Special Theory of Relativity

Description

Cover Contents Preface Historical Perspective Chapter 1 : Newtonian Mechanics and Galilean Principle of Relativity 1.1 Difficulties of Pre-Relativity Physics.Galilean Transformation 1.2 Newton’s Laws and Inertial Frames of Reference 1.3 Absolute Time and Absolute Space 1.4 Wave Equation Under Galilean Transformation 1.5 Search for a Universal Frame of Reference 1.5.1 Michelson–Morley Experiment 1.5.2 Kennedy–Thorndyke Experiment 1.5.3 Trouton and Noble Experiment 1.5.4 Experiment with Ammonia Masers References Problems Chapter 2 : Lorentz Transformation and Its Kinematic Consequences.Intervals and Causality 2.1 Einstein’s Postulates of Special Theory of Relativity. Principle of Relativity and Constancy of Velocity of Light 2.1.1 Invariance of the Velocity of Light 2.2 Lorentz Transformations12. Axiomatic Derivation 2.3 Kinematic Consequences of Lorentz Transformation 2.3.1 Lorentz–Fitzgerald Contraction 2.3.2 Time Dilation or Apparent Slowing of Moving Clocks 2.3.3 Relativity of Simultaneity 2.3.4 Causality and Maximum Signal Velocity 2.3.5 Addition of Velocities 2.3.6 The Fizeau Effect 2.3.7 Aberration of Light 2.4 Geometric Interpretation of Lorentz Transformation 2.5 The Light Cone 2.6 Transformation of Velocity and Acceleration References Problems Chapter 3 : Mathematical Background 3.1 Linear Orthogonal Transformation and its Invariants 3.2 Minkowski’s Four-Dimensional Space–Time World 3.2.1 Notation 3.3 Lorentz Transformation as Rotation in Four-Space 3.4 Four-Vectors 3.4.1 Transformation of a Four-Vector 3.4.2 Covariant Form of the Lorentz Condition and Equation of Continuity 3.5 Tensor Algebra. Anti-Symmetric Four-Tensor 3.6 Group Property of Lorentz Transformation Reference Problems Chapter 4 : Relativistic Mechanics of a Particle.Collisions and Conservation Laws 4.1 Relativistic Lagrangian for a Free Particle 4.2 Energy and Momentum of a Free Particle 4.2.1 Three-dimensional Form 4.2.2 Four-dimensional Formulation.Energy–Momentum Four-Vector 4.3 The Conservation of Momentum. Variation of Mass with Velocity 4.3.1 Transformation of Mass 4.4 Four-Dimensional Velocity and Acceleration 4.5 Relativistic Equation of Motion. Minkowski Force 4.5.1 Transformation of Force 4.6 Energy–Mass Equivalence 4.6.1 Mass Defect: Binding Energy 4.7 Centre of Momentum Transformation 4.8 Kinematic Relations for Collisions References Problems Chapter 5 : Optical Applications of Lorentz Transformation 5.1 Elements of Wave Propagation 5.2 Frequency and Wave-Vector Transformations 5.3 The Relativistic Doppler Effect. Aberration 5.3.1 The Longitudinal Doppler Effect 5.3.2 The Transverse Doppler Effect 5.4 Reflection of Light by a Moving Mirror 5.5 Propagation of Light in a Moving Medium:Fresnel’s Dragging Coefficient2 References Problems Chapter 6 : Covariant Electrodynamics 6.1 Invariance of Maxwell’s Equations Under Lorentz Transformation 6.2 Transformation of Electromagnetic Field Intensities 6.3 Electromagnetic Field Tensor 6.3.1 Electromagnetic Field Invariants 6.3.2 Transformation of Electromagnetic Fields 6.4 Covariant form of Maxwell’s Equations 6.5 Lagrangian and Hamiltonian for a Charged Particle in an Electromagnetic Field 6.6 Equation of Motion of a Charge in an Electromagnetic Field 6.6.1 Three-dimensional Vector Form 6.6.2 Four-dimensional Form 6.7 Maxwell’s Equations by Variational Technique 6.8 Electromagnetic Energy–Momentum Tensor 6.8.1 Conservation Laws of Vacuum Electrodynamics 6.9 Field of a Charge in Uniform Motion 6.10 Retarded Potentials. Lienard-Wiechert Potentials 6.10.1 The Lienard–Wiechert Potentials 6.11 Field Strengths of an Accelerated Charge Problems Chapter 7 : Applications of Special Theory of Relativity 7.1 Experimental Verification of the Special Theory 7.1.1 Testing the Postulates 7.1.2 Testing the Consequences 7.1.3 Test of Time Dilatation and Transverse Doppler Effect 7.1.4 Motivation for Testing Special Relativity 7.1.5 Recent Tests of CPT and Lorentz Invariance22 7.2 Thomas Precession: Spin–Orbit Interaction 7.3 Relativistic Classification of Particles 7.4 Zero Rest-Mass Particles: Photons and Neutrinos 7.4.2 Moving Faster Than Light 7.5 De Broglie Wavesfor a Free Particle 7.6 The Uncertainty Principle References Problems Chapter 8 : Introduction to General Relativity 8.1 Equivalence of Inertial and Gravitational Mass 8.1.1 Gravitational Mass of the Photon 8.2 The Principle of Equivalence 8.3 Einstein Elevator 8.4 The Principle of Covariance 8.5 Gravitational Effect on Clocks 8.6 Classical Tests of General Relativity 8.6.1 The Gravitational Red-Shift 8.6.2 Solar Bending of Starlight 8.6.3 Precession of the Perihelion of Mercury 8.7 The Renaissance of General Relativity References Problems Bibliography Index