Understanding Relativity: A Simplified Approach to Einstein's Theories

384 Pages·2012·5.17 MB·English

by  Leo Sartori

Understanding Relativity
Thispageintentionallyleftblank
Understanding
Relativity
A Simplified Approach to Einstein's Theories
LEO SARTORI
UNIVERSITY OF NEBRASKA-LINCOLN
University of California Press
BERKELEY LOS ANGELES LONDON
UniversityofCaliforniaPress
BerkeleyandLosAngeles,California
UniversityofCaliforniaPress
London, England
Copyright© 1996byTheRegentsoftheUniversityofCalifornia
LibraryofCongressCataloging-in-PublicationData
Sartori,Leo.
Understandingrelativity:asimplifiedapproachtoEinstein's
theories/ LeoSartori.
p. em.
Includesbibliographicalreferencesandindex.
ISBN 978-0-520-20029-6 (ph.:alk.paper)
1. Relativity(Physics) I. Title.
QC173.55.S367 1996
530.1'1-dc20 94-49358
PrintedintheUnitedStatesofAmerica
08 07
9 8
Thepaperusedinthispublicationmeetstheminimumrequeirementsof
ANSIINISOZ39.48-1992(R1997)(PermanenceofPaper).
To Eva, Anne, andJenny
Thispageintentionallyleftblank
Contents
Preface xi
Acknowledgments xiii
1. GALILEAN RELATIVITY 1
1.1. Relativity and Common Sense 1
1.2. Events, Observers, and Frames of Reference 5
1.3. The Principle of Relativity and Inertial Frames 8
1.4. The Galilean Transformation 12
1.5. Stellar Aberration 17
1.6. The Covariance ofPhysical Laws 19
1.7. The Conservation ofMomentum 21
Problems 24
2. THE MICHELSON-MORLEY EXPERIMENT 26
2.1. The Ether 26
2.2. Prelude to Michelson-Morley 27
2.3. The Experiment 29
2.4. Attempts to Salvage the Ether 39
Problems 46
3. THE POSTULATES OF RELATIVITY AND THEIR
IMPLICATIONS 48
3.1. The Postulates 48
3.2. The Role ofthe Michelson-Morley Experiment in
the Genesis of Relativity 51
3.3. The Relativity ofTime: Simultaneity 54
3.4. The Synchronization ofClocks 60
3.5. Time Dilation 68
viii / Contents
3.6. The Decay ofMuons 79
3.7. Length Contraction 83
3.8. Transverse Lengths 88
3.9. Summary 93
Problems 94
4. THE LORENTZ TRANSFORMATION 97
4.1. Introduction 97
4.2. The Transformation Equations 98
4.3..Some Consequences ofthe Transformation
Equations 103
4.4. The Transformation ofVelocity 107
4.5. Fizeau's Experiment 111
4.6. The Transformation ofDirection and Relativistic
Aberration 114
4.7. Acceleration in Special Relativity 116
4.8. The Doppler Effect 117
4.9. The Role ofLorentz and Poincare in the Birth of
Relativity 122
Appendix. The Low-Velocity Approximation 134
Problems 135
5. SPACE-TIME DIAGRAMS 139
5.1. World Lines 139
5.2. The Light Cone 142
5.3. Relativity and Causality 144
5.4. Timelike and Spacelike Intervals 150
5.5. The Loedel Diagram 151
5.6. Applications ofthe Loedel Diagram 156
5.7. The Doppler Effect Revisited 160
Appendix SA. Mathematical Basis for the Loedel
Diagram 162
Appendix SB. The Doppler Formula 163
Problems 164
6. PARADOXES OF RELATIVITY 166
6.1. Introduction 166
6.2. The "Pole and Barn" Paradox 166
6.3. What Ifthe Pole Stops? 173
6.4. Other Length Paradoxes 185
6.5. The Paradox ofthe Twins 192
Problems 200
Contents / IX
7. RELATIVISTIC MECHANICS 202
7.1. The Equivalence ofMass and Energy 202
7.2. Kinetic Energy and Total Energy 208
7.3. Relativistic Momentum 213
7.4. Relativity in Nuclear and Particle Physics 219
7.5. Beta Decay and the Neutrino 225
7.6. The Transformation Law for Energy and
Momentum; Four-vectors 227
7.7. Photons 229
7.8. Tachyons 235
Appendix. Transformation ofMomentum
and Energy 237
Problems 239
8. GENERAL RELATIVITY 243
8.1. Introduction 243
8.2. The Principle ofEquivalence 246
8.3. The Gravitational Red Shift 255
8.4. Bending ofLight in aGravitational Field 263
8.5. Curved Space 267
8.6. General Relativity: Gravity as Geometry 277
Appendix. Curvature ofaSpherical Space 289
Problems 291
9. COSMOLOGY 293
9.1. Basic Facts: The Cosmological Principle 293
9.2. Hubble's Law and the Expansion ofthe Universe 297
9.3. The Big Bang 310
9.4. The Hubble Sphere and Horizons 313
9.5. Cosmological Models: Friedmann Universes 315
9.6. The Steady-State Universe 327
9.7. Observational Tests 332
9.8. The History ofthe Universe 337
9.9. Did the Big Bang Really Happen? 352
Problems 354
Index 357