Gravity in an Energy Domain
Conceptual Foundation: CA Theory
Mathematical Framework
The Charge Admittance (CA) model reinterprets gravity as an emergent phenomenon arising from the equalization of energy density across a medium governed by the electromagnetic constants μ0 (vacuum permeability) and ε0 (vacuum permittivity). Unlike General Relativity (GR), which attributes gravity to spacetime curvature, CA posits that spatial variations in these constants, driven by energy density, create gradients that manifest as gravitational effects. This section develops the mathematical backbone of CA, demonstrating how bound energy concentrations (termed “blobs,” representing mass) couple with an unbound energy field to produce the observed 1/r2 gravitational behavior. The following derivations build on fundamental electromagnetic and energy relations, culminating in a gravitational gradient consistent with Newtonian gravity.
Maxwell Propagation Speed
The speed of electromagnetic field propagation in a vacuum is defined by Maxwell’s relation:
c = 1/√(ε0μ0)
where ( c ) is the speed of light, typically constant in free space (c0≈3×108 m/sc). In CA, however, ( c ) varies spatially with energy density, reflecting changes in μ0 and ε0. Near a bound energy mass—conceptualized as a localized, mass-like concentration analogous to atoms or molecules—high energy density perturbs the vacuum properties, reducing ( c ) locally. Farther away, as energy density diminishes, ( c ) approaches its baseline value c0.
To model this, consider a spherical mass with energy ( E ) distributed within it according to the energy contained within each “atomic” constituent. The energy density influence on μ0ε0 decays with distance, and we propose a simple perturbation form:
c(r) ≈ c0(1+kE/r2)−1/2
where ( r ) is the radial distance, ( k ) is a proportionality constant (to be calibrated), and the 1/r2 term reflects an inverse square decay, consistent with field gradients discussed later. As ( E ) increases near the mass, μ0ε0 rises (e.g., via increased μ0 or decreased ε0), slowing ( c ). This dynamic variation establishes the field’s gradient structure, a cornerstone of CA’s gravitational mechanism.
Mass-Energy Equivalence
Einstein’s mass-energy equivalence provides the link between bound blobs and the field:
E=mc2
Substituting c2=1/(μ0ε0), we rewrite this as:
E = m(1/μ0ε0)
Here, ( m ) represents the mass of a stable concentration of energy held together by internal forces (e.g., electromagnetic interactions within atomic structures). The energy ( E ) of the blob perturbs the local μ0, creating a source term that couples to the surrounding unbound energy field. For example, in a hydrogen atom, the electromagnetic binding of the electron and proton concentrates energy, increasing the local energy density and altering the vacuum properties.
This relation grounds the concept of mass: their energy, tied to μ0ε0, generates the field gradients responsible for gravitational effects. Unlike GR, where mass curves spacetime directly, CA treats mass as a secondary manifestation of energy density within an electromagnetic framework.
Coulomb Field Gradient
The electrostatic force follows an inverse square law:
F= ke*(q1* q2) / r2
where ke is Coulomb’s constant, q1 and q2 are charges, and ( r ) is the separation. In CA, this serves as a template for how energy density gradients decay from charges. We adapt it to describe the perturbation in μ0ε0 caused by a mass’s energy:
Δ(μ0ε0) ∝ E/r2
Using E=mc2, and assuming c≈c0 as a baseline, we propose:
Δ(μ0ε0) = k⋅mc02/r2
where ( k ) is a constant to be determined. This gradient reflects the mass’s energy density influence decreasing with distance squared, akin to classical field behavior. Near the mass, μ0ε0 increases, reducing ( c ); at larger ( r ), the perturbation fades, and c→c0.
This inverse square form departs from GR’s geometric approach, rooting CA in electromagnetic principles. It aligns with Newtonian gravity’s 1/r2
dependence, suggesting that energy density gradients can replicate observed gravitational effects without invoking curvature.
Lorentz Force
The Lorentz force describes electromagnetic interactions:
F=qE+qv*B
where ( q ) is charge, ( E ) is the electric field, ( v ) is velocity, and ( B ) is the magnetic field. In CA, this underpins the internal cohesion of bound
mass. For instance, in atoms, the electric attraction (( qE )) between electrons and nuclei, supplemented by magnetic effects (qv×B) in moving charges, stabilizes the energy concentration. This distinguishes bound mass from the diffuse, unbound field.
While not central to the gravitational derivation, the Lorentz force explains how blobs maintain their integrity, coupling their concentrated energy to the external field via perturbations in μ0ε0. This coupling initiates the gradient-driven energy flow that CA equates with gravity.
Gradient in Field Density
The spatial variation in ( c ) due to energy density gradients connects CA to relativistic effects:
Δc/c ≈ gh/c2
This resembles GR’s weak-field time dilation, where ( g ) is gravitational acceleration and ( h ) is height. In CA, Δc arises from changes in μ0ε0:
c = 1/√(ε0μ0)
Δc/c = −1/2⋅Δ(μ0ε0)/μ0ε0
From the Coulomb-inspired gradient:
Δ(μ0ε0) = k⋅mc02/r2
Assuming μ0ε0 ≈ μ0ε0 (baseline value) far from the mass:
Δc/c = −1/2⋅kmc02/r2/μ0ε0∣0
Since c02 = 1/(μ0ε0∣0):
Δc/ c = km/2r2
Comparing to gh/c2, with h ≈ r in a radial context, we calibrate ( k ):
gr/c02 = km/2r2
g = kc02m/2r3⋅r = kc02m/2r2
To match Newtonian gravity (g=Gm/r2), set:
k = 2G/c02
Thus:
Δ(μ0ε0) = 2Gm/r2
Δc/c = −Gm/c02r
This validates CA against GR’s weak-field limit, showing energy density gradients scale appropriately.
CA Gravitational Gradient
The gravitational effect in CA is defined as:
Gv = – (dc/ dx) → flow toward slower c regions (higher energy density), where energy density gradient is exponential.
where ( x ) is the spatial coordinate (radial ( r ) here). We derive gv from ( c(r) ):
c(r) = c0 (1 + 2Gm/c02r)−1/2
This adjusts our earlier form for consistency with Δc/c. For small perturbations (2Gm/(c02r)≪1:
c(r) ≈ c0 (1 – 2Gm/c02r)
Differentiate:
dc/dr = c0⋅d/dr(1−Gm/c02r) = c0⋅Gm/c02r2 = Gm/c0r2
gv = −dc/dr = −Gm/c0r2
Adjusting c0 as a baseline (since ( c ) varies), the exact form uses the full derivative:
dc/dr = −1/2 c0(1+2Gm/c02r)−3/2⋅(−2Gm/c02r )
= c0⋅Gm/c02r2 (1+2Gm/c02r)−3/2
For r≫ 2Gm/c02r (weak field):
gv ≈ −Gm/c0r2⋅c0 = −Gm/r2
This matches Newtonian gravity, proving CA’s gravitational effect emerges from energy gradients.