CONTENTS -- PREFACE -- 1 INTRODUCTION AND SURVEY -- 2 WAVE MEANING OF THE SPECIAL RELATIVITY THEORY -- 2-1 Critical Review of the Interpretation of Special Relativity -- 2-2 Calculation of the Rectilinear Accelerated Motion of a Particle -- 2-3 Analysis of the Lorentz-Poincare Transformation -- 2-3-1 Constant Acceleration Motion -- 2-3-2 Constant Velocity Motion -- 2-4 Wave Meaning of the Lorentz-Poincare Transformation -- 2-5 Length Contraction and Time Dilation of a Moving Body -- 2-6 Comparison Between Elbaz and De Broglie Approaches -- 2-7 Different Meanings of the Lorentz-Poincare Transformation -- 2-8 The Concept of Simultaneity -- 2-9 Definition of Eulerian and Lagrangian Coordinates -- 2-9-1 Path Vector Definition -- 2-9-2 Lagrangian Definition -- 2-9-3 Eulerian Definition -- 2-9-4 Moving Grid Definition -- 2-9-5 Special Relativity Definition -- 3 CHANGE OF REFERENCE FRAME -- 3-1 Change of Reference Frame without Rotation -- 3-2 Change of Reference Frame with Rotation -- 3-2-1 Calculation of Positions in a Change of Reference Frame -- 3-2-2 Invariance of Distances in a Change of Reference Frame -- 3-2-3 Calculation of Velocities in a Change of Reference Frame -- 3-2-4 Calculation of Accelerations in a Change of Reference Frame -- 3-2-5 Derivative of a Vector in a Rotating Reference Frame -- 3-2-6 Equivalence Between the Lorentz Force and Non-inertial Terms -- 3-2-7 Calculation of the Stress and Rotation Dyads in a Change of Reference Frame -- 3-2-8 Covariance and Invariance of Quantities in a Change of Coordinates -- 3-2-9 Covariance and Invariance of Quantities in a Change of Reference Frame -- 3-3 The Relativistic Invariants and the Definition of Velocities -- 3-3-1 The Relativistic Invariants and the Lorentz Transformations.

3-3-2 The Relativistic Invariants in Frequency-wave Number -- 3-3-3 The Relativistic Invariants in Space-time -- 4 RELATIVISTIC AND CLASSICAL MECHANICS -- 4-1 Definition of Absolute and Relative Quantities -- 4-2 The Addition Law of Velocities -- 4-3 Newton's Third Law and the Principle of Energy Conservation -- 4-3-1 Work of a Force Along a Trajectory -- 4-3-2 Work of a Force Along a Curve -- 4-3-3 Particular Definition of the Conservation Law of Energy -- 4-3-4 Fluid Definition of the Conservation Law of Energy -- 4-4 Principles of Relativity and Covariance in Galilean Mechanics -- 4-4-1 Principle of Relativity in Galilean Mechanics -- 4-4-2 Covariance and Invariance in a Change of Coordinates -- 4-4-3 Principle of Covariance in Galilean Mechanics -- 4-5 Principles of Relativity and Covariance in Relativistic Mechanics -- 4-5-1 Inertial Reference Frame and Principle of Equilibrium -- 4-5-2 The Reciprocity Concept and Newton's Third Law -- 4-5-3 The Concept of Speed Limit -- 4-5-4 Dependance of the Light Velocity on the Receiver Motion -- 4-6 Definitions of Potential and Kinetic Energies -- 4-6-1 Application of Newton's Third Law -- 4-6-2 Internal and External Forces in a System of Particles -- 4-6-3 Partition of Forces Using Jacobi Coordinates -- 4-7 Review of Angular Momentum Definition -- 4-7-1 Definition of Angular Momentum -- 4-7-2 Orbital and Spin Angular Momentums of a Particle System -- 4-8 Experimental Tests of Partition of Forces Between Internal and External Forces -- 4-8-1 Elastic Collision Between Two Particles -- 4-8-2 Inelastic Collision Between Two Particles -- 4-8-3 Energy and Momentum of a System of Relativistic Particles -- 4-8-4 Collision of Radiation with Matter -- 4-8-5 The Tolman Experiment -- 4-8-6 The Graham and Lahoz Experiment -- 4-8-7 The Barnett Experiment.

5 EXPERIMENTAL TESTS OF SPECIAL RELATIVITY -- 5-1 Doppler and Aberration Effects -- 5-1-1 Definition of Wave Propagation -- 5-1-2 Classical Doppler Effect and the Galilean Transformation -- 5-1-3 Classical Doppler Effect and the Inhomogeneous Waves -- 5-1-4 The Doppler Radar -- 5-1-5 Relativistic Doppler Effect -- 5-1-6 Aberration Effect -- 5-1-7 Aberration Effect for a Wave -- 5-2 The Sagnac and Michelson Interferometer Experiments -- 5-2-1 The Sagnac Experiment -- 5-2-2 The Michelson and Morley Experiment -- 5-3 The Fizeau Effect -- 5-4 Compton Effect -- 5-4-1 Corpuscular Theory of the Compton Effect -- 5-4-2 Analysis of Recoil Electrons -- 5-4-3 Wave Theory of the Compton Effect -- 5-5 The Mossbauer Effect -- 5-5-1 Experimental Confirmation of the Mossbauer Effect -- 5-5-2 Applications of the Mossbauer Effect -- 5-5-3 Corpuscular Theory of the Mossbauer Effect -- 5-6 The Twin Paradox -- 5-6-1 Case of a Rectilinear Motion -- 5-6-2 Case of a Rotational Motion -- 5-7 The Luminiferous Ether a Necessity -- 5-8 Are the Relativistic Effects Second-order in U/c? -- 6 PARTIAL DIFFERENTIAL EQUATIONS OF SECOND ORDER -- 6-1 Definition of the Wave Equation -- 6-1-1 Case of a Homogeneous Medium -- 6-1-2 Case of an Inhomogeneous Medium -- 6-1-3 Differential Calculus and Second-order Particular Derivative -- 6-1-4 Operators Applied to Functions of Two Variables -- 6-1-5 Operators and Jacobi Coordinates -- 6-2 Spectral Analysis of the Wave Equation -- 6-3 Conservation Laws of the Wave Equation -- 6-4 Method of Separation of Variables -- 6-4-1 Case of Cartesian Coordinates -- 6-4-2 Case of Cylindrical Coordinates -- 6-4-3 Case of Spherical Coordinates -- 6-4-4 Solution of the Helmholtz Inhomogeneous Equation -- 6-5 Review of the Dissipation Concept -- 6-5-1 Definition of Dissipation.

