Advanced electromagnetism and vacuum physics

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 Absolute Quantities......Page 718
19-9-3 Definition of the Magnetic Dipole Moment......Page 721
19-10 Calculation of an Integral Related to the Wave Equation......Page 727
19-11-1 Absolute Green Function......Page 728
19-11-2 Relative Green Function......Page 730
19-12-1 Definition of the Scalar Solid Angle......Page 731
19-12-3 Definition of the Dyadic Solid Angle......Page 732
19-13 Elementary Properties of Bessel Functions......Page 733
19-14 Elementary Properties of Dirac Distribution......Page 734
19-15 Vectorial and Tensorial Relations......Page 735
20 BIBLIOGRAPHY......Page 742
INDEX......Page 778