关于时间：相对论的数学基础（影印版）
定价：￥169.00
作者： Roger Cooke
出版社：高等教育出版社
- 高等教育出版社
- 9787040630930
- 1版
- 47266237-8
- 特殊
- 680
- 理学
- 数学类
- 数学类
- 本科 研究生及以上
目录
目录
前辅文
Preface
Pedagogical Aims
Humanistic Aims
Special Features of This Book
Other Works on the Subject
Background Necessary to Read This Book
Plan of the Work
Acknowledgments
Part 1. The Special Theory
Chapter 1. Time, Space, and Space-Time
1. Simultaneity and Sequentiality
2. Synchronization in Newtonian Mechanics
3. An Asymmetry in Newtonian Mechanics: Electromagnetic Forces
4. The Lorentz Transformation
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 Transformations 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. Work, 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. Four-Vectors and Tensors*
11. Problems
Chapter 3. Electromagnetic Theory*
1. Charge and Charge Density
2. Current and Current Density
3. Transformation 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 Orbits
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. Differential 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 G¨odel 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
前辅文
Preface
Pedagogical Aims
Humanistic Aims
Special Features of This Book
Other Works on the Subject
Background Necessary to Read This Book
Plan of the Work
Acknowledgments
Part 1. The Special Theory
Chapter 1. Time, Space, and Space-Time
1. Simultaneity and Sequentiality
2. Synchronization in Newtonian Mechanics
3. An Asymmetry in Newtonian Mechanics: Electromagnetic Forces
4. The Lorentz Transformation
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 Transformations 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. Work, 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. Four-Vectors and Tensors*
11. Problems
Chapter 3. Electromagnetic Theory*
1. Charge and Charge Density
2. Current and Current Density
3. Transformation 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 Orbits
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. Differential 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 G¨odel 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
前辅文
Preface
Pedagogical Aims
Humanistic Aims
Special Features of This Book
Other Works on the Subject
Background Necessary to Read This Book
Plan of the Work
Acknowledgments
Part 1. The Special Theory
Chapter 1. Time, Space, and Space-Time
1. Simultaneity and Sequentiality
2. Synchronization in Newtonian Mechanics
3. An Asymmetry in Newtonian Mechanics: Electromagnetic Forces
4. The Lorentz Transformation
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 Transformations 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. Work, 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. Four-Vectors and Tensors*
11. Problems
Chapter 3. Electromagnetic Theory*
1. Charge and Charge Density
2. Current and Current Density
3. Transformation 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 Orbits
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. Differential 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 G¨odel 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
前辅文
Preface
Pedagogical Aims
Humanistic Aims
Special Features of This Book
Other Works on the Subject
Background Necessary to Read This Book
Plan of the Work
Acknowledgments
Part 1. The Special Theory
Chapter 1. Time, Space, and Space-Time
1. Simultaneity and Sequentiality
2. Synchronization in Newtonian Mechanics
3. An Asymmetry in Newtonian Mechanics: Electromagnetic Forces
4. The Lorentz Transformation
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 Transformations 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. Work, 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. Four-Vectors and Tensors*
11. Problems
Chapter 3. Electromagnetic Theory*
1. Charge and Charge Density
2. Current and Current Density
3. Transformation 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 Orbits
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. Differential 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 G¨odel 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
