The Special Theory of Relativity - A Mathematical Approach

Preface to the Second Edition
Preface to the First Edition
Contents
About the Author
1 Pre-relativity and Galilean Transformation
1.1 Failure of Newtonian Mechanics
1.2 Galilean Transformations
1.3 Galilean Transformations in Vector Form
1.4 Non-inertial Frames
1.5 Galilean Transformation and Laws of Electrodynamics
1.6 Attempts to Locate the Absolute Frame
2 Michelson–Morley Experiment and Velocity of Light
2.1 Attempts to Locate Special Privileged Frame
2.2 The Michelson–Morley Experiment (M–M)
2.3 Phenomena of Aberration: Bradley's Observation
2.4 Fizeau's Experiment
2.5 The Relativistic Concept of Space and Time
3 Lorentz Transformations
3.1 Postulates of Special Theory of Relativity
3.2 Lorentz Transformations
3.2.1 Lorentz Transformation Between Two Inertial Frames of Reference (Non-axiomatic Approach)
3.2.2 Axiomatic Derivation of Lorentz Transformation
3.2.3 Lorentz Transformation Based on the Postulates of Special Theory of Relativity
3.3 The General Lorentz Transformations
3.4 Thomas Precession
4 Mathematical Properties of Lorentz Transformations
4.1 Length Contraction (Lorentz–Fitzgerald Contraction)
4.2 Time Dilation
4.3 Relativity of Simultaneity
4.4 Twin Paradox in Special Theory of Relativity
4.5 Car–Garage Paradox in Special Theory of Relativity
4.6 Real Example of Time Dilation
4.7 Terrell Effects
5 More Mathematical Properties of Lorentz Transformations
5.1 Interval
5.2 The Interval Between Two Events Is Invariant Under Lorentz Transformation
6 Geometric Interpretation of Space–Time
6.1 Space–Time Diagrams
6.2 Some Possible and Impossible World Lines
6.3 Importance of Light Cone
6.4 Relationship Between Space–Time Diagrams in S and S1 Frames
6.5 Geometrical Representation of Simultaneity, Space Contraction and Time Dilation
6.5.1 Simultaneity
6.5.2 Space Contraction
6.5.3 Time Dilation
7 Relativistic Velocity and Acceleration
7.1 Relativistic Velocity Addition
7.2 Relativistic Velocity Transformations
7.3 Relativistic Acceleration Transformations
7.4 Uniform Acceleration
7.5 Relativistic Transformations of the Direction Cosines
7.6 Application of Relativistic Velocity and Velocity Addition Law
7.6.1 The Fizeau Effect: The Fresnel's Coefficient of Drag
7.6.2 Aberration of Light
7.6.3 Relativistic Doppler Effect
8 Four-Dimensional World
8.1 Four-Dimensional Space–Time
8.2 Proper Time
8.3 World Velocity or Four Velocities
8.4 Lorentz Transformation of Space and Time in Four-Vector Form
9 Mass in Relativity
9.1 Relativistic Mass
9.1.1 First Method Based on Hypothetical Experiment of Tolman and Lews
9.1.2 Second Method Based on a Thought Experiment
9.1.3 Third Method
9.2 Experimental Verification of Relativistic Mass
9.3 Lorentz Transformation of Relativistic Mass
10 Relativistic Dynamics
10.1 Four Forces or Minkowski Force
10.2 Four Momenta
10.3 Relativistic Kinetic Energy
10.4 Mass–Energy Relation
10.5 Relation Between Momentum and Energy
10.6 Evidence in Support of Mass–Energy Relation
10.7 Force in Special Theory of Relativity
10.8 Covariant Formulation of Newton's Law
10.9 Examples of Longitudinal Mass and Transverse Mass
10.10 The Lorentz Transformation of Momentum
10.11 The Expression p2 - E2c2 Is Invariant Under Lorentz Transformation
11 Photon in Relativity
11.1 Photon
11.2 Compton Effect
11.3 The Lorentz Transformation of Momentum of Photon
11.4 Minkowski Force for Photon
12 Relativistic Lagrangian and Hamiltonian
12.1 Relativistic Lagrangian
12.2 Relativistic Hamiltonian Function
12.3 Covariant Lagrangian and Hamiltonian Formulation
12.4 Lorentz Transformation of Force
12.5 Relativistic Transformation Formula for Density
13 Electrodynamics in Relativity
13.1 Relativistic Electrodynamics
13.2 Equation of Continuity
13.3 Maxwell's Equations
13.4 Derivation of Equation of Continuity from Maxwell's Equations
13.5 Displacement Current
13.6 Transformation for Charge Density
13.7 Four Current Vector
13.8 Equation of Continuity in Covariant Form
13.9 Transformation of Four Current Vector
13.10 Maxwell's Equations in Covariant Form
13.10.1 The d'Alembertian Operator is Invariant Under Lorentz Transformation
13.10.2 Lorentz-Gauge Condition in Covariant Form
13.10.3 Gauge Transformations
13.11 Transformation of Four Potential Vector
13.12 The Electromagnetic Field Tensor
13.13 Lorentz Transformation of Electromagnetic Fields
13.14 Maxwell's Equations Are Invariant Under Lorentz Transformations
13.15 Lorentz Force on a Charged Particle
13.16 Electromagnetic Field Produced by a Moving Charge
13.17 Relativistic Lagrangian and Hamiltonian Functions …
14 Electromagnetic Waves
14.1 Introduction
14.2 Wave Equation for Magnetic Intensity "0245H
14.3 Wave Equation for Electric Field Strength "0245E
14.4 Electromagnetic Waves in a Non-conducting Dielectric Medium
14.5 Poynting's Theorem (Energy Conservation)
14.6 Boundary Conditions
14.7 Plane Electromagnetic Waves in a Non-conducting Isotropic Medium
14.8 Plane Electromagnetic Waves in a Conducting Medium
14.9 Skin Depth
14.10 Wave Guides
14.11 Coulomb Gauge
14.12 Hertz Vector
14.13 A Brief Introduction of Relativistic Wave Equation
15 Relativistic Mechanics of Continua
15.1 Relativistic Mechanics of Continuous Medium (Continua)
Appendix Appendix A
Appendix Appendix B
Appendix References
Index