Advanced Electromagnetism and Vacuum Physics (21) (World Scientific Series in Contemporary Chemical Physics, 21)

PREFACE......Page 6 CONTENTS......Page 8 1 INTRODUCTION AND SURVEY......Page 20 2-1 Critical Review of the Interpretation of Special Relativity......Page 24 2-2 Calculation of the Rectilinear Accelerated Motion of a Particle......Page 27 2-3-2 Constant Velocity Motion......Page 29 2-4 Wave Meaning of the Lorentz-Poincare Transformation......Page 30 2-5 Length Contraction and Time Dilation of a Moving Body......Page 33 2-6 Comparison Between Elbaz and De Broglie Approaches......Page 34 2-7 Different Meanings of the Lorentz-Poincare Transformation......Page 35 2-8 The Concept of Simultaneity......Page 40 2-9-1 Path Vector Definition......Page 42 2-9-2 Lagrangian Definition......Page 44 2-9-3 Eulerian Definition......Page 50 2-9-4 Moving Grid Definition......Page 52 2-9-5 Special Relativity Definition......Page 53 3-1 Change of Reference Frame without Rotation......Page 54 3-2 Change of Reference Frame with Rotation......Page 56 3-2-1 Calculation of Positions in a Change of Reference Frame......Page 57 3-2-3 Calculation of Velocities in a Change of Reference Frame......Page 58 3-2-4 Calculation of Accelerations in a Change of Reference Frame......Page 60 3-2-5 Derivative of a Vector in a Rotating Reference Frame......Page 61 3-2-6 Equivalence Between the Lorentz Force and Non-inertial Terms......Page 62 3-2-7 Calculation of the Stress and Rotation Dyads in a Change of Reference Frame......Page 64 3-2-8 Covariance and Invariance of Quantities in a Change of Coordinates......Page 65 3-2-9 Covariance and Invariance of Quantities in a Change of Reference Frame......Page 66 3-3-1 The Relativistic Invariants and the Lorentz Transformations......Page 67 3-3-2 The Relativistic Invariants in Frequency-wave Number......Page 70 3-3-3 The Relativistic Invariants in Space-time......Page 71 4-1 Definition of Absolute and Relative Quantities......Page 74 4-2 The Addition Law of Velocities......Page 78 4-3-1 Work of a Force Along a Trajectory......Page 85 4-3-2 Work of a Force Along a Curve......Page 86 4-3-3 Particular Definition of the Conservation Law of Energy......Page 87 4-3-4 Fluid Definition of the Conservation Law of Energy......Page 91 4-4-1 Principle of Relativity in Galilean Mechanics......Page 93 4-4-2 Covariance and Invariance in a Change of Coordinates......Page 97 4-4-3 Principle of Covariance in Galilean Mechanics......Page 100 4-5 Principles of Relativity and Covariance in Relativistic Mechanics......Page 103 4-5-1 Inertial Reference Frame and Principle of Equilibrium......Page 105 4-5-2 The Reciprocity Concept and Newton's Third Law......Page 107 4-5-3 The Concept of Speed Limit......Page 111 4-6 Definitions of Potential and Kinetic Energies......Page 113 4-6-1 Application of Newton's Third Law......Page 114 4-6-2 Internal and External Forces in a System of Particles......Page 118 4-6-3 Partition of Forces Using Jacobi Coordinates......Page 121 4-7-1 Definition of Angular Momentum......Page 124 4-7-2 Orbital and Spin Angular Momentums of a Particle System......Page 125 4-8-1 Elastic Collision Between Two Particles......Page 128 4-8-2 Inelastic Collision Between Two Particles......Page 132 4-8-3 Energy and Momentum of a System of Relativistic Particles......Page 133 4-8-4 Collision of Radiation with Matter......Page 134 4-8-5 The Tolman Experiment......Page 139 4-8-6 The Graham and Lahoz Experiment......Page 141 4-8-7 The Barnett Experiment......Page 144 5-1-1 Definition of Wave Propagation......Page 148 5-1-2 