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:
Force (F) -> Grad p Charge (q) -> Div p Magnetism (B) -> Curl p
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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:
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
$ V_\mathbf{E} = - \int_C \mathbf{E} \cdot \mathrm{d} \mathbf{\ell} $,
$ \mathbf{E} = - \mathbf{\nabla} V_\mathbf{E}. \, $
$ \mathbf{\nabla} \cdot \mathbf{E} = \mathbf{\nabla} \cdot \left (- \mathbf{\nabla} V_\mathbf{E} \right ) = -\nabla^2 V_\mathbf{E} = \theta / \varepsilon_0, \, $
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} \, $
In Stowe's "Atomic Vortex Hypothesis", we find the following (pg. 2,3):
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
$ \frac{\partial \rho}{\partial t} + \rho \nabla \cdot \mathbf{v} = 0 $
$ \rho \nabla \cdot \mathbf{v} = 0 $
$ \nabla \cdot \mathbf{v} = 0 $
$ s \rho \nabla \cdot \mathbf{v} = - s \frac{\partial \rho}{\partial t}$
$ m \nabla \cdot \mathbf{v} = - \frac{\partial m}{\partial t} $
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.