Monday, February 20, 2012

2.9 The Navier-Stokes as conjectured equations of the unified macroscopic solar system gravitational and electromagnetic field in the absence of matter






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. THE MAIN PROOF OF THE  EXISTENCE OF MICRO-PROTON , MICRO-ELECTRON AND MICRO-NEUTRON  IS THE FAMOUS IN QUANTUM MECHANICS, 2-SLIT ELECTRON EXPERIMENT WHERE IT IS PHOTOGRAPHED NOT ONLY THE ELECTRON THIS HITS THE PHOTOGRAPHIC PLATE BUT ALSO THE WAVE OF CHARGE BY SUCH MICRO-PARTICLES THAT THE ELECTRON MOTION CREATES. 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


To be transferred from the published paper  of the other scientific site.

For a derivation of the Navier-Stokes equations see



The relevant form, of Navier-Stokes equations, of Newtonian, isotropic, compressible fluids is

Compressible flow of Newtonian fluids

There are some phenomena that are closely linked with fluid compressibility. One of the obvious examples is compression waves (sound in air and aether-sound in aether). Description of such phenomena requires more general presentation of the Navier–Stokes equation that takes into account fluid compressibility. If viscosity is assumed a constant, one additional term appears, as shown here:[1][2]
\rho \left(\frac{\partial \mathbf{v}}{\partial t} + \mathbf{v} \cdot \nabla \mathbf{v}\right) = -\nabla p + \mu \nabla^2 \mathbf{v} + \left(\zeta + \frac{\mu}{3}\right) \nabla (\nabla \cdot \mathbf{v}) + \mathbf{f},
where \zeta is the second viscosity.


  1. [1]  Landau & Lifshitz (1987) pp. 44–45.
  2. Jump up[2] Batchelor (1967) pp. 147 & 154.

We must notice that as the pressure can be eliminated from the Navier-Stokes equations in the case of in-compressible flows and the equation stated equivalenty either only with the vector potential (velocities) or magnetic field only (vorticity) in the case of incompressible flows of aether (see e.g. Lerays formulations of in-compressible Navier-Stokes and vorticity-stream equivalent formulation of the in-compressible Navier-Stokes in chapters 1,2 of the book Vorticity and incompressible flows by Majda and Bertozzi  https://www.google.gr/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&cad=rja&uact=8&ved=0CDYQFjAD&url=http%3A%2F%2Fiate.oac.uncor.edu%2F~manuel%2Flibros%2FModern%2520Physics%2Ftheoretical%2520Physics%2FVorticity%2520and%2520incompressible%2520flow%2520-%2520Majda%2C%2520Bertozzi..pdf&ei=5ubIVM_kEYj1atf1gOgN&usg=AFQjCNG-9mKY6eyneIwJ7MAIcKk0835Y1Q&sig2=-bsFEJKCr--tNxRfkeb3Nw&bvm=bv.84607526,d.d2s ) Then we conclude that ins such special cases of incompressible aether flows the equations of the electromagnetised aether (in the absence of matter) can be written as the vorticity  equation, which therefore would contain only the vorticity which is essentially only the magnetic field B or only   the scalar electromagnetic potential which is proportional to the pressure.  Then the equations are not longer partial differential equations but integro-differential equations. 


To the navier-Stokes equation we should add the ideal gas law, that involves the temperature

(see e.g. http://en.wikipedia.org/wiki/Ideal_gas_law  and http://en.wikipedia.org/wiki/Ideal_gas    and http://en.wikipedia.org/wiki/Gas_laws) which is proportional the Newtonian gravitational scalar potential .

The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behaviour of many gases under many conditions, although it has several limitations. It was first stated by Émile Clapeyron in 1834 as a combination of Boyle's law and Charles's law.[1] The ideal gas law is often introduced in its common form:
PV=nRT\,
where P is the pressure of the gas, V is the volume of the gas, n is the amount of substance of gas (measured inmoles), R is the ideal, or universal, gas constant, and T is the temperature of the gas.
It can also be derived microscopically from kinetic theory, as was achieved (apparently independently) by August Krönigin 1856[2] and Rudolf Clausius in 1857.[3]

Or

p = \rho R_s T\,\! \,\!
Where:
  • p\,\! = Pressure
  • T\,\! = Temperature
  • R_s\,\! = Gas constant for the specific gas 


Also other forms of the energy conservation in fluids, which involves the internal energy  and the energy density of the fluid are relevant equations. 