6-5-2 Relationship Between Dissipation Causality and the Wave Concept -- 6-6 Review of the Dispersion Concept -- 6-6-1 Definition of Dispersion -- 6-6-2 Analysis of Dispersion in the Vacuum -- 6-6-3 Definition of Light Velocity -- 6-6-4 Transmission Line Theory -- 6-6-5 Vacuum Conductivity and the Speed Limit -- 6-6-6 The Tired-light Mechanism of Redshift in the Vacuum -- 6-7 Hyperbolic Equations of Second-order and the Soliton -- 6-7-1 The Schrodinger Equation -- 6-7-2 The Wave Equation and the Focus Wave Modes -- 6-7-3 The de Broglie and Klein-Gordon Equations -- 6-7-4 The Telegrapher Equation -- 6-7-5 Finite Energy Solutions -- 6-8 The Helmholtz Theorem -- 6-8-1 Integral Spatial Solution -- 6-8-2 Fourier Analysis -- 6-8-3 Integral Solution in Space-time -- 6-8-4 Application to Maxwell-Ferrier Equations -- 6-9 Analysis of Rotational Fields -- 6-9-1 Analysis of Beltrami and Trkal Fields -- 6-9-2 Force-free Fields and the Virial Theorem -- 6-9-3 Ordinary Fields and the Superposition Principle -- 6-9-4 Hansen Decomposition and the Beltrami Field -- 6-9-5 Hansen Decomposition in Different Coordinate Systems -- 7 THE WAVE PACKET CONCEPT -- 7-1 Point-particle Versus Wave Packet -- 7-2 Spectral Analysis of the Mackinnon Wave Packet -- 7-3 Acceleration of a Wave Packet -- 7-4 The Electron as a Wave Packet -- 7-5 Vibration Wave and Propagation -- 7-6 Analysis of the Size of a Signal -- 7-6-1 Analysis of Radiation of an Extended Source -- 7-6-2 Space-time Analysis of a Signal -- 7-6-3 Heisenberg Uncertainty Principle -- 7-7 Quantization of Oscillating Waves of the Ether -- 7-7-1 Continuity Versus Discontinuity -- 7-7-2 Case of Classical Mechanics -- 7-7-3 Case of a Harmonic Oscillator -- 7-7-4 Case of Relativistic Mechanics -- 7-8 The Relativistic Mass-increase with Velocity.

7-8-1 Constant Force and Hyperbolic Motion -- 7-8-2 Classical Explanation of the Gamma Term -- 7-8-3 The Bertozzi Experiment -- 7-9 Matter Waves -- 7-9-1 The Lande Paradox and the Doppler Effect -- 7-9-2 Matter Waves Radiation and Creation of Particles -- 7-9-3 Matter Waves and Inhomogeneous Waves -- 7-10 Formalism of Lagrange-Hamilton -- 7-10-1 Case of Classical Mechanics -- 7-10-2 Case of Relativistic Mechanics -- 7-10-3 Variational Formulation -- 7-11 The Ray Theory -- 7-11-1 Analysis of Propagation in an Inhomogeneous Medium -- 7-11-2 Geometrical Optics -- 7-11-3 Electron Optics -- 8 ELECTROMAGNETISM -- 8-1 The Wave-particle Duality of Light -- 8-2 Analysis of the Phase Concept -- 8-2-1 Pfaff Phase Definition -- 8-2-2 Whitham Phase Definition -- 8-2-3 Analysis of a Fourier Mode -- 8-3 Analogy Between the Moving Grid Formulation and the Transmission Line Theory -- 8-3-1 Maxwell-Proca Equations -- 8-3-2 Maxwell-Proce and De Broglie Equations -- 8-3-3 Signification of the Photon Mass -- 8-4 The Integrating Factor Method -- 8-4-1 Maxwell-Ferrier Equations -- 8-4-2 Different Formulations of Potential -- 8-5 Definitions of Energy and Momentum Conservation Laws -- 8-5-1 Conservation Laws for the Potentials -- 8-5-2 Conservation Laws for the Electromagnetic Field -- 8-5-3 Maxwell's Equations and Newton's Third Law -- 8-5-4 The Angular Momentum of the Electromagnetic Field -- 8-6 The Principle of Superposition of Fields -- 8-6-1 Case of Light Interferences -- 8-6-2 Case of Electrostatic Fields -- 8-6-3 The Linear Circuit Theory -- 8-6-4 The Carson Reciprocity Theorem -- 8-6-5 Case of the Antenna Radiation -- 8-7 The Energy Conservation and the Radiation Reaction Force -- 8-8 Different Formulations of Maxwell's Equations -- 8-8-1 Maxwell's Equations and the Galilean Transformation.

8-8-2 Mathematical Formulations of Faraday and Ampere Laws.