On Space Time And The Fabric Of Nature Sand Box

Paul Stowe's compressible aether model

Now that we have formulated a basic conceptual model of electromagnetism, which requires a model of a compressible aether, we can consider how to describe such a model. Paul Stowe already proposed such a model, which he outlined as follows:

I have determined that in my opinion all of physical processes can be defined in terms of the aether populational momenta (p). Such that, 
          Force     (F) -> Grad p
          Charge    (q) ->  Div p
          Magnetism (B) -> Curl p
Gravity for example is Grad E where E is the electric potential at x. This resolves to Le Sagian type process as outlined in the Pushing Gravity models. The electric potential E in turn is created by charge which is Div p...
My model is a direct extension of Maxwell's vortex model of interacting rings (the smoke ring model). I have been able to define all fundamental constants in terms of basic parameters, including the gravitational constant G. Further, G is, within this system, seamlessly integrated to all others, fitting into a unified system.
The key to this system's definition is the realization that charge is fundamentally a result AND the measure of the compressibility of Maxwell's aether.

[...]

Quantity SI Conversion Factor to Maxwell's Ether Based Units 

Length meter   (m)                  meter(m)
Mass Kilogram  (kg)                 Kilogram (kg)
Time Second    (sec)                second (sec)
Force Newton   (Nt)                 kg-m/sec^2
Energy Joules  (J)                  kg-m^2/sec^2
Power Watts                         kg-m^2/sec^3
Action         [h] (Planck's Const) kg-m^2/sec
Permitivitty   [z] (Q^2/kg-m^3)     kg/m^3 {1}
Permeability   [u] (kg-m-sec^2/Q^2) m-sec^2/kg {2}
Charge         [q] (Coulomb)        kg/sec
Boltzmann's    [k] (J/°K)           m-sec
Current        [I] (Amp)            kg/sec^2
Electric Field [E]                  m/sec
Potential      [V] (Voltage)        m^2/sec {3}
Displacement   [D]                  kg/m^2-sec
Resistance     [R] (Ohms)           m^2-sec/kg
Capacitance    [C]                  kg/m^2
Magnetic Field [H] (Henries)        m^2
Magnetic Flux  [B] (Gauss)          (dimensionless)
Inductance     [L]                  m^2-sec^2/kg
Temperature   [°K] (Kelvin)         kg-m/sec^3

{1} - density
{2} - modulus
{3} - Kinematic Viscosity

The basic physical quantities in this system are the medium properties identified by Maxwell in his 1860-61 "On Physical Lines of Force". We quantify the mean momentum (quanta) [ß], characteristic mean interaction length (quanta) [L], the root mean speed [c], and a mass attenuation coefficient [¿].

Their values are, 

ß = 5.154664E-27 kg-m/sec
L = 6.430917E-08 m
¿ = 3.144609E-06 m^2/kg
c = 2.997925E+08 m/sec

In other words, all of the major observed and measured constants of physics can be derived from the above terms.

Note that he directly associates the concept of electric elasticity with the compressibility of the aether itself, as we proposed would be necessary. He worked this out in his artlcle "The nature of Charge"(1999).

In his paper "A Foundation for the Unification of Physics"(1996) he gives the following introduction to his model:

Many of apparent inconsistencies that exist in our current understanding of physics have results from a basic lack of understanding of what are called fields. These fields, electric, magnetic, gravitational...etc, have been the nemesis of physicists since the birth of modern science, and continues unresolved by quantum mechanics. A classical example of this is the problem of an electron interacting with it's own field. This case results in the equations of quantum mechanics diverging to infinity. To overcome this problem, Bethe introduced the process of ignoring the higher order terms that result from taking these equations to their limit of zero distance, in what is now a common practice called renormalization.
These field problems result in class of entities called virtual, existing only to balance and explain interactions. These entities can (and do) violate accepted physical laws. This is deemed acceptable since they are assumed to exist temporarily at time intervals shorter than the Heisenberg's uncertainty limit. It has been known for some time that such virtual entities necessitate the existence of energy in this virtual realm (Field), giving rise to the concept of quantum zero point energy.
As a result of this presentation I will propose the elimination of both the need for renormalization and any such virtual fields. This will be accomplished by replacing the virtual field with a real physical media within which we define elemental particles (which more precisely should be called structures) and the resultant forces which act between them.

Gauss' law

Notation:

gradient : ∇

divergence: ∇⋅

curl : ∇

Note: on WP, $\rho$ is used for charge density, while in our model this is already used for mass density. In order to avoid confusion, we will use $\theta$ instead

https://en.wikipedia.org/wiki/Electric_potential#Electrostatics

The electric potential at a point r in a static electric field E is given by the line integral

$ V_\mathbf{E} = - \int_C \mathbf{E} \cdot \mathrm{d} \mathbf{\ell} $,

where C is an arbitrary path connecting the point with zero potential to r. When the curl ∇ × E is zero, the line integral above does not depend on the specific path C chosen but only on its endpoints. In this case, the electric field is conservative and determined by the gradient of the potential:

$ \mathbf{E} = - \mathbf{\nabla} V_\mathbf{E}. \, $

Then, by Gauss's law, the potential satisfies Poisson's equation:

$ \mathbf{\nabla} \cdot \mathbf{E} = \mathbf{\nabla} \cdot \left (- \mathbf{\nabla} V_\mathbf{E} \right ) = -\nabla^2 V_\mathbf{E} = \theta / \varepsilon_0, \, $

where $\theta$ is the total charge density (including bound charge) and ∇· denotes the divergence.

This holds in the case the field is conservative, which means that $ \theta $ is considered to be constant over the volume wherein path C can be chosen. This also holds in infinitesimal consideration when the volume goes to zero, provided we also include the partial derivative of $ \theta $ with respect to time ($ \frac{\partial \theta}{\partial t} $).

Gauss' law in differential vorm is given as:

$ \mathbf{\nabla} \cdot \mathbf{E} = \frac{\theta}{\varepsilon_0} \, $

where ∇ · E is the divergence of the electric field, ε0 is the electric constant, and $\theta$ is the total electric charge density (charge per unit volume).

In Stowe's "Atomic Vortex Hypothesis", we find the following (pg. 2,3):

"In any compressible media there exist cyclic fluctuations in the physical contents of every point. The scalar magnitude of the point momentum variance is Divergence. [...] The textbook dimensions of charge ( in terms of mass/length/time) remains undefined and is assigned arbitrary names ( Coulombs in SI, ESU in cgs, ... etc .) in different unit systems. In this model this is not the case and for the SI unit system it is defined as one (1) Coulomb equals 1 kg/sec".

Thus, we can write:

$ \theta = \frac{\partial \rho}{\partial t} $

Substituting this into Gauss' equation, we get:

$ \mathbf{\nabla} \cdot \mathbf{E} = \frac{1}{\varepsilon_0} \frac{\partial \rho}{\partial t} $

This is a rather remarkable find. It fundamentally not only couples the concept of charge to the compressibility of the aether itself, it also couples it fundamentally to time variations of the mass density of the aether itself, which is quite logical given the model used for describing the aether as a super fluid, consisting of "particles" defined in terms of average momentum, or the distribution of mass times velocity.

This pretty much implies that longitudinal waves, involving the movements of aether mass, are the fundamental phenomenon that creates the electric field. This suggests that at the atomic scale, the concept of a "charge carrier" is akin to a "Helmholtz resonator" in the acoustic domain, which is capable of producing "jet streams", which can create a (propulsive) force:

http://www.youtube.com/watch?v=PoEyIJx3uM0

http://www.tuks.nl/wiki/index.php/Main/StoweNatureOfCharge

The basic continuity equation of Continuum Mechanics is given as:

$ \frac{\partial \rho}{\partial t} + \rho \nabla \cdot \mathbf{v} = 0 $

Where $ \rho $ is the field density, and v is the mean velocity. If the field is incompressible this simplifies to:

$ \rho \nabla \cdot \mathbf{v} = 0 $

Since with the incompressible assumption, there can be no change in density. We can further simplify the equation by removing density (dividing it from both sides) we then get:

$ \nabla \cdot \mathbf{v} = 0 $

This definition requires infinite propagation speeds of any perturbations in such incompressible systems, eliminating any possibility of wave activity.
Conversely, in compressible mediums we see that $ \rho \nabla \cdot \mathbf{v} $ equals the time rate of change in the density ($\frac{\partial \rho}{\partial t}$). For the limit, as a volume element s go to zero, we get:

$ s \rho \nabla \cdot \mathbf{v} = - s \frac{\partial \rho}{\partial t}$

This is based on the observation that for the two terms to sum to zero, and therefore must have opposite signs. This leads directly to:

$ m \nabla \cdot \mathbf{v} = - \frac{\partial m}{\partial t} $

And cannot be zero. This is an important finding, it describes a unique characteristic of all compressible systems. The result of this is a fixed finite propagation speed for any perturbations in the resulting continuum, leading to standard acoustic behavior.

Note: See eq. 8 in "Atomic Vortex Hypothesis" : ρ = nm , with n the density of Stowe's "aether populational momenta" p, which are defined as: p = m v.