These next equations of 3-dimensional vortex motions as solutions of the Navier-Stokes equations for compressible Newtonian, non-viscous fluids, are the standard for a whirl from fluid dynamics that all academic physicists know,  so there is no mystery at all. The key to correspond known magnitudes from electromagnetism and gravitation to the fluid dynamic magnitudes are as in the published paper of the Lancaster lecture, or as in post 1.




The involved magnitudes are:

φ :gravitostatic scalar potential (that is proportional to the aether temperature)
Α :Vector electromagnetic potential (which is proportional to the momenum density of charged or electromagnetised aether)
α0 :Scalar electromagnetic potential (which is proportional to the pressure of the  charged or ionized or electromagnetised aether )
Macroscopic geometric parameters of the whirl

 E : electric field as              

which is the external body force to aether (usually from atomic material charges) minus the convective acceleration of the ionized or changed aether. Here the density is the density of the charged or ionized aether and the pressure is the change pressure of the charged aether. The vector electromagnetic potential is the velocity of the changed aether. We notice that the Navier-Stokes equations of the charged aether e.g.inthe absence of matter of electrons , protons Neutrons is not the two Linear PDE that are Dalambertian wave equations but the non-Linear PDE of Navier-Stokes that involve more magnitudes than just the the scalar and vector electromagnetic potential of Maxwell. We may assume though that the viscosity is almost zero. But this is not the case when e.g. the electromagnetic waves of the light of sun at infrared ,as slowed down by friction and lose their energy which becomes thermal energy of the charged or neutral aether , and as we we discuss elsewhere this means that it changes the potential energy of the gravitational field. (Which is essentially what the underground inventors including N. Tesla call free-energy).

Here we are referring to the Navier-Stokes equations by  
the meaning of each term (compare to the Cauchy momentum equation):
\overbrace{\rho \Big( \underbrace{\frac{\partial \mathbf{v}}{\partial t}}_{ \begin{smallmatrix} \text{Unsteady}\\ \text{acceleration} \end{smallmatrix}} + \underbrace{\mathbf{v} \cdot \nabla \mathbf{v}}_{ \begin{smallmatrix} \text{Convective} \\ \text{acceleration} \end{smallmatrix}}\Big)}^{\text{Inertia (per volume)}} = \overbrace{\underbrace{-\nabla p}_{ \begin{smallmatrix} \text{Pressure} \\ \text{gradient} \end{smallmatrix}} + \underbrace{\mu \nabla^2 \mathbf{v}}_{\text{Viscosity}}}^{\text{Divergence of stress}} + \underbrace{\mathbf{f}.}_{ \begin{smallmatrix} \text{Other} \\ \text{body} \\ \text{forces} \end{smallmatrix}}




B : magnetic field as 
New electromagnetic and gravitational constants in the equations.
Derived magnitudes
Extracted power as energy per time unit.



These equations is conjectured to be very relevant  to most of the free-energy electromagnetic devices.

BUT we must point out that these next equations maybe for example the whirl of Rodin coil, but it is not what we really want for a general whirl that produces free-energy. And the reason is that the equation below are of a symmetric whirl, where no extraction of heat is made from the fluid. What we really need is a modification of the equations below, so that heat is extracted from the fluid and converted to extra kinetic energy of the fluid (much like equations of atmospheric tornados).



We present here a very well known solution to the Navier-Stokes equations of Newtonian-isotropic compressible fluids, of a whirl (small tornado) motion. This can be a solution both to neutral aether (a form of dynamic gravity) or to the electromagnetised aether (a more correct form of the electromagnetic field e.g. of Rodin's coil, although to be correct here this solution of aether wirl is assumed in the absence of matter, that is not created by a coil. But there is similar solution in the presence of the matter of a coil). 