Classical Doppler Effect and the Galilean Transformation......Page 149 5-1-3 Classical Doppler Effect and the Inhomogeneous Waves......Page 153 5-1-5 Relativistic Doppler Effect......Page 155 5-1-7 Aberration Effect for a Wave......Page 161 5-2-1 The Sagnac Experiment......Page 164 5-2-2 The Michelson and Morley Experiment......Page 169 5-3 The Fizeau Effect......Page 176 5-4-1 Corpuscular Theory of the Compton Effect......Page 179 5-4-2 Analysis of Recoil Electrons......Page 182 5-4-3 Wave Theory of the Compton Effect......Page 183 5-5 The Mossbauer Effect......Page 184 5-5-1 Experimental Confirmation of the Mossbauer Effect......Page 185 5-5-2 Applications of the Mossbauer Effect......Page 187 5-5-3 Corpuscular Theory of the Mossbauer Effect......Page 188 5-6 The Twin Paradox......Page 189 5-6-1 Case of a Rectilinear Motion......Page 191 5-6-2 Case of a Rotational Motion......Page 194 5-7 The Luminiferous Ether a Necessity......Page 199 5-8 Are the Relativistic Effects Second-order in U/c?......Page 203 6-1-1 Case of a Homogeneous Medium......Page 206 6-1-2 Case of an Inhomogeneous Medium......Page 207 6-1-3 Differential Calculus and Second-order Particular Derivative......Page 208 6-1-4 Operators Applied to Functions of Two Variables......Page 211 6-1-5 Operators and Jacobi Coordinates......Page 213 6-2 Spectral Analysis of the Wave Equation......Page 216 6-3 Conservation Laws of the Wave Equation......Page 218 6-4-1 Case of Cartesian Coordinates......Page 220 6-4-2 Case of Cylindrical Coordinates......Page 221 6-4-3 Case of Spherical Coordinates......Page 222 6-4-4 Solution of the Helmholtz Inhomogeneous Equation......Page 224 6-5-1 Definition of Dissipation......Page 227 6-5-2 Relationship Between Dissipation Causality and the Wave Concept......Page 229 6-6-1 Definition of Dispersion......Page 232 6-6-2 Analysis of Dispersion in the Vacuum......Page 236 6-6-4 Transmission Line Theory......Page 238 6-6-5 Vacuum Conductivity and the Speed Limit......Page 241 6-6-6 The Tired-light Mechanism of Redshift in the Vacuum......Page 242 6-7-1 The Schrodinger Equation......Page 243 6-7-2 The Wave Equation and the Focus Wave Modes......Page 246 6-7-3 The de Broglie and Klein-Gordon Equations......Page 249 6-7-4 The Telegrapher Equation......Page 253 6-7-5 Finite Energy Solutions......Page 254 6-8 The Helmholtz Theorem......Page 258 6-8-1 Integral Spatial Solution......Page 259 6-8-2 Fourier Analysis......Page 260 6-8-3 Integral Solution in Space-time......Page 262 6-8-4 Application to Maxwell-Ferrier Equations......Page 263 6-9 Analysis of Rotational Fields......Page 264 6-9-1 Analysis of Beltrami and Trkal Fields......Page 268 6-9-2 Force-free Fields and the Virial Theorem......Page 270 6-9-3 Ordinary Fields and the Superposition Principle......Page 271 6-9-4 Hansen Decomposition and the Beltrami Field......Page 273 6-9-5 Hansen Decomposition in Different Coordinate Systems......Page 275 7-1 Point-particle Versus Wave Packet......Page 280 7-2 Spectral Analysis of the Mackinnon Wave Packet......Page 282 7-3 Acceleration of a Wave Packet......Page 286 7-4 The Electron as a Wave Packet......Page 289 7-5 Vibration Wave and Propagation......Page 291 7-6-1 Analysis of Radiation of an Extended Source......Page 293 7-6-2 Space-time Analysis of a Signal......Page 296 7-6-3 Heisenberg Uncertainty Principle......Page 298 7-7 Quantization of Oscillating Waves of the Ether......Page 301 7-7-1 Continuity Versus Discontinuity......Page 303 7-7-2 Case of Classical Mechanics......Page 306 7-7-3 Case of a Harmonic Oscillator......Page 309 7-7-4 