目錄
Preface
Pedagogical Aims
Humanistic Aims
Special Features of This Book
Other Works on the Subject
Background Necessary to Read This Book
Plan ofthe W6rk
Acknowledgments
Part 1.The Special Theory
Chapter 1.Time, Space, and Space—Time
1.Simultaneity and Sequentiality
2.Svnchronization in Newtonian Mechanics
3.An Asymmetry in Newtonian Mechanics: Electromagnetic Forces
4.The LorentZ TraDSformation
5.Contraction of Length and Time
6.Composition of Parallel Velocities
7.The Twin Paradox
8.Relativistic Triangles
9.Composition of Relativistic Velocities as a Binary Operation
10.Plane Trigonometry
11.The Lorentz Group
12.Closure of Lorentz Transfclrmations under Composition
13.Rotational Motion and a Non.Euclidean Geometry
14.Problems
Chapter 2.Relativistic Mechanics
1.The Kinematics of a Particle
2.From Kinematics to Dynamics: Mass and Momentum
3.Relativistic Force
4.W10rk.Energy.and the Famous E=mc2
5.Newtonian Potential Energy
6.Hamilton's Principle
7.The Newtonian Lagrangian
8.The Relativistic Lagrangian
9.Angular Momentum and Torque
10.Fbur—Vectors and Tensors
11.Problems
Chapter 3.Electromagnetic Theory
1.Charge and Charge Density
2.Current and Current Density
3.nansformation of Electric and Magnetic Fields
4.Derivation of the Curl Equations from the Divergence Equations
5.Problems
Part 2.The General Theory
Introduction to Part 2
Chapter 4.Precession and Deflection
1.Gravitation as Curvature of Space
2.First Analysis: Newtonian 0rbits
3.Second Analysis: Newton's Law with Relativistic Force
4.Third Analysis: Newtonian Orbits as Geodesics
5.Fourth Analysis: General Relativity
6.Einstein's Law of Gravity
7.Computation of the Relativistic Orbit
8.The Speed of Light
9.Deflection of Light Near the Sun
10.Problems
Chapter 5.Concepts of Curvature, 1700—1850
1.Diiferential Geometry
2.Curvature, Phase 1: Euler
3.Curvature.Phase 2: Gauss
4.Problems
Chapter 6.Concepts of Curvature, 1850—1950
1.Second—Order Derivations
2.Curvature.Phase 3: Riemann
3.Parallel Transport
4.The Exponential Mapping and Normal Coordinates
5.Sectional Curvature
6.The Laplace—Beltrami Operator
7.Curvature.Phase 4: Ricci
8.Problems
Chapter 7.The Geometrization of Gravity
1.The Einstein Field Equations
2.Further Developments
3."Temporonautics"and the GSdel Rotating Universe
4.Black Holes
5.Problems
Part 3.Historical and Philosophical Context
Chapter 8.Experiments, Chronology, Metaphysics
1.Experimental Tests of General Relativity
2.Chronology
3.Space and Time
4.The Reality of Physical Concepts
5.The Harmony Between Mathematics and the Physical World
6.Knowledge of Hypothetical Objects: An Example
7.Knowledge of the Physical World
8.A Few Words from the Discoverers
9.Epilogue: The Reception of Relativity
Bibliography
Subject Index
Name Index
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