Advanced Electromagnetism and Vacuum Physics

The following sections are included:

• PREFACE

• CONTENTS

This book is dedicated to a large audience of researchers: scientists, engineers, professors and students wise enough to keep a critical look whenever confronted to the chilling dogmas of contemporary physics. In the following pages, the reader will find a tantalizing amount of material carved out to nurture their thoughts and arise their suspicion, to some degree at least, on the so-called validity of today's most celebrated physical theories. As it may happen, many physicists may be blinded or mystified by the shinny glimmers of technological progress, leading to the belief that today's greatest physical theories give a coherent account and fully understandable picture of matter and radiation, in all of their aspects. After decades of work, the author is intimately convinced that we have not even began to touch upon the surface of things, nor even began to unveil the true secrets of Nature. To put it more plainly: everything has to be started all over again. Indeed, a number of well-known physicists criticized certain aspects of contemporary physics. The great majority of their criticisms has systematically been silenced by some sort of censorship system empowered, if not institutionalized, within the scientific community itself. This statement may surprise those of the readers who still ignore how the system of anonymous referees, as it is being used by scientific journals and magazines, operates and negates every attempt to dismiss or criticize today's mainstream physics and models. One must keep in mind the very fact that this system offers no guarantee concerning the scientific validity of papers which have been subject to publication. On this particular point, the gradual power rise of the Internet favored the birth of a yet unknown space of freedom of speech and communications which, hopefully, has already begun to short-circuit all sorts of systems and strategies set up in the past to mute the scientific spirit…

The following sections are included:

• Critical review of the interpretation of special relativity

• Calculation of the rectilinear accelerated motion of a particle

• Analysis of the Poincaré-Lorentz transformation
  • Constant acceleration motion
  • Constant velocity motion

• Wave meaning of the Lorentz-Poincaré transformation

• Length contraction and time dilation of a moving body

• Comparison between Elbaz and de Broglie approaches

• Different meanings of the Lorentz-Poincaré transformation

• The concept of simultaneity

• Definition of Eulerian and Lagrangian coordinates
  • Path vector definition
  • Lagrangian definition
  • Eulerian definition
  • Moving grid definition
  • Special relativity definition

The following sections are included:

• Change of reference frame without rotation

• Change of reference frame with rotation
  • Calculation of positions in a change of reference frame
  • Invariance of distances in a change of reference frame
  • Calculation of velocities in a change of reference frame
  • Calculation of accelerations in a change of reference frame
  • Derivative of a vector in a rotating reference frame
  • Equivalence between the Lorentz force and non-inertial terms
  • Calculation of the stress and rotation dyads in a change of reference frame
  • Covariance and invariance of quantities in a change of coordinates
  • Covariance and invariance of quantities in a change of reference frame

• The relativistic invariants and the definition of velocities
  • The relativistic invariants and the Lorentz transformations
  • The relativistic invariants in frequency-wave number
  • The relativistic invariant in space-time

The following sections are included:

• Definition of absolute and relative quantities

• The addition law of velocities

• Newton's third law and the principle of conservation of energy
  • Work of the force along a trajectory
  • Work of a force along a curve
  • Particular description of the conservation law of energy
  • Fluid definition of the conservation law of energy

• Principles of relativity and covariance in Galilean mechanics
  • Principle of relativity in Galilean mechanics
  • Covariance and invariance in a change of coordinates
  • Principle of covariance in Galilean mechanics

• Principles of covariance and relativity in relativistic mechanics
  • Inertial reference frame and principle of equilibrium
  • The reciprocity concept and Newton's third law
  • The concept of speed limit
  • Dependence of the light velocity on the receiver motion

• Definitions of potential and kinetic energies
  • Application of Newton's third law
  • Internal and external forces in a system of particles
  • Partition of forces using Jacobi coordinates

• Review of angular momentum definition
  • Definition of angular momentum
  • Orbital and spin kinetic angular momentums of a particle system

• Experimental tests of partition of forces between internal and external forces
  • Elastic collision between two particles
  • Inelastic collision of two particles
  • Energy and momentum of a system of relativistic particles
  • Collision of radiation with matter
  • The Tolman experiment
  • The Graham and Lahoz experiment
  • The Barnett experiment

The following sections are included:

• Doppler and aberration effects
  • Definition of wave propagation
  • Classical Doppler effect and the Galilean transformation
  • Classical Doppler effect and the inhomogeneous waves
  • The Doppler radar
  • Relativistic Doppler effect
  • Aberration effect
  • Aberration effect for a wave

• The Sagnac and Michelson interferometer experiments
  • The Sagnac experiment
  • The Michelson and Morley experiment

• The Fizeau effect

• The Compton effect
  • Corpuscular theory of the Compton effect
  • Analysis of recoil electrons
  • Wave theory of the Compton effect

• The Mössbauer effect
  • Experimental confirmation of the Mössbauer effect
  • Applications of the Mössbauer effect
  • Corpuscular theory of the Mössbauer effect

• The twin paradox
  • Case of a rectilinear motion
  • Case of a rotational motion

• The luminiferous ether, a necessity

• Are relativistic effects second-order effects in U/c ?

The following sections are included:

• Definition of the wave equation
  • Case of a homogeneous medium
  • Case of an inhomogeneous medium
  • Differential calculus and second-order particular derivative
  • Operators applied to functions of two variables
  • Operators and Jacobi coordinates

• Spectral study of the wave equation

• Conservation laws of the wave equation

• Method of separation of variables
  • Case of cartesian coordinates
  • Case of cylindrical coordinates
  • Case of spherical coordinates
  • Solution of the Helmholtz inhomogeneous equation

• Review of the dissipation concept
  • Definition of dissipation
  • Relation between dissipation, causality and the wave concept

• Review of the dispersion concept
  • Definition of dispersion
  • Analysis of dispersion in the vacuum
  • Definition of light velocity
  • Transmission line theory
  • Vacuum conductivity and the speed limit
  • The tired-light mechanism of redshift in the vacuum

• Hyperbolic equations of second-order and the soliton
  • The Schrödinger equation
  • The wave equation and the focus wave modes
  • The de Broglie and Klein-Gordon equations
  • The telegrapher equation
  • Finite energy solutions

• The Helmholtz theorem
  • Integral spatial solution
  • Fourier analysis
  • Integral solution in space-time
  • Application to Maxwell-Ferrier equations

• Analysis of rotational fields
  • Analysis of Beltrami and Trkal fields
  • Force-free fields and the virial theorem
  • Ordinary fields and the superposition principle
  • Hansen decomposition and the Beltrami field
  • Hansen decomposition in different coordinate systems

The following sections are included:

• Point-particle versus wave packet

• Spectral analysis of the Mackinnon wave packet

• Acceleration of a wave packet

• The electron as a wave packet

• Vibration, wave and propagation

• Analysis of the size of a signal
  • Analysis of radiation of an extended source
  • Space-time analysis of a signal
  • Heisenberg uncertainty principle

• Quantization of oscillating waves of the ether
  • Continuity versus discontinuity
  • Case of classical mechanics
  • Case of a harmonic oscillator
  • Case of relativistic mechanics

• The relativistic mass-increase with velocity
  • Constant force and hyperbolic motion
  • Classical explanation of the gamma term
  • The Bertozzi experiment

• Matter waves
  • The Landé paradox and the Doppler effect
  • Matter waves, radiation and creation of particles
  • Matter waves and inhomogeneous waves

• Formalism of Lagrange-Hamilton
  • Case of classical mechanics
  • Case of relativistic mechanics
  • Variational formulation

• The ray theory
  • Analysis of propagation in an inhomogeneous medium
  • Geometrical optics
  • Electron optics

The following sections are included:

• The wave-particle duality of light

• Analysis of the phase concept
  • Pfaff phase definition
  • Whitham phase definition
  • Analysis of a Fourier mode

• Analogy between the moving grid formulation and the transmission line-theory
  • Maxwell-Proca equations
  • Maxwell-Proca and de Broglie equations
  • Signification of the photon mass

• The integrating factor method
  • Maxwell-Ferrier equations
  • Different formulations of potentials

• Deflnitions of energy and momentum conservation laws
  • Conservation laws for the potentials
  • Conservation laws for the electromagnetic field
  • Maxwell's equations and Newton's third law
  • The angular momentum of the electromagnetic field

• The principle of superposition of fields
  • Case of light interferences
  • Case of electrostatic fields
  • The linear circuit theory
  • The Carson reciprocity theorem
  • Case of antenna radiation

• The energy conservation and the radiation reaction force

• Different formulations of Maxwell's equations
  • Maxwell's equations and the Galilean transformation
  • Mathematical formulation of Faraday and Ampère laws

• The Lorentz magnetic force and the definition of velocity

The following sections are included:

• Theoretical analysis of electromagnetic induction
  • Case of the transformer
  • Analysis of the Lenz law
  • Experimental analysis of the induction phenomenon

• Investigation of topological effects in physics
  • Analysis of helicity
  • Time derivative of helicity
  • Topological effect associated to voltage measurement
  • The Aharonov-Bohm effect

• Decomposition of the electromagnetic field
  • Gauge transforms
  • Lorenz and Coulomb gauges

The following sections are included:

• Description of Ampère experiments

• Comparison of Ampère and Lorentz forces

• Volume expressions of Ampère and Lorentz forces

• Calculation of the self-interaction of a circuit

• Experimental tests of the Ampère force

• Curvilinear expression of the Ampère force

• The Weber potential

• Calculation of the Lorentz force between two charged particles

• Fluid approach of the stimulated force calculation

• The Trouton-Noble experiment

• The Biefeld-Brown experiment

• Experiments with charged discs

• The electrostatic pendulum experiment

• The concept of charge
  • Analysis of the charge concept
  • Quantization of charge

The following sections are included:

• The Liénard-Wiechert potential for a constant velocity
  • Calculation of the potential for U < c
  • Calculation of the potential for U > c
  • Calculation of the potential with a null initial condition
  • Calculation of the advanced and retarded potentials
  • The Liénard-Wiechert potential and the Lorentz transformation
  • The Liénard-Wiechert potential and the Galilean transformation

• Calculation of the Liénard-Wiechert potential for any velocity
  • The Fourier-Bessel Method
  • The Green method

• Calculation of the vector potential in the Coulomb gauge

The following sections are included:

• Remarks on the concept of speed limit

• Conditions for the existence of radiation
  • Analysis from the potential
  • Analysis from the electromagnetic field

• Critical review of the radiation concept

• Calculation of the Lamb shift

• Derivation of retarded and advanced quantities
  • Calculation of time derivatives
  • Calculation of the space derivatives

• Field calculations from the Liénard-Wiechert formulation

• Field calculations from the Feynman formulation

• Field calculations with initial conditions

• Field calculations far from the charge

• Relation between the radiated power and the absorbed power by unit of solid angle

• Power radiated by a charge
  • Calculation from the electric field
  • Calculation from the particle acceleration
  • Angular and spectral distribution of the energy received by an observer

The following sections are included:

• Definitions and basic concepts in radiative transfer
  • Spectral radiative intensity
  • Spectral radiative energy
  • Spectral radiative flux
  • Spectral radiative pressure
  • The ray concept

• The blackbody radiation

• Working principle of the laser

• The correlation function

• Comparison between photonics and electromagnetism

• Decomposition of the radiation field in Fourier modes

• Stochastic electrodynamics

The following sections are included:

• Analysis of the dipole in uniform motion
  • The Hertz formulation
  • Calculation of the electromagnetic field