Case of Relativistic Mechanics......Page 313 7-8 The Relativistic Mass-increase with Velocity......Page 317 7-8-1 Constant Force and Hyperbolic Motion......Page 320 7-8-2 Classical Explanation of the Gamma Term......Page 321 7-9-1 The Lande Paradox and the Doppler Effect......Page 325 7-9-2 Matter Waves Radiation and Creation of Particles......Page 326 7-9-3 Matter Waves and Inhomogeneous Waves......Page 327 7-10-1 Case of Classical Mechanics......Page 330 7-10-2 Case of Relativistic Mechanics......Page 332 7-10-3 Variational Formulation......Page 335 7-11-1 Analysis of Propagation in an Inhomogeneous Medium......Page 338 7-11-2 Geometrical Optics......Page 344 7-11-3 Electron Optics......Page 349 8-1 The Wave-particle Duality of Light......Page 352 8-2-1 Pfaff Phase Definition......Page 355 8-2-2 Whitham Phase Definition......Page 357 8-2-3 Analysis of a Fourier Mode......Page 358 8-3 Analogy Between the Moving Grid Formulation and the Transmission Line Theory......Page 360 8-3-1 Maxwell-Proca Equations......Page 362 8-3-2 Maxwell-Proce and De Broglie Equations......Page 364 8-3-3 Signification of the Photon Mass......Page 365 8-4 The Integrating Factor Method......Page 366 8-4-1 Maxwell-Ferrier Equations......Page 368 8-4-2 Different Formulations of Potential......Page 373 8-5 Definitions of Energy and Momentum Conservation Laws......Page 375 8-5-1 Conservation Laws for the Potentials......Page 376 8-5-2 Conservation Laws for the Electromagnetic Field......Page 378 8-5-3 Maxwell's Equations and Newton's Third Law......Page 383 8-6 The Principle of Superposition of Fields......Page 386 8-6-1 Case of Light Interferences......Page 387 8-6-2 Case of Electrostatic Fields......Page 389 8-6-3 The Linear Circuit Theory......Page 391 8-6-4 The Carson Reciprocity Theorem......Page 395 8-6-5 Case of the Antenna Radiation......Page 400 8-7 The Energy Conservation and the Radiation Reaction Force......Page 406 8-8-1 Maxwell's Equations and the Galilean Transformation......Page 410 8-8-2 Mathematical Formulations of Faraday and Ampere Laws......Page 414 8-9 The Lorentz Magnetic Force and the Definition of Velocity......Page 423 9-1 Theoretical Analysis of Electromagnetic Induction......Page 428 9-1-1 Case of the Transformer......Page 430 9-1-2 Analysis of the Lenz Law......Page 432 9-1-3 Experimental Analysis of the Induction Effect......Page 440 9-2 Investigation of Topological Effects in Physics......Page 444 9-2-1 Analysis of Helicity......Page 445 9-2-2 Time Derivative of Helicity......Page 449 9-2-3 Topological Effect Associated to Voltage Measurement......Page 453 9-2-4 The Aharonov-Bohm Effect......Page 456 9-3 Decomposition of the Electromagnetic Field......Page 464 9-3-1 Gauge Transforms......Page 467 9-3-2 Lorenz and Coulomb Gauges......Page 469 10-1 Description of Ampere Experiments......Page 472 10-2 Comparison of Ampere and Lorentz Forces......Page 473 10-3 Volume Expressions of Ampere and Lorentz Forces......Page 476 10-4 Calculation of the Self-interaction of a Circuit......Page 481 10-5 Experimental Tests of the Ampere Force......Page 484 10-6 Curvilinear Expression of the Ampere Force......Page 486 10-7 The Weber Potential......Page 489 10-8 Calculation of the Lorentz Force Between Two Charged Particles......Page 492 10-9 Fluid Approach of the Stimulated Force Calculation......Page 503 10-10 The Trouton-Noble Experiment......Page 505 10-11 The Biefeld-Brown Experiment......Page 509 10-12 Experiments with Charged Discs......Page 511 10-13 The Electrostatic Pendulum Experiment......Page 513 10-14-1 Analysis of the Charge Concept......Page 517 10-14-2 Quantization of Charge......Page 519 11-1 The Lienard-Wiechert Potential for a Constant Velocity......Page 520 11-1-2 Calculation of the Potential for U> c......Page 522 11-1-3 Calculation of the Potential with a Null Initial Condition......Page 523 11-1-4 Calculation of Advanced and Retarded Potentials......Page 525 11-1-5 The Lienard-Wiechert Potential and the Lorentz Transformation......Page 527 11-1-6 The Lienard-Wiechert Potential and the Galilean Transformation......Page 528 11-2-1 The Fourier-Bessel Method......Page 533 11-2-2 The Green Method......Page 535 11-3 Calculation of the Vector Potential in Coulomb Gauge......Page 538 12-1 Remarks on the Concept of Speed Limit......Page 542 12-1-1 Analysis from the Potential......Page 543 12-1-2 Analysis from the Electromagnetic Field......Page 545 12-3 Critical Review of the Radiation Concept......Page 548 12-4 Calculation of the Lamb Shift......Page 549 12-5 Derivation of Retarded and Advanced Quantities......Page 552 12-5-1 Calculation of Time Derivatives......Page 553 12-5-2 Calculation of Space Derivatives......Page 554 12-6 Field Calculations from the Lienard-Wiechert Formulation......Page 556 12-7 Field Calculations from the Feynman Formulation......Page 559 12-8 Field Calculations with Initial Conditions......Page 560 12-9 Field Calculations Far from the Charge......Page 561 12-10 Relationship Between the Radiated Power and the Absorbed Power by Unit of Solid Angle......Page 563 12-11-1 Calculation from the Electric Field......Page 564 12-11-2 Calculation from the Particle Acceleration......Page 566 12-11-3 Angular and Spectral Distribution of the Energy Received by an Observer......Page 567 13-1-1 Spectral Radiative Intensity......Page 570 13-1-3 Spectral Radiative Flux......Page 571 13-1-4 Spectral Radiative Pressure......Page 572 13-1-5 The Ray Concept......Page 573 13-2 The Blackbody Radiation......Page 574 13-4 The Correlation Function......Page 577 13-5 Comparison Between Photonics and Electromagnetism......Page 581 13-6 Decomposition of the Radiation Field in Fourier Modes......Page 585 13-7 Stochastic Electrodynamics......Page 587 14-1-1 The Hertz Formulation......Page 590 14-1-2 Calculation of the Electromagnetic Field......Page 591 14-2-1 Analysis of the Antenna Radiation Field......Page 594 14-2-2 The Part Played by the Ions in the Operation of an Antenna......Page 598 14-2-3 Different Operating Modes of an Antenna......Page 599 14-3-1 Operation of a Free Electron Laser......Page 602 14-3-2 Analysis of a Free Electron Laser......Page 606 14-3-3 Analysis of the Smith-Purcell Radiation......Page 607 15-1-1 Scalar Case......Page 610 15-1-3 Dyadic Case......Page 611 15-2-1 Scalar Case......Page 613 15-2-2 Vectorial Case......Page 615 15-2-3 Dyadic Case......Page 618 15-2-4 Stratton Formulation......Page 621 15-3-1 Scalar Formulation of the Helmholtz-Kirchhoff Principle......Page 623 15-3-2 The Fresnel and Fraunhofer Diffraction......Page 627 15-4 Application to Electromagnetism in a Material Medium......Page 628 15-4-1 The Fizeau Effect First Approach......Page 630 15-4-2 The Fizeau Effect Second Approach......Page 631 15-4-3 Case of a Medium at Rest......Page 633 15-5 The Green Formulation in an Infinite Space......Page 634 15-6 The Green Formulation in Space-time......Page 638 16-1 The Polarization Vector......Page 644 16-2 The Lalor Extinction Theorem......Page 646 16-3 The Sein Extinction Theorem......Page 648 16-4-1 Case of a Source Localized in V'......Page 649 16-4-2 Case of a Source Localized in V......Page 650 16-4-3 Discontinuities of the Electromagnetic Field......Page 651 16-4-4 The Formulation of Pattanayak-Wolf......Page 652 16-5-2 The Laws of Diffusion and Diffraction......Page 654 17 PLASMA EQUATION......Page 656 17-1 Moments of the Boltzmann Equation......Page 657 17-2 The Maxwellian Distribution Function......Page 659 17-3-1 Case of a Two-fluid Plasma......Page 660 17-3-2 Case of a One-fluid Plasma......Page 662 17-3-3 Energetic Balance of a Moving Plasma......Page 668 17-3-4 Calculation of the Generalized Ohm's Law......Page 670 17-3-5 Motion of Magnetic Field Lines......Page 673 17-4 Link with the Maxwell's Equations......Page 674 17-5 Analysis of Plasma Rotations in Pinches......Page 675 17-6-1 Virial Theorem......Page 679 17-6-2 Self-confinement of a Plasma......Page 680 17-6-3 Bennett Conditions for the 9-Pinch and Z-Pinch......Page 682 18 CONCLUSION......Page 686 19-1 Elementary Relations of Fluid Mechanics......Page 690 19-1-1 Application to the Case of an Inhomogeneous Wave......Page 692 19-1-2 Calculations of Length Surface and Volume Variations......Page 693 19-2-1 Kinematics of a Line Integral......Page 695 19-2-2 Kinematics of a Surface Integral......Page 696 19-2-3 Kinematics of a Volume Integral......Page 697 19-3 Cauchy Method of Integration......Page 701 19-4-2 Definition of the Dirac Distributions......Page 703 19-4-3 Definition of the Heaviside Distributions......Page 704 19-4-4 Definitions of Convolution Laws......Page 705 19-5 Review of Operations with Complex Quantities......Page 707 19-6 Analysis of a Definite Positive Quadratic From......Page 709 19-7-2 Case of a Moving Volume without Flux......Page 712 19-7-4 Conservation of Charge......Page 713 19-8 Eulerian Formulation of the Energy Density Conservation Law......Page 714 19-9 Macroscopic Models of Matter......Page 715 19-9-1 Relative Quantities......Page 716 19-9-2 Absolu 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-Poincaré transformation. 2.4. Wave meaning of the Lorentz-Poincaré 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-Poincaré transformation. 2.8. The concept of simultaneity. 2.9. Definition of Eulerian and Lagrangian coordinates -- 3. Change of reference frame. 3.1. Change of reference frame without rotation. 3.2. Change of reference frame with rotation. 3.3. The relativistic invariants and the definition of velocities -- 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. 4.4. Principles of relativity and covariance in Galilean mechanics. 4.5. Principles of relativity and covariance in relativistic mechanics. 4.6. Definitions of potential and kinetic energy. 4.7. Review of angular momentum definition. 4.8. Experimental tests of partition of forces between internal and external forces -- 5. Experimental tests of special relativity. 5.1. Doppler and aberration effects. 5.2. The Sagnac and Michelson interferometer experiments. 5.3. The Fizeau effect. 5.4. Compton effect. 5.5. The Mössbauer effect. 5.6. The twin paradox. 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. 6.2. Spectral analysis of the wave equation. 6.3. Conservation laws of the wave equation. 6.4. Method of separation of variables. 6.5. Review of the dissipation concept. 6.6. Review of the dispersion concept. 6.7. Hyperbolic equations of second-order and the soliton. 6.8. The Helmholtz theorem. 6.9. Analysis of rotational fields 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. 7.7. Quantization of oscillating waves of the ether. 7.8. The relativistic mass-increase with velocity. 7.9. Matter waves. 7.10. Formalism of Lagrange-Hamilton. 7.11. The ray theory -- 8. Electromagnetism. 8.1. The wave-particle duality of light. 8.2. Analysis of the phase concept. 8.3. Analogy between the moving grid formulation and the transmission line theory. 8.4. The integrating factor method. 8.5. Definitions of energy and momentum conservation laws. 8.6. The principle of superposition of fields. 8.7. The energy conservation and the radiation reaction force. 8.8. Different formulations of Maxwell's equations. 8.9. The Lorentz magnetic force and the definition of velocity -- 9. Electromagnetic induction. 9.1. Theoretical analysis of electromagnetic induction. 9.2. Investigation of topological effects in physics. 9.3. Decomposition of the electromagnetic field -- 10. Ampère and Lorentz forces. 10.1. Description of Ampère experiments. 10.2. Comparison of Ampère and Lorentz forces. 10.3. Volume expressions of Ampère and Lorentz forces. 10.4. Calculation of the self-interaction of a circuit. 10.5. Experimental tests of the Ampère force. 10.6. Curvilinear expression of the Ampère force. 10.7. The Weber potential. 10.8. Calculation of the Lorentz force between two charged particles. 10.9. Fluid approach of the stimulated force calculation. 10.10. The Trouton-Noble experiment. 10.11. The Biefeld-Brown experiment. 10.12. Experiments with charged discs. 10.13. The electrostatic pendulum experiment. 10.14. The concept of charge -- 11. The Liénard-Wiechert potential. 11.1. The Liénard-Wiechert potential for a constant velocity. 11.2. Calculation of the Liénard-Wiechert potential for any velocity. 11.3. Calculation of the vector potential in Coulomb gauge 12. Analysis of the electromagnetic field. 12.1. Remarks on the concept of speed limit. 12.2. Conditions for the existence of radiation. 12.3. Critical review of the radiation concept. 12.4. Calculation of the Lamb shift. 12.5. Derivation of retarded and advanced quantities. 12.6. Field calculations from the Liénard-Wiechert formulation. 12.7. Field calculations from the Feynman formulation. 12.8. Field calculations with initial conditions. 12.9. Field calculations far from the charge. 12.10. Relationship between the radiated power and the absorbed power by unit of solid angle. 12.11. Power radiated by a charge -- 13. Photonics versus electromagnetism. 13.1. Definitions and basic concepts in radiative transfer. 13.2. The blackbody radiation. 13.3. Working principle of the laser. 13.4. The correlation function. 13.5. Comparison between photonics and electromagnetism. 13.6. Decomposition of the radiation field in Fourier modes. 13.7. Stochastic electrodynamics -- 14. Radiation of extended sources. 14.1. Analysis of the dipole in uniform motion. 14.2. The radiation of antennas. 14.3. Analysis of the radiative wiggler -- 15. The Green formulation. 15.1. Definition of the Green formulation. 15.2. Analysis of the Green formulation. 15.3. The Helmhotz-Kirchhoff principle. 15.4. Application to electromagnetism in a material medium. 15.5. The Green formulation in an infinite space. 15.6. The Green formulation in space-time -- 16. Wave extinction in a dielectric. 16.1. The polarization vector. 16.2. The Lalor extinction theorem. 16.3. The Sein extinction theorem. 16.4. The Pattanayak-Wolf extinction theorem. 16.5. Application of the extinction theorem -- 17. Plasma equation. 17.1. Moments of the Boltzmann equation. 17.2. The Maxwellian distribution function. 17.3. Hydrodynamic equations of a plasma. 17.4. Link with the Maxwell's equations. 17.5. Analysis of plasma rotations in pinches. 17.6. Plasma confinement and the Bennett condition -- 18. Conclusion