space-Time 161
5.1 Prologue 161
5.1.1 Electromagnetic Four-Potential 162
5.2 Lagrangian Dynamics of an Electromagnetic Charge 165
5.2.1 Field Transformations Between Inertial Frames 179
5.3 Electromagnetism for Arbitrary Inertial Observers 182
5.3.1 Curvilinear Electromagnetic Theory 192
Part II: Relativity With the Gravitational Field 203
6. Gravitational Structure of Space-Time 205
6.1 Prologue 205
6.2 The Weak Gravitational Field 209
6.3 Constant or Stationary Gravitational Field 215
6.4 Strong Gravitational Field 222
6.4.1 The Schwarzschild Metric 222
6.4.2 Orbital Precession and Light Bending in a
Schwarzschild Geometry 229
6.4.3 Kerr Metric Outside a Rotating Mass 240
6.4.4 Relativistic Continua 244
6.4.5 The Curvature of Space-Time 247
Index 257
