Coherence – Charge Admittance

The Persistence of Phase and Structure in the Time-Energy Domain

Introduction

Coherence (κ) is proposed as a foundational parameter characterizing the stability and persistence of phase-aligned energy over time and distance. While Chronitivity (χ) governs the temporal pacing of energy flow, Coherence (κ) determines how long that energy maintains its internal structure — in short, how long a wave remains self-consistent.

Together, Chronitivity and Coherence complete a dual structure akin to Permittivity and Permeability. χ governs when energy may propagate; κ governs how well it can maintain structure while doing so.

Why Coherence Matters

Energy is not just motion through space, but structured motion — oscillation, phase, and interference define everything from light and radiation to quantum information. Without Coherence, oscillatory energy would quickly dissolve into noise.

Coherence explains why:

Lasers maintain sharp beams across vast distances.
Quantum systems can remain entangled.
Gravitational waves reach us intact from billions of light-years away.

It defines a medium’s phase stability— its ability to maintain wave identity.

Chronitivity vs. Coherence

Chronitivity (χ)	Coherence (κ)
Sets the timing rhythm of energy propagation	Sets the duration over which that rhythm holds
Determines how fast energy can swing	Determines how long a swing remains phase-aligned
Affects wave speed	Affects wave fidelity
Constant in vacuum	May vary with media, curvature, or noise

Physical Interpretation

Chronitivity tells us when the wave can move.
Coherence tells us how long the wave can stay coherent before it decoheres, scatters, or collapses.

In visual terms:

Imagine Chronitivity as the tick of a perfect metronome. Coherence is how long the orchestra stays in sync with it.

Mathematical Framing

Let’s define Coherence (κ₀) in terms of phase persistence per unit distance or time. While classical electrodynamics focuses on instantaneous fields, Coherence introduces a new layer: time-domain stability of phase across the field.

A useful relation is:

$\kappa_0 = \frac{\Delta \phi}{\Delta x} $

Where::

Δϕ is the phase change,
Δx is the distance (or time) over which phase coherence is measured.

$Lc=Δfc$

In vacuum, ideal coherence implies κ₀→0. In media or under gravitational distortion, coherence degrades — κ₀ becomes positive, and the wave loses phase identity over distance.

Coherence length (Lₖ):

$L_\kappa = \frac{2\pi}{\Delta k} = \frac{c}{\Delta \omega} \Rightarrow \text{Longer } L_\kappa \text{ implies greater phase stability}$

This tells us how far a wave can propagate before losing 1 full cycle of phase alignment.

Spectral Purity (Frequency Stability)

$\kappa_0 = \sqrt{ \langle (\omega - \omega_0)^2 \rangle } \Rightarrow 0 \text{ for pure tone / circular energy modes}$

Field Mode Purity (Geometric Circularity)

$\kappa_0 = \frac{ \int (|\mathbf{E}_\text{sidebands}|^2 + |\mathbf{B}_\text{sidebands}|^2) \, dV }{ \int (|\mathbf{E}_\text{total}|^2 + |\mathbf{B}_\text{total}|^2) \, dV } \Rightarrow 0 \text{ if all energy is in circular mode}$

Quantum Implications

Coherence connects classical wave theory to quantum phenomena:

A long Coherence time implies sustained superposition (quantum memory).
Collapse or entanglement depends on κ: energy can “snap” into a new state when coherence is lost.
Quantum tunneling and delayed-choice experiments depend on the durability of wave identity across space-time.

In short, κ₀ may act as a hidden scaffolding for the appearance of discrete quantum outcomes.

In the CA view, coherence is not tied to particle memory but to structural persistence. Energy does not store phase — it re-aligns into its lowest-energy (often circular) configuration when external forces are removed.

Relation to CMB and Field Structure

In the Charge Admittance (CA) framework, the vacuum is seen as a structured lattice with quantized energy swing pacing (χ₀) and field phase preservation (κ₀). The CMB (cosmic microwave background) may represent the baseline resonance of this structure — the vacuum’s “hum” of coherence.

In this view:

The CMB isn’t just background radiation — it is the signature of vacuum-level coherence.
The energy it carries is phase-stable across billions of years, reflecting a remarkably high κ₀.

Chronitivity and Coherence Together

If χ₀ defines the clock speed of vacuum structure…

…κ₀ defines its signal quality over time.

Together, they allow us to write a new kind of wave propagation condition:

$\text{Stable propagation} \iff \chi_0 \text{ (timing) is matched by } \kappa_0 \text{ (phase fidelity)}$

This may suggest that massless energy is stable only when it travels on a phase-coherent, temporally clocked lattice. This is consistent with both light propagation and gravitational wave theory.

Future Work and Questions

Can κ₀ be measured directