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Special Theory of Relativity

Book Description

Special Theory of Relativity is primarily intended as a textbook for the students of physics at the undergraduate level. Examining developments in the field as well as the predictions of special relativity that have taken place since 1959, its comprehensive coverage includes engaging explanations of the mathematical treatment as well as the applications of the special theory of relativity.

Table of Contents

  1. Cover
  2. Title Page
  3. Contents
  4. Preface
  5. Historical Perspective
  6. Chapter 1: Newtonian Mechanics and Galilean Principle of Relativity
    1. 1.1 Difficulties of Pre-relativity Physics. Galilean Transformation
    2. 1.2 Newton’s Laws and Inertial Frames of Reference
    3. 1.3 Absolute Time and Absolute Space
    4. 1.4 Wave Equation Under Galilean Transformation
    5. 1.5 Search for a Universal Frame of Reference
    6. Problems
  7. Chapter 2: Lorentz Transformation and Its Kinematic Consequences. Intervals and Causality
    1. 2.1 Einstein’s Postulates of Special Theory of Relativity. Principle of Relativity and Constancy of Velocity of Light
    2. 2.2 Lorentz Transformations. Axiomatic Derivation
    3. 2.3 Kinematic Consequences of Lorentz Transformation
    4. 2.4 Geometric Interpretation of Lorentz Transformation
    5. 2.5 The Light Cone
    6. 2.6 Transformation of Velocity and Acceleration
    7. Problems
  8. Chapter 3: Mathematical Background
    1. 3.1 Linear Orthogonal Transformation and Its Invariants
    2. 3.2 Minkowski’s Four-dimensional Space-Time World
    3. 3.3 Lorentz Transformation as Rotation in Four-space
    4. 3.4 Four-vectors
    5. 3.5 Tensor Algebra. Anti-symmetric Four-tensor
    6. 3.6 Group Property of Lorentz Transformation
    7. Problems
  9. Chapter 4: Relativistic Mechanics of a Particle. Collisions and Conservation Laws
    1. 4.1 Relativistic Lagrangian for a Free Particle
    2. 4.2 Energy and Momentum of a Free Particle
    3. 4.3 The Conservation of Momentum. Variation of Mass with Velocity
    4. 4.4 Four-dimensional Velocity and Acceleration
    5. 4.5 Relativistic Equation of Motion. Minkowski Force
    6. 4.6 Energy–Mass Equivalence
    7. 4.7 Centre of Momentum Transformation
    8. 4.8 Kinematic Relations for Collisions
    9. Problems
  10. Chapter 5: Optical Applications of Lorentz Transformation
    1. 5.1 Elements of Wave Propagation
    2. 5.2 Frequency and Wave-vector Transformations
    3. 5.3 The Relativistic Doppler Effect. Aberration
    4. 5.4 Reflection of Light by a Moving Mirror
    5. 5.5 Propagation of Light in a Moving Medium: Fresnel’s Dragging Coefficient
    6. Problems
  11. Chapter 6: Covariant Electrodynamics
    1. 6.1 Invariance of Maxwell’s Equations Under Lorentz Transformation
    2. 6.2 Transformation of Electromagnetic Field Intensities
    3. 6.3 Electromagnetic Field Tensor
    4. 6.4 Covariant form of Maxwell’s Equations
    5. 6.5 Lagrangian and Hamiltonian for a Charged Particle in an Electromagnetic Field
    6. 6.6 Equation of Motion of a Charge in an Electromagnetic Field
    7. 6.7 Maxwell’s Equations by Variational Technique
    8. 6.8 Electromagnetic Energy–Momentum Tensor
    9. 6.9 Field of a Charge in Uniform Motion
    10. 6.10 Retarded Potentials. Lienard-Wiechert Potentials
    11. 6.11 Field Strengths of an Accelerated Charge
    12. Problems
  12. Chapter 7: Applications of Special Theory of Relativity
    1. 7.1 Experimental Verification of the Special Theory
    2. 7.2 Thomas Precession: Spin-Orbit Interaction
    3. 7.3 Relativistic Classification of Particles
    4. 7.4 Zero Rest-mass Particles: Photons and Neutrinos
    5. 7.5 De Broglie Waves for a Free Particle
    6. 7.6 The Uncertainty Principle
    7. Problems
  13. Chapter 8: Introduction to General Relativity
    1. 8.1 Equivalence of Inertial and Gravitational Mass
    2. 8.2 The Principle of Equivalence
    3. 8.3 Einstein Elevator
    4. 8.4 The Principle of Covariance
    5. 8.5 Gravitational Effect on Clocks
    6. 8.6 Classical Tests of General Relativity
    7. 8.7 The Renaissance of General Relativity
    8. Problems
  14. Endnotes
  15. Bibliography
  16. Copyright
  17. Back Cover