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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