A three-dimensional steady-state vortex solution[edit]

Some of the flow lines along a Hopf fibration.
A nice steady-state example with no singularities comes from considering the flow along the lines of a Hopf fibration. Let r be a constant radius to the inner coil. One set of solutions is given by:[28]
\begin{align} \rho(x, y, z) &= \frac{3B}{r^2 + x^2 + y^2 + z^2} \\ p(x, y, z) &= \frac{-A^2B}{(r^2 + x^2 + y^2 + z^2)^3} \\ \mathbf{v}(x, y, z) &= \frac{A}{(r^2 + x^2 + y^2 + z^2)^2}\begin{pmatrix} 2(-ry + xz) \\ 2(rx + yz) \\ r^2 - x^2 - y^2 + z^2 \end{pmatrix} \\ g &= 0 \\ \mu &= 0 \end{align}
for arbitrary constants A and B. This is a solution in a non-viscous gas (compressible fluid) whose density, velocities and pressure goes to zero far from the origin. (Note this is not a solution to the Clay Millennium problem because that refers to incompressible fluids where \rho is a constant, neither does it deal with the uniqueness of the Navier–Stokes equations with respect to any turbulence properties.) It is also worth pointing out that the components of the velocity vector are exactly those from the Pythagorean quadruple parametrization. Other choices of density and pressure are possible with the same velocity field:

See also a relevant video (which applies is to the aggregate of galaxies and stars rather that to the local laboratory aether field).


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Monday, January 9, 2012

2.10 The conjectured new laws of interaction of matter and aether at laboratory scale and at solar system scale





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. THE MAIN PROOF OF THE  EXISTENCE OF MICRO-PROTON , MICRO-ELECTRON AND MICRO-NEUTRON  IS THE FAMOUS IN QUANTUM MECHANICS, 2-SLIT ELECTRON EXPERIMENT WHERE IT IS PHOTOGRAPHED NOT ONLY THE ELECTRON THIS HITS THE PHOTOGRAPHIC PLATE BUT ALSO THE WAVE OF CHARGE BY SUCH MICRO-PARTICLES THAT THE ELECTRON MOTION CREATES. 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.

  


 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.
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 1) THE MAXWELL'S ELECTROMAGMETIC FIELD (OR ELECTROMAGNETIZED AETHER AS MAXWELL WAS CALLING IT) 2) THE QUANTUM VACUUM THAT AS SUBSTRATUM GIVES RANDOMNESS TO MOTIONS OF PROTONS, NEUTRONS, ELECTRONS THROUGH THE SCHRODINGER WAVE EQUATION (DIRAC'S AETHER)

Electromagetised aether-field acting on  matter


Lorenz force equation.

Matter acting on the  Electromagetised aether-field

Static

1) The Coulomb law (Es static electric field)

 or in general the 1st of the maxwell scalar potential equations

where a0 is the algebraic (signed) density of the charged aether )

Dynamic 
2) The Biot-Savard law of creation of the magnetic field by a moving charge (current).

3) Moving charges (current) creates in a dynamic way vector electromagnetic potential  and electric field (Ed) , which CANNOT be derived from the Coulobs law after superimposing the motion

 Or simply 

where A is the vector of the momentum of the charged aether, and J is the momentum of a charge. 

The Maxwell equations on the scalar and vector potential (pressure and momentum density of charged aether) that are the Linear DAlambertian forced wave equations. Such equation are linear, and represent the aether drag by chargef matter, for relatively uniform not chaotic non-linear motion of matter, that also create rather smooth electromagnetization and motion in aether
The Helmholtz-Hodge decomposition of any velocity field (see e.g. http://en.wikipedia.org/wiki/Helmholtz_decomposition ), will give that the aether velocity field can be decomposed in to a part with scalar velocity potential (potential or non-rotational flow) , and a vector velocity potential (divergence free or solenoidal or in-compressible  flow). 

If the Helmholtz-Hodge decomposition is applied to the vector field of the forces due to the electomagetised aether, it is the guidline of the decomposed description of the electromagetism to Electric and magnetic field or scalar and vector potential 
The first part with the  Landau derivation will derive the forced wave of the scalar electromagnetic potential potential, while the second part will derive the forced wave equation of the vector electromagnetic potential. Both are nevertheless linearizations of the non-Linear Navier-Stokes equations of velocities (ad pressures)
As we shall see later, after the basic charged aether parameters interpretation of the vector and scalar electromagnetic potential, 
We may notice that both  above equations  are the equations of forced waves (the D' Alembert's wave equation) The first forced wave  of charged aether pressures,  from the spin of a static charged (free permanent) elementary material particle (proton or electron) , and the second, 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 course the foul interaction is non-linear.


Neutral aether-field acting on  matter


The extension to  (weak)  Lorenz-like  force to include  a) Neutral aether temperature gradient (Newtonian gravitostatics, and aether heat gravitistatics) b) neutral aether acceleration c) Neutral aether magnetism .
Of course under normal conditions and body sizes the latter two terms are very weak compared to the static part

Matter acting on   neutral  aether-field

Static 
a) Newton's matter density , gravitostatics
Aether temperature gradient  gravitostatics

 Linear inertia equation

This equation simple states that any particle (e.g. a neutron) because of its spin, it creates a scalar compression wave ("sound" ) in the neutral aether (here a0 is the density of the neutral aether) which propagates at the speed of light c. Notice that in acoustics the above equation is nothing else that a forced sound wave, if it was to be interpreted in air rather than aether. This equation is mainly microscopic, in other words for particles at a classical laboratory

Dynamic
b)  Constant linear velocity moving matter creates aether linear velocity   and neutral aether magetism. Of course largely weaker. The quantitative details of this law cannot be derived neither from the static Newtonian gravitation, neither from Einsteinian gravitation. 
This equation for this interaction of aether and matter is  mainly macroscopic, in other words for celestal bodies like planets, stars and is strong and measurable as the celestial body is electromagnetised (e.g. magnetic field of a planet, is synonymous to the magnetized aether following the motion of the planet etc ) 

 We may simply state the Maxwell-like equations on the scalar and vector potential (pressure and momentum density of charged aether)  that are the Linear DAlembertian forced wave equations. But in this case as equation describing the effect of neutral particles like neutron, on the neutral aether. The effect is of course much more week than that of chatged particles (electromagnetism) that electromagetise (charge) aether too. Such equation would be laboratory scale valid and not say macroscopic planetary scale, of moving planets in aether. 
The motion of the particles with spin  is constrained by the field-gas (aether) so that at every state of the motion is created a wave of velocities on aether due to the spin of the particle and the next  equation holds of the interaction of the moving particle with spin and the aether, 
(2.0.1) 


where A is the vector of the momentum  of the (neutral) aether, and j is the momentum of the moving particle. Notice again that this equation is identical with the Maxwell equation of the vector electromagnetic potential , except that in the Maxwell equations the momentum J is of charges. 
This equation is mainly microscopic, in other words for particles at a classical laboratory


The role in the aether-matter interaction of the frequency of the spin of protons/neutrons/electrons of matter. 

 Higher frequency creates larger correlation of matter and aether-field motion.

The role of the level of human consciousness to the frequency of the spin of protons/neutrons/electrons in the human body. 


Where classical laboratoty electromagnetism is wrong
1) Moving charges (current) create in a dynamic way vector electromagnetic potential  and electric field, which CANNOT be derived from the Coulobs law after superimposing the motion.In particular accelerating charge is producing electric field which cannot be derived simply from the Maxwell equations by the changing magnetic field of the moving charge. 
2) For fast moving (e.g. rotating) magnets, the magnetic field seazes to be conservative! 
Rarely in fluid dynamics the field of rotations (curl) of a fluid is conservative! The fact that for static magnets is at a very good aproximation conservative does not mean that in general and at all possible states, that the magetic field is always conservative. 
3)Because of the nature of magnetism which is the curl or rot of the velocity of the charged (and not neutral) aether, at the end of a magnetic field is obligatory that will exist very week at least electric field too (when charged aether becomes again neutral) In other words the idea of a purely magnetic field is is so ideal that it does not exist in reality. 


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Monday, December 19, 2011

2.11 The solution of the equations of the electromagnetised aether whirl. Further speculations on the conjectured Unified-Aether field







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. THE MAIN PROOF OF THE  EXISTENCE OF MICRO-PROTON , MICRO-ELECTRON AND MICRO-NEUTRON  IS THE FAMOUS IN QUANTUM MECHANICS, 2-SLIT ELECTRON EXPERIMENT WHERE IT IS PHOTOGRAPHED NOT ONLY THE ELECTRON THIS HITS THE PHOTOGRAPHIC PLATE BUT ALSO THE WAVE OF CHARGE BY SUCH MICRO-PARTICLES THAT THE ELECTRON MOTION CREATES. 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.
THIS WORK DOES THE BEST ONE CAN DO TO DISCOVER THE TRUTH BEHIND THE STANDARD EQUATIONS OF GRAVITATION AND ELECTROMAGNETISM AS FAR AS A 2ND MATERIAL LAYER UNIFICATION IS  INTENDED, WHEN NO LABORATORIES EXPERIMENTS AND LARGE GROUPS OF SCIENTISTS WITH  WELL FUNDED RESEARCH IS POSSIBLE.  THE MAIN 3 CONTRIBUTIONS ARE 
1) THE REVEALING OF THE TRUE MEANING OF THE POISSON EQUATION OF NEWTON'S SPHERICAL GRAVITATIONAL POTENTIAL IN RELATION TO THE POISSON EQUATION OF SPHERICAL HEAT PROPAGATION IS THE KEY SHIFT IN THE CORRECT PHYSICAL INTERPRETATION OF GRAVITATION WHICH ALLOWS FOR  DISCOVERING SOLAR RENEWABLE ENERGY STORED IN IT. 
2) THE REVEALING INTERPRETATION OF MAXWELL'S  ELECTROMAGNETIC MAGITUTES IN RELATION TO AN IONIZED OR CHANGED 2ND MATERIAL LAYER SUBSTRATUM  AND 
3) THE PRELIMINARY UNIFYING ROLE OF NAVIER-STOKES EQUATIONS OF THE SUBSTRATUM MATERIAL FLUID FOR  GRAVITATION AND ELECTROMAGNETISM  WHICH ALLOWS FOR THE EXISTENCE OF NEW ELECTROMAGNETIC PROPULSION FOR TRANSPORTATIONS. 

  IT IS ALSO SPECULATED  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 MORE DETAILED  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.



We write here the energy conservation for a small   conical electro- magnetised aether whirl or tornado, where aether heat is extracted (aether temperature proportional to the scalar gravitostatic potential φ ) and converted to aether charge acceleration (E electric field) and aether charge rotation B or magnetic field. 

 Such equations CANNOT BE DERIVED FROM THE MAXWELL'S EQUATIONS AND THE CLASSICAL EQUATIONS OF GRAVITATION (NEWTON'S OR EINSTEIN'S).

 The relevant form, of Navier-Stokes equations, of Newtonian, isotropic, compressible fluids is

Compressible flow of Newtonian fluids

There are some phenomena that are closely linked with fluid compressibility. One of the obvious examples is compression waves (sound in air and aether-sound in aether). Description of such phenomena requires more general presentation of the Navier–Stokes equation that takes into account fluid compressibility. If viscosity is assumed a constant, one additional term appears, as shown here:[1][2]
\rho \left(\frac{\partial \mathbf{v}}{\partial t} + \mathbf{v} \cdot \nabla \mathbf{v}\right) = -\nabla p + \mu \nabla^2 \mathbf{v} + \left(\zeta + \frac{\mu}{3}\right) \nabla (\nabla \cdot \mathbf{v}) + \mathbf{f},
where \zeta is the second viscosity.




  1. [1]  Landau & Lifshitz (1987) pp. 44–45.
  2. Jump up[2] Batchelor (1967) pp. 147 & 154.

These equations are the standard for a whirl from fluid dynamics from the Navier-Stokes equations, that all academic physicists know,  so there is  no mystery at all. The key to correspond known magnitudes from electromagnetism and gravitation to the fluid dynamic magnitudes are as in the published paper of the Lancaster lecture, or as in post 1.

We  should involve also the equation 
p = \rho R_s T\,\! \,\!
Where:
  • p\,\! = Pressure
  • T\,\! = Temperature
  • R_s\,\! = Gas constant for the specific gas 
 ρ is the density

The involved field magnitudes are:

φ gravitostatic scalar potential
Α Vector electromagnetic potential
a Scalar electromagnetic potential
Macroscopic geometric parameters of the whirl
E electric field
B magnetic field. 
New electromagnetic and gravitational constants in the equations.
Derived magnitudes
Extracted power as energy per time unit.

These equations is conjectured to apply to most of the free-energy electromagnetic devices.

 We present here a very well known solution to the Navier-Stokes equations of Newtonian-isotropic compressible fluids, of a whirl (small tornado) motion. This can be a solution both to neutral aether (a form of dynamic gravity) or to the electromagnetised aether (a more correct form of the electromagnetic field e.g. of Rodin's coil). 
See http://en.wikipedia.org/wiki/Navier_Stokes

BUT we must point out that these equations maybe for example the whirl of Rodin coil, but it is not what we really want for a general whirl that produces free-energy. And the reason is that the equation below are of a symmetric whirl, and non-isothermic   where no extraction of heat is made from the fluid. Instead the temperature of the fluid increases due to friction. What we really need is a modification of the equations below, so that heat is extracted from the fluid and converted to extra kinetic energy of the fluid (much like equations of atmospheric tornados).
In other words the flow is not isothermal, or isentropic or barotropic. 

A three-dimensional steady-state vortex solution


Some of the flow lines along a Hopf fibration.
A nice steady-state example with no singularities comes from considering the flow along the lines of a Hopf fibration. Let r be a constant radius to the inner coil. One set of solutions is given by:
\begin{align} \rho(x, y, z) &= \frac{3B}{r^2 + x^2 + y^2 + z^2} \\ p(x, y, z) &= \frac{-A^2B}{(r^2 + x^2 + y^2 + z^2)^3} \\ \mathbf{v}(x, y, z) &= \frac{A}{(r^2 + x^2 + y^2 + z^2)^2}\begin{pmatrix} 2(-ry + xz) \\ 2(rx + yz) \\ r^2 - x^2 - y^2 + z^2 \end{pmatrix} \\ g &= 0 \\ \mu &= 0 \end{align}
for arbitrary constants A and B. This is a solution in a non-viscous gas (compressible fluid) whose density, velocities and pressure goes to zero far from the origin. (Note this is not a solution to the Clay Millennium problem because that refers to incompressible fluids where \rho is a constant, neither does it deal with the uniqueness of the Navier–Stokes equations with respect to any turbulence properties.) It is also worth pointing out that the components of the velocity vector are exactly those from the Pythagorean quadruple parametrization. Other choices of density and pressure are possible with the same velocity field:

See also a relevant video (which applies is to the aggregate of galaxies and stars rather that to the local aether field).

http://www.youtube.com/watch?v=EKtevjrZOGs

The next work describes a vortex motion of tornados that do extract thermal energy from the atmospheric fluid, and thus closer to the case of the (aether) field vortex motions in free energy.

http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19700032427.pdf

Also here are classical models of the tornadoes vortex motion.

 The Rankine model, the Burgers-Rott vortex model, and the Sullivan vortex model

 http://www.kilty.com/pdfs/models.pdf

Note however that tornados models that the density is constant (incompressible flow) would not be of much interest, as we are interested for thermal energy extraction by decompression. 

 See also the thesis of JIANJUN XIA 

 http://wvuscholar.wvu.edu:8881//exlibris/dtl/d3_1/apache_media/L2V4bGlicmlzL2R0bC9kM18xL2FwYWNoZV9tZWRpYS82MDc0.pdf


HEAT EXTRACTION VORTEX

As far as I know there have not been formulated in simple equations a steady curve-linear conical-like vortex motion of a compressible  fluid (e.g. air) with temperature gradient along the curve-linear conical axis, where there is detonation or pressure decrease, from the narrow diameter of the  curve-linear cone to its wide diameter , at the cost of  heat of the fluid, which sustains the vortex motion. (Heat-extraction vortex). But if such a formulation would ever be given then this would be a quantitative mathematical model for "free-energy" devices. Of course in the case of aether, this "free-energy" would be nothing else than the aether heat which is synonymous to the gravitational potential energy, which surprisingly for the perceptions of classical Newtonian gravitostatics is mainly not heat from matter, but heat from the infrared solar radiation stored in the aether gravitational field as gravitational potential energy. (See posts 2.7, 2.8) 

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