Special Theory of Relativity

Costas ChristodoulidesProfessor EmeritusDepartment of PhysicsSchool of Applied Mathematical and Physical SciencesNational Technical University of Athens, Greece

• Historical Introduction.- The Main Landmarks in the Development of the Special Theory of Relativity.- The Principle of Relativity of Galileo. Galileo’s Invariance Hypothesis. The Law of Inertia. Inertial Frames of Reference Relativity.- Rømer and the Speed of Light.- Newton’s Laws of Motion. Inertia and Inertial Frames of Reference.- The Aberration of Light.- Arago’s Measurements Concerning the Constancy of the Speed of Light from Stars.- Measurements of the Speed of Light in the Laboratory.- Attempts to Measure the Dragging of Aether by Moving Media.- Maxwell’s Equations and the Wave Equation.- The Experiment of Michelson and Morley.- The Lorentz-Fitzgerald Contraction Hypothesis.- The Increase of the Mass of the Electron with Speed.- The Invariance of Maxwell’s Equations and the Lorentz Transformation.- The Formulation of the Special Theory of Relativity.- Prolegomena.- Inertial Frames of Reference.- The Calibration of a Frame of Reference and the Synchronization of its Clocks.- TheRelativity of Simultaneity.- The Relativity of Time and Length.- The Inevitability of the Special Theory of Relativity.- Relativistic Kinematics.- The Lorentz Transformation for the Coordinates of an Event.- The Transformation of Velocity.- The Transformation of Acceleration.- Applications of Relativistic Kinematics.- The ‘Meson’ Paradox.- The apparent focusing of fast charged particle beams due to the dilation of time.- The Sagnac Effect.- Clocks Moving Around the Earth.- The Experiment of Hafele and Keating.- Einstein’s Train.- The Twin Paradox.- Motion with a Constant Proper Acceleration. Hyperbolic Motion.- Two Successive Lorentz Transformations. The Wigner Rotation.- Optical Phenomena.- The Aberration of Light.- Fizeau’s Experiment. Fresnel’s Aether Dragging Theory.- The Doppler Effect.- Relativistic Beaming or the Headlight Effect.- The Pressure Exerted by Light.- Relativistic Dynamics.- The Dfinition of Relativistic Momentum. Relativistic Mass.- Relativistic Energy.- The Relationship Between Momentum and Energy.- Classical Approximations.- Particles with Zero Rest Mass.- The Conservation of Momentum and of Energy.- The Equivalence of Mass and Energy.- The Transformation of Momentum and Energy.- The Zero-Momentum Frame of Reference.- The Transformation of the Total Momentum and the Total Energy of a System of Particles.- The Collision of two Identical Particles.- The Transformation of Force.- Motion Under the Influence of a Constant Force. The Motion of a Charged Particle in a Constant Uniform Electric Field.- The Motion of a Charged Particle in a Constant Homogeneous Magnetic Field.- Applications of Relativistic Dynamics.- The Compton Effect.- The Inverse Compton Effect.- The Consequences of the Special Theory of Relativity on the Design of Particle Accelerators.- Mass Defect and Binding Energy of the Atomic Nucleus.- Threshold Energy.- The General Equations for the Motion of a Relativistic Rocket.- Minkowski’s Spacetime and Four-Vectors.- The ‘World’ of Minkowski.- Four-Vectors.- Electromagnetism.- Introduction.- The Invariance of Electric Charge.- The Transformations of the Electric Field and the Magnetic Field.- The Fields of a Moving Electric Charge.- The Derivation of the Differential form of the Biot-Savart Law from Coulomb’s Law.- The Force Exerted on a Moving Charge by an Electric Current.- Experiments.- The Speed of Light.- The Aether.- The Dilation of Time.- The Relativistic Doppler Effect.- The Contraction of Length.- The Test of the Predictions of Relativistic Kinematics.- The Sagnac Effect.- The Relativistic Mass.- The Equivalence of Mass and Energy.- The Test of the Predictions of Relativistic Dynamics.- The Invariance of Electric Charge.- Appendix 1. The Paradox of the Room and the Rod.- Appendix 2. The Appearance of Moving Bodies.- Appendix 3. The Derivation of the Expression for the Relativistic Mass in General.- Appendix .4. The Invariance of the Equations of Maxwell and the Wave Equation Under the Lorentz Transformation.- Appendix 5. Tachyons.- Appendix 6. The Lorentz Transformation in Matrix Form.- Appendix 7. Table of Some Functions of the Speed.- Solutions of the Problem.