Monday, July 30, 2012

2.4.Review of the linear equations of the Maxwell’s "Electromagnetised aether" or Electromagnetism.





THE CURRENT BLOG (ONLINE BOOK) HAS MAINLY SPECULATIVE CHARACTER AND IS  INTRODUCING ONLY VERY PARTIALLY NEW QUANTITATIVE FORMULAE OF PHYSICAL PHENOMENA. IT IS MAINLY A CHANGE OF PERCEPTION OF THE PHYSICAL REALITY AS WE KNOW IT, TO ONE THAT HAS ALSO A 2ND  MICROSCOPIC LAYER BASED ON THE ANALOGUE OF THE TRIAD OF FREE AND PERMANENT PARTICLES OF PROTON ELECTRON AND NEUTRON BUT ON A SMALLER SCALE AS MICRO-TRIAD OF FREE AND PERMANENT PARTICLES OF MICRO-PROTON MICRO-ELECTRON AND MICRO-NEUTRON (BUT ALSO MACROSCOPIC LAYER) , THAT CURRENTLY WE KNOW PARTIALLY AS FIELDS LIKE GRAVITATIONAL FIELD, ELECTROMAGNETIC FIELD OR QUANTUM VACUUM. WE LEAVE OPEN THE MANY DIFFERENT WAYS THAT THE MATTER OF PROTONS/NEUTRONS/ELECTRONS CAN COUPLE WITH THE 2ND LAYER MATTER OF MICRO-PROTINS/MICRO-NEUTRONS/MICRO-ELECTRONS IN OTHER WORDS THE GRAVITATIONAL FIELD THE ELECTROMAGNETIC FIELD AND THE "QUANTUM VACUUM".
THE ONLY NEW SPECULATION OF QUANTITATIVE DESCRIPTION IS THE APPLICATION OF THE WELL KNOWN NAVIER-STOKES EQUATIONS FOR THIS 2ND MICROSCOPIC FLUID LAYER IN THE ABSENCE OF COUPLING WITH THE VISIBLE MATTER (OF ELECTRONS PROTONS NEUTRONS OR PLANETS ). THEREFORE A QUANTITATIVE FORMULATION WHICH IS OF APPLICATIONS TO A RATHER  MACROSCOPIC SCALE E.G. SOLAR SYSTEM SCALE. IT IS SPECULATED THOUGH HOW BY CHANGING THE PERCEPTION OF MATERIAL REALITY FROM A SINGLE LAYER (OR FREQUENCY) OF THE STANDARD ABOVE FREE AND PERMANENT TRIAD OF PARTICLES TO AT LEAST A DOUBLE LAYER (OR FREQUENCIES) PHYSICAL REALITY WITH BOTH THE STANDARD TRIAD OF FREE AND PERMANENT PARTICLES BUT ALSO MICRO-TRIAD  OF FREE AND PERMANENT PARTICLES WE COULD DO THE NEXT:
A) REFORMULATE EQUATIONS OF GRAVITATION WHICH INCLUDE THOSE OF I. NEWTON AND ARE MORE EXACT AND PHYSICALLY MEANINGFUL AND REALISTIC THAN THOSE OF A. EINSTEIN. 
B) REFORMULATE AND PROVE AGAIN THE SPECIAL RELATIVITY FORMULAE AS A KIND OF "LINEARIZED WAVED INERTIA" OF E.G. AN ELECTRON ON THE SUBSTRATUM 2ND LAYER PHYSICAL REALITY, BUT UNDER TOTALLY DIFFERENT AXIOMS THAT DO NOT INVOLVE THAT NOTHING GOES FASTER THAN LIGHT.
C) REFORMULATE NON-LINEAR EQUATIONS FOR THE CLASSICAL ELECTROMAGNETISM WHICH INVOLVE THOUGH MAGNITUDES OF GRAVITATION TOO, FOR  LARGE SCALE PHENOMENA E.G. SOLAR SYSTEM SCALE PHENOMENA . THE CLASSICAL ELECTROMAGNETISM IS ONLY THE LINEAR COUPLING OF THE ELECTROMAGNETIC FIELD WHICH IS MADE FROM THE MICRO-TRIAD OF MICRO-PROTONS MICRO-NEUTRONS AND MICRO-ELECTRONS, WITH THE MATTER OF ELECTRONS/PROTONS/NEUTRONS AND IS ACCEPTABLE APPROXIMATELY CORRECT AT SMALL LABORATORY SCALE.  
D) AFTER THE JOIN REFORMULATION OF CLASSICAL GRAVITATION AND CLASSICAL ELECTROMAGNETISM IN THE NEXT DECADES PREDICT  THE EXISTENCE OF ELECTROMAGNETIC DEVICES THAT MAY EXTRACT RENEWABLE SOLAR ENERGY STORED IN THE GRAVITATIONAL FIELD (FREE ENERGY). AND THE EXISTENCE OF ELECTROMAGNETIC PROPULSION FLYING VEHICLES IN VARIOUS SHAPES, INCLUDING DISC-SHAPES, THAT MAY USE THE ABOVE ENERGY FOR FLYING .
E) DERIVE THE SCHRODINGER WAVE MECHANICS OR THE EQUIVALENT HEISENBERG MATRIX MECHANICS FROM A LINEAR COUPLING OF THE  SUBSTRATUM  LAYER NEUTRAL FLUID OF MICRO-TRIAD OF FREE AND PERMANENT PARTICLES (CALLED ERRONEOUSLY QUANTUM VACUUM) OR GRAVITATIONAL FIELD WITH THE MATTER OF ELECTRONS/PROTONS/NEUTRONS. 

IN SUMMARY MORE THAN 80% THE CONTENT OF THE CURRENT WORKS IS TO CHANGE DEEPLY AND IN A PROFOUND WAY OUR QUALITATIVE PERCEPTIONS ABOUT THE PHYSICAL REALITY WHICH CAN LEAD IN  THE FUTURE DECADES TO A  UNIFIED QUANTITATIVE APPROACH TO GRAVITATION AND ELECTROMAGNETISM. IN LESS THAN 20% OF THE SPECULATIONS, THE ONLY QUANTITATIVE SET OF FORMULAE (THOSE OF NAVIER-STOKES) THAT ARE INTRODUCED ARE ONLY A PRELIMINARY STEP THAT CAN BE DONE IN RATHER EASIER WAY FOR THIS UNIFICATION, AND HAS APPLICATIONS MAINLY TO LARGER SCALE PHENOMENA E.G.  SOLAR SYSTEM SCALE GRAVITATION AND ELECTROMAGNETISM.


  
REMARK ABOUT THE USE OF THE TERM "AETHER" IN THE CURRENT BOOK BECAUSE THE TERM AETHER IS KNOWN TO BE DISCREDITED AT LEAST FOR A WHOLE CENTURY, WE NEED TO CLARIFY ITS RELEVANCY TO THE THEORIES OF FIELDS WHICH ARE WELL ACCEPTED.

1) SPECIAL AND GENERAL RELATIVITY ARE NOTHING MORE THAN MODELS OF AETHER FOR INERTIAL MASS, AND FOR THE UNIVERSAL ATTRACTION. ANY MODEL OF AETHER  AS CLASSICAL "FIELD" (GRAVITATIONAL OR ELECTROMAGNETIC ETC) THAT DOES NOT GET DEEPLY TO THE INDIVISIBLE FREE AND PERMANENT PARTICLES MATERIAL STRUCTURE OF THE FIELD ITSELF, IS INADEQUATE FOR A FULL MODEL OF AETHER AS WE SHALL SEE.  THE INDIVISIBLEs OR PARTICLES OF A FIELD ARE OBVIOUSLY NONE OF THE KNOWN PARTICLES, BUT STILL THEY CAN BE AS SIMPLE AS THE KNOWN TRIADS OF PROTON, NEUTRON ELECTRON ONLY AT RADICALLY SMALLER SIZE.

OTHER CLASSICAL MODELS OF AETHER ARE 
2) THE MAXWELL'S ELECTROMAGMETIC FIELD (OR ELECTROMAGNETIZED AETHER AS MAXWELL WAS CALLING IT) 
3) THE QUANTUM VACUUM THAT AS SUBSTRATUM GIVES RANDOMNESS TO MOTIONS OF PROTONS, NEUTRONS, ELECTRONS THROUGH THE SCHRODINGER WAVE EQUATION (DEBROGLIE-SCHROENDINGER-DIRAC'S AETHER)

A MODERN SUCCESSFUL UNIFYING THEORY OF "AETHER" AS A GASEOUS FLUID ,OR IN BETTER TERMS 2ND FREQUENCY MATERIAL PHYSICAL REALITY (SEE ALSO POST 6 ) SHOULD BE ABLE TO DERIVE ALL THE ABOVE 20TH CENTURY CONCEPTS OF ""AETHER" IN OTHER WORDS 
FROM THE CONCEPT OF 2ND FREQUENCY MATERIAL REALITY AND IN PARTICULAR FROM THE CONCEPT OF GASEOUS FLUID FROM 3 TYPES OF PERMANENT AND FREE PARTICLES (LIKE MICRO-ELECTRON, MICRO-PROTON, MICRO-NEUTRON) WE SHOULD BE ABLE TO DERIVE AS SPECIAL TYPE APPROXIMATIONS UNDER SIMPLIFYING ASSUMPTIONS

1) THE MACROSCOPIC LINEAR CLASSICAL MAXWELL EQUATIONS OF THE ELECTROMAGNETIC FIELD
2) THE MACROSCOPIC EINSTEINS AND NEWTONS EQUATIONS OF TH GRAVITATIONAL FIELD, AND EINSTEINS EQUATIONS OF SPECIAL RELATIVITY

3) THE MICROSCOPIC SCHROENDINGERS EQUATIONS OF MOTION OF PARTICLES



HERE WE REVIEW THE MAXWELL'S LINEAR EQUATIONS OF THE ELECTROMAGNETISM  (=ELECTROMATETISED AETHER) IN THE PRESENCE OR ABSENCE OF CHARGED MATTER.
BUT THE TRUE EQUATIONS OF ELECTRO-MAGENTISM DEVIATE FROM THE MAXWELL'S EQUATIONS IN TO THAT 
1) NEITHER IN THE ABSENCE OF MATTER THE EQUATIONS OF ELECTROMANETISED AETHER ARE LINEAR (AS ASSUMED AT THE SCALAR AND VECTOR POTENTIALS BY MAXWELL) , 
2) NEITHER THE INTERPLAY OF CHARGED MATTER WITH THE ELECTROMAGETISED AETHER IS LINEAR AS ASSUMED IN THE MAXWELL'S EQUATIONS


We shall try to go back to the original mentality of Maxwell, that talked not of the electromagnetic field but of the electromagnetised field-gas. It seems as if  the linear equations of Maxwell, (that can also be summarized by the D’Alamberts hyperbolic wave equations on the scalar and vector electromagnetic potentials ) were design specifically and only for one only category of applications: “Communications through electromagnetic waves”! As we see it under the light of the present article’s new physics, the conventional equations are hardly appropriate for “Propulsion”. It has also been remarked that the conventional electric motors (a design usually credited to N. Tesla) are to be as if a ”wrong turn” in the future history of electromagnetic motors, and I say in a milder attitude, that maybe they were a necessary “hard twisted design” in order to get as much as possible in exchanging electric energy with mechanical energy under the limited validity of a system of linear equations (Maxwell’s equations) that are nevertheless exactly appropriate for communicational applications. Maybe behind this order of steps in the evolution of science there is a hidden wisdom: First to develop the mind before we proceed to power.
The equations that govern the Maxwell’s electromagnetism are the next:


The Langrangian of the Maxwell’s Electromagnetised aether :






(4.1)


Where the vectors E and B are the intensity of the electric and magnetic field  in the vacuum relative to matter made of protons, electrons and neutrons (1st micro scale matter) and are given by the scalar and vector electromagnetic potentials a 0 and A  by the formulas :
              (4.2)



              (4.3)

The other terms are also self evident : m for the particle’s mass ,e for its charge u its velocity .In a continuous formulation we may use ρ for the charge density and j (=ρu ) for the current density .
The conservation of charge gives
(4.4)


this, by its turn, gives for the potentials (in the case of barotropic flow of the electromagnetised aether, in other words with density proportional to pressure) :
(4.5)




This equation of the potentials is also called Lorentz gauge

By variation of the previous energy density relative to the velocity of the particle we get the Lorentz force.
(4.6)


This force is a momentum exchange when the electromagnetised field-gas and charged matter do not balance.
By variation of  the potentials we get the Maxwell’s equations :

 (4.7)






(4.8)








As we shall see later, after the basic charged aether parameters interpretation of the vector and scalar electromagnetic potential, 
We may notice that both  equations (4.7), (4.8) , are the equations of forced waves (the D' Alembert's wave equation) The (4.7) forced wave  of charged aether pressures,  from the spin of a static charged (free permanent) elementary material particle (proton or electron) , and the (4.8), the forced wave on the charged aethers velocities (or vector momentum density) from the spin of moving material elementary particles (like electron, proton) .
In short the linear electromagnetism (Maxwell's electromagnetism) simply formulates, that the static or moving (free permanent ) elementary particles create waves due to heir intrinsic spin frequency. 

This is the basic linearized  interaction of changed matter and charged aether. Of cource the foul interaction is non-linear.






From these equations we get directly the familiar form of the Maxwell’s equations :
              (4.9) 
              (4.10)
              (4.11)

              (4.12)


Maxwell calculated the electromagnetised field-gas energy density as:
                
(4.13)
                 
while he also calculated that the electromagnetised field-gas excess pressure (due to electro magnetisation) matrix as :
                 (4.14)
                

He made no distinction of these stresses as being  inside a dielectric and magnetised material body, in which case E and B must include the constant of dielectrics and of magnetisation ,or if it is in field-gas or the “vacuum” as we say to day.

From these formulas is deduced the momentum  density of the electromagnetised field-gas by dividing with c2 the Poyning vector :
                 (4.15)
                 
              (4.16)
              
In the modern fashion, we write these as the entries of the energy momentum matrix (tensor)

              (4.17)
             

              or
Tik=
ε
Sx/c
Sy/c
Sz/c
Sx/c
σxx
σxy
σxz
Sy/c
σyx
σyy
Σyz
Sz/c
σzx
σzy
σzz

The previous review was made in order to make use of the formulas and proceed to the concepts of non-linear Electromagnetism.

Here we may tabulate the Maxwell's equations both in the Integral and differential form

See http://en.wikipedia.org/wiki/Maxwell%27s_equations

Conventional formulation in SI units[edit]

The equations in this section are given in the convention used with SI units. Other units commonly used are Gaussian units based on the cgs system,[1] Lorentz–Heaviside units (used mainly in particle physics), and Planck units (used in theoretical physics). See below for the formulation with Gaussian units.
NameIntegral equationsDifferential equations
Gauss's law\oiint{\scriptstyle\partial \Omega }\mathbf{E}\cdot\mathrm{d}\mathbf{S} = \frac{1}{\varepsilon_0} \iiint_\Omega \rho \,\mathrm{d}V\nabla \cdot \mathbf{E} = \frac {\rho} {\varepsilon_0}
Gauss's law for magnetism\oiint{\scriptstyle \partial \Omega }\mathbf{B}\cdot\mathrm{d}\mathbf{S} = 0\nabla \cdot \mathbf{B} = 0
Maxwell–Faraday equation (Faraday's law of induction)\oint_{\partial \Sigma} \mathbf{E} \cdot \mathrm{d}\boldsymbol{\ell}  = - \frac{d}{dt} \iint_{\Sigma} \mathbf{B} \cdot \mathrm{d}\mathbf{S} \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}
Ampère's circuital law (with Maxwell's addition)\oint_{\partial \Sigma} \mathbf{B} \cdot \mathrm{d}\boldsymbol{\ell} = \mu_0 \iint_{\Sigma} \mathbf{J} \cdot \mathrm{d}\mathbf{S} + \mu_0 \varepsilon_0 \frac{d}{dt} \iint_{\Sigma} \mathbf{E} \cdot \mathrm{d}\mathbf{S} \nabla \times \mathbf{B} = \mu_0\left(\mathbf{J} + \varepsilon_0 \frac{\partial \mathbf{E}} {\partial t} \right)
where the universal constants appearing in the equations are
In the differential equations, a local description of the fields,
The sources are taken to be
In the integral equations; a description of the fields within a region of space,
  • Ω is any fixed volume with boundary surface ∂Ω, and
  • Σ is any fixed open surface with boundary curve ∂Σ,
  • \oiint{\scriptstyle\partial \Omega } is a surface integral over the surface ∂Ω (the oval indicates the surface is closed and not open),
  • \iiint_\Omega is a volume integral over the volume Ω,
  • \iint_\Sigma is a surface integral over the surface Σ,
  • \oint_{\partial \Sigma} is a line integral around the curve ∂Σ (the circle indicates the curve is closed).
Here "fixed" means the volume or surface do not change in time. Although it is possible to formulate Maxwell's equations with time-dependent surfaces and volumes, this is not actually necessary: the equations are correct and complete with time-independent surfaces. The sources are correspondingly the total amounts of charge and current within these volumes and surfaces, found by integration.
Q = \iiint_\Omega \rho \, \mathrm{d}V\,,
where dV is the differential volume element, and
I = \iint_{\Sigma} \mathbf{J} \cdot \mathrm{d} \mathbf{S}\,,
where dS denotes the differential vector element of surface area S normal to surface Σ. (Vector area is also denoted by A rather than S, but this conflicts with themagnetic potential, a separate vector field).
The "total charge or current" refers to including free and bound charges, or free and bound currents. These are used in the macroscopic formulation below.

Electric currents (throughout conductor volume) in the absence of time varying electric field.

The formulations if the conductor has some thickness, the proper formulation of the Biot–Savart law (again in SI units) is (in the absence of time varying electric field):
 \mathbf B (\mathbf r) = \frac{\mu_0}{4\pi}\iiint_V\ \frac{(\mathbf{J}\,dV)\times\mathbf r'}{|\mathbf r'|^3}
or, alternatively:
 \mathbf B (\mathbf r) = \frac{\mu_0}{4\pi}\iiint_V \ \frac{(\mathbf J\,dV)\times\mathbf{\hat r'}}{|\mathbf r'|^2}
where dV is the volume element and \mathbf{J} is the current density vector in that volume.