• The radiation of antennas
  • Analysis of the antenna radiation field
  • The part played by the ions in the operation of an antenna
  • Different operating modes of an antenna

• Analysis of the radiative wiggler
  • Operation of a free electron laser
  • Analysis of a free electron laser
  • Analysis of the Smith-Purcell radiation

The following sections are included:

• Definition of the Green formulation
  • Scalar case
  • Vectorial case
  • Dyadic case

• Analysis of the Green formulation
  • Scalar case
  • Vectorial case
  • Dyadic case
  • Stratton formulation

• The Helmholtz-Kirchhoff principle
  • Scalar formulation of the Helmholtz-Kirchhoff principle
  • The Fresnel and Fraunhofer diffraction
  • Vectorial formulation of the Helmholtz-Kirchhoff principle

• Application to electromagnetism in a material medium
  • The Fizeau effect, first approach
  • The Fizeau effect, second approach
  • Case of a medium at rest

• The Green formulation in an infinite space

• The Green formulation in space-time

The following sections are included:

• The polarization vector

• The Lalor extinction theorem

• The Sein extinction theorem

• The Pattanayak-Wolf extinction theorem
  • Case of a source localized in V′
  • Case of a source localized in V
  • Discontinuities of the electromagnetic field
  • The formulation of Pattanayak-Wolf

• Application of the extinction theorem
  • The laws of reflection and refraction
  • The laws of diffusion and diffraction

The following sections are included:

• Moments of the Boltzmann equation

• The Maxwellian distribution function

• Hydrodynamic equations of a plasma
  • Case of a two-fluid plasma
  • Case of one-fluid plasma
  • Energetic balance of a moving plasma
  • Calculation of the generalized Ohm's law
  • Motion of magnetic field lines

• Link with the Maxwell's equations

• Analysis of plasma rotations in Pinches

• Plasma confinement and the Bennett condition
  • Virial theorem
  • Self-confinement of a plasma
  • Bennett condition for the Θ-Pinch and Z-Pinch

The book was originally written in French. Its writing spanned over a fourteen year period so as to provide the greatest mathematical and physical rigor. Consequently, there should not be too many errors in this book to avoid any possible contesting because this book contains a number of concepts and new theoretical results of which some are in conaradiction with the interpretation generally admitted by the scientific community. However, we are convinced that the formulation of Physics from a wave point of view, point of view shared by some physicists quoted in the bibliography, brings a consistent interpretation of our surrounding physical universe and pave the way for brighter insights and better understandings of matter and radiation. We shall now review some of the most salient features the reader may find in this book…

The following sections are included:

• APPENDIX
  • Elementary relations of fluid mechanics
    • Application to the case of an inhomogeneous wave
    • Calculation of length, surface and volume variations
  • Particular derivatives of an integral
    • Kinematics of a line integral
    • Kinematics of a surface integral
    • Kinematics of a volume integral
  • Cauchy method of integration
  • Fourier transforms
    • Definitions of Fourier transforms
    • Definitions of Dirac distributions
    • Definitions of Heaviside distributions
    • Definition of convolution laws
  • Review of operations with complex quantities
  • Analysis of a definite positive quadratic form
  • Analysis of the continuity equation
    • Case of a fixed volume with flux
    • Case of a moving volume without flux
    • Case of a moving volume with flux
    • Conservation of charge
  • Eulerian formulation of the energy density conservation law
  • Macroscopic model of matter
    • Relative quantities
    • Absolute quantities
    • Definition of the magnetic dipole moment
  • Calculation of an integral related to the wave equation
  • Calculation of the Green function with the Fourier transform
    • Absolute Green function
    • Relative Green function
  • Definition of the solid angle
    • Definition of the scalar solid angle
    • Definition of the vectorial solid angle
    • Definition of the dyadic solid angle
  • Elementary properties of Bessel functions
  • Elementary properties of Dirac distribution
  • Vectorial and tensorial relations

• BIBLIOGRAPHY

• INDEX