Understanding Relativity (eBook)

Preface 
Acknowledgments 
1. GALILEAN RELATIVITY 
1.1. Relativity and Common Sense 
1.2. Events, Observers, and Frames of Reference 
1.3. The Principle of Relativity and Inertial Frames 
1.4. The Galilean Transformation 
1.5. Stellar Aberration 
1.6. The Covariance of Physical Laws 
1.7. The Conservation of Momentum 
Problems 
2. THE MICHELSON-MORLEY EXPERIMENT 
2.1. The Ether 
2.2. Prelude to Michelson-Morley 
2.3. The Experiment 
2.4. Attempts to Salvage the Ether 
Problems 
3. THE POSTULATES OF RELATIVITY AND THEIR
IMPLICATIONS 
3.1. The Postulates 
3.2. The Role of the Michelson-Morley Experiment in
the Genesis of Relativity 
3.3. The Relativity of Time: Simultaneity 
3.4. The Synchronization of Clocks 
3.5. Time Dilation 
3.6. The Decay of Muons 
3.7. Length Contraction 
3.8. Transverse Lengths 
3.9. Summary 
Problems 
4. THE LORENTZ TRANSFORMATION 
4.1. Introduction 
4.2. The Transformation Equations 
4.3 . .Some Consequences of the Transformation
Equations 
4.4. The Transformation of Velocity 
4.5. Fizeau's Experiment 
4.6. The Transformation of Direction and Relativistic
Aberration 
4.7. Acceleration in Special Relativity 
4.8. The Doppler Effect 
4.9. The Role of Lorentz and Poincare in the Birth of
Relativity 
Appendix. The Low-Velocity Approximation 134
Problems 
5. SPACE-TIME DIAGRAMS 
5.1. World Lines 
5.2. The Light Cone 
5.3. Relativity and Causality 
5.4. Timelike and Spacelike Intervals 
5.5. The Loedel Diagram 
5.6. Applications of the Loedel Diagram 
5.7. The Doppler Effect Revisited 
Appendix SA. Mathematical Basis for the Loedel
Diagram 
Appendix SB. The Doppler Formula 
Problems 
6. PARADOXES OF RELATIVITY 
6.1. Introduction 
6.2. The "Pole and Barn" Paradox 
6.3. What If the Pole Stops? 
6.4. Other Length Paradoxes 
6.5. The Paradox of the Twins 
Problems 
7. RELATIVISTIC MECHANICS 
7.1. The Equivalence of Mass and Energy 
7.2. Kinetic Energy and Total Energy 
7.3. Relativistic Momentum 
7.4. Relativity in Nuclear and Particle Physics 
7.5. Beta Decay and the Neutrino 
7.6. The Transformation Law for Energy and
Momentum; Four-vectors 
7.7. Photons 
7.8. Tachyons 
Appendix. Transformation of Momentum
and Energy 
Problems 
8. GENERAL RELATIVITY 
8.1. Introduction 
8.2. The Principle of Equivalence 
8.3. The Gravitational Red Shift 
8.4. Bending of Light in a Gravitational Field 
8.5. Curved Space 
8.6. General Relativity: Gravity as Geometry 
Appendix. Curvature of a Spherical Space 
Problems 
9. COSMOLOGY 
9.1. Basic Facts: The Cosmological Principle 
9.2. Hubble's Law and the Expansion of the Universe 
9.3. The Big Bang 
9.4. The Hubble Sphere and Horizons 
9.5. Cosmological Models: Friedmann Universes 
9.6. The Steady-State Universe 
9.7. Observational Tests 
9.8. The History of the Universe 
9.9. Did the Big Bang Really Happen? 
Problems 
Index