Maxwell Extensions – Charge Admittance

Maxwell Extensions M5–M8: A Unified Field Framework for the Four Fundamental Forces

Overview

This document introduces a proposed extension of classical electromagnetic theory by incorporating four additional field dynamics that align with and reinterpret the four fundamental forces (gravity, electromagnetism, strong, and weak). These new terms emerge from the temporal and structural behaviors of the vacuum’s permittivity (ε₀) and permeability (μ₀), seen not as fixed constants but as spatially and temporally variable field parameters within a structured vacuum lattice (Ξ-lattice).

Each force is reframed not as a separate phenomenon, but as a manifestation of specific “C-States” (Chronitivity, Coherence, Confinement, Coupling), each associated with a unique behavior of the underlying lattice.

Concept, General: Possibilities of ε₀–μ₀ Field Interactions in Other Modes

The Charge Admittance (CA) framework originated with a single question: What is gravity? That question led to a core insight — that gravity emerges not from mass curvature but from a gradient in the local propagation rate of energy, as governed by changing values of permittivity (ε₀) and permeability (μ₀). The resulting field expression,

$g_v = -\frac{dc}{dx}$

became the foundation of the CA approach.

μ₀ and ε₀ are not exclusive to gravity. They define the character of all electromagnetic interactions. If their spatial and temporal behaviors can give rise to gravity, might other interaction modes — when structured differently — yield the other fundamental forces?

This possibility expands CA beyond gravity into a broader investigation of force emergence through ε₀–μ₀ dynamics. Within this context, four core interaction modes have been proposed, each associated with a distinct field behavior:

Force	Field Concept	Symbol	Field Range	Phase Character	Interpretation
Gravity	Temporal gradient	χ₀ (Gv)	Near-field	–j (lagging phase)	Change in c due to ε₀μ₀ gradients; local time delay creates directional energy flow
Electromagnetism	Phase coherence	κ₀	Near-field	0j (balanced phase)	Maintains wave integrity when ε₀/μ₀ ratio is stable; governs coherence and signal transfer
Strong Force	Field confinement	ψ₀	Extreme near-field	+j (leading/locked phase)	Knotting or pinching in the ε₀μ₀ field; self-reinforcing loops or minima (like quark confinement)
Weak Force	Asymmetric coupling	ϕ₀	Far-field decay	–j (dissipative phase)	Unstable coupling dominated by μ₀; loss of coherence, energy leakage, particle decay

Explanatory Notes:

The near/far-field classification relates to how tightly bound or radiative the interaction is:
Gravity and EM operate across scale (EM propagates far, but its coherence is tested in the near-field).
The strong force is highly local, constrained to subnucleonic ranges.
The weak force becomes dominant only in instability zones — in energy leaks, decay events, or long-range, low-intensity interactions.
κ₀ and ψ₀ represent very different field architectures:
κ₀ is a flat field coherence: signal travels unscattered.
ψ₀ is a folded topology: energy loops back or locks in.

Sidebar: ψ₀ States — Glimpses of a Pre-Qubit Topology?

Could energy confinement in ε₀–μ₀ fields hint at more than just binding forces? The ψ₀ mode, described as a folded topology where energy loops back on itself, may resemble more than just strong-force behavior. When field lines close into a self-reinforcing toroid, no external electric or magnetic poles remain — yet the internal energy persists, phase-locked and shielded from decoherence.
This resembles some features of qubits:
– Stability from self-binding (non-radiative loop)
– Hidden internal states encoded in field phase
– Resistance to decoherence via isolation from the far field
– State transitions governed by ε₀–μ₀ configuration shifts
While ψ₀ is not a qubit in any formal sense, the structural similarities suggest that the same field mechanics responsible for confinement might also underpin primitive informational states. In this view, matter, memory, and measurement could all emerge from topological structures in the field itself.
Speculation? Yes. But perhaps also a glimpse of how information and energy intertwine at the root of physical structure.

These conceptual field parameters are not fundamental particles or forces themselves — they are modes of interaction through which ε₀ and μ₀ express different types of energy structuring. While χ₀ and κ₀ are grounded in measurable effects like redshift and decoherence, ψ₀ and ϕ₀ remain exploratory — open hypotheses awaiting deeper mathematical framing and experimental insight.

CA does not yet claim a unified field theory. But it opens the door to one, by revealing how classical constants, long considered fixed, may instead be dynamic descriptors of field behavior. The idea that ε₀ and μ₀ underlie all forces suggests a deeper unity — perhaps one already hinted at by Maxwell, but never fully pursued.

M5: Chronitivity (χ₀) — The Gravity Extension

Interpretation: Gravity arises from gradients in the local propagation rate (a local change in the speed of light), as ε₀ and μ₀ vary together while preserving their ratio, thereby producing curvature-like effects through time delay, not geometry.
Definition:

$\nabla \chi_0 = \frac{d}{dx}\left(\frac{1}{\sqrt{\varepsilon_0(x) \mu_0(x)}}\right) = gv$

Description: A varying clocking rate across the vacuum lattice introduces a curvature-like effect via delay, not geometry. Mass appears as an emergent property of energy’s delayed propagation.

M6: Coherence (κ₀) — Electromagnetic Phase Integrity

Interpretation: Electromagnetic phenomena depend on the maintained balance (ratio) of ε₀ to μ₀. When their ratio is constant, c is constant, and coherent propagation is maintained.
Definition:

$\kappa_0 = \frac{\varepsilon_0}{\mu_0} \Rightarrow \nabla \kappa_0 = 0 \text{ preserves wave stability}$

Description: Coherence represents the phase durability and energy integrity in EM waves. Decoherence results in energy dispersion or gravitational redshift.

M7: Confinement (ψ₀) — Strong Force and Lattice Pinning

Interpretation: The strong force is a result of intense localized variations or knots in ε₀ and μ₀, forming self-reinforcing loops or impedance minima.
Definition:

$\nabla \psi_0 \rightarrow \infty \text{ at field knots or pinches (quark binding)}$

Description: These self-interlocking points of lattice compression form tightly bound energy configurations (e.g., hadrons) resistant to spatial separation.

M8: Coupling (ϕ₀) — Weak Force and Near-Field Drift

Interpretation: Weak interactions arise from asymmetrical field behavior, where permeability dominates permittivity, resulting in unstable, lossy energy decay.
Definition:

$\mu_0 \gg \varepsilon_0 \Rightarrow \nabla \phi_0 \neq 0 \text{ (decoupling)}$

Description: This asymmetry leads to energy leakage, particle decay, and phase decoherence in weak interactions. Analogous to lossy inductive coupling.