The Special Theory of Relativity: Foundations, Theory, Verification, Applications

ISBN-13: 9783319252728 / Angielski / Miękka / 2016 / 480 str.

Costas Christodoulides

Opis

This book offers a comprehensive, university-level introduction to Einstein's Special Theory of Relativity. In addition to the purely theoretical aspect, emphasis is also given to its historical development as well as to the experiments that preceded the theory and those performed in order to test its validity.The main body of the book consists of chapters on Relativistic Kinematics and Dynamics and their applications, Optics and Electromagnetism. These could be covered in a one-semester course. A more advanced course might include the subjects examined in the other chapters of the book and its appendices.As a textbook, it has some unique characteristics: It provides detailed proofs of the theorems, offers abundant figures and discusses numerous examples. It also includes a number of problems for readers to solve, the complete solutions of which are given at the end of the book.It is primarily intended for use by university students of physics, mathematics and engineering. However, as the mathematics needed is of an upper-intermediate level, the book will also appeal to a more general readership.

Spis treści

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.- The Relativity 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.

O autorze

Costas Christodoulides

Professor Emeritus

Department of Physics

School of Applied Mathematical and Physical Sciences

National Technical University of Athens, Greece