The special theory of relativity : a mathematical approach / / Farook Rahaman

• Autore: Rahaman Farook
• Pubblicazione: Singapore : , : Springer, , [2022]; ©2022
• Edizione: Second edition.
• Descrizione fisica: 1 online resource (339 pages)
• Disciplina: 530.11
• Soggetto topico: Mathematical physics; Relativitat especial (Física)
• Soggetto genere / forma: Llibres electrònics
• Note generali: Includes index.
• Nota di contenuto: Intro -- 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.
• Titolo autorizzato: The Special Theory of Relativity
• ISBN: 9789811904974; 9789811904967
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996472039003316
• Lo trovi qui: Univ. di Salerno
• Serie: Unitext