Advanced electromagnetism and vacuum physics

Description

This book is aimed at a large audience: scientists, engineers, professors and students wise enough to keep a critical stance whenever confronted with the chilling dogmas of contemporary physics. Readers will find a tantalizing amount of material calculated to nurture their thoughts and arouse their suspicion, to some degree at least, on the so-called validity of today's most celebrated physical theories. 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