关于时间：相对论的数学基础(影印版)

本书介绍了相对论的数学基础的相关理论知识 。目标读者是数学、其他科学和工程专业的高年级 本科生和研究生。读者应了解高等微积分的基础知 识、一些解微分方程的技巧、一些线性代数知识以 及集合论和群论的基础知识。本书适合对相对论的 数学方面感兴趣的高年级本科生、研究生以及数学 研究人员阅读参考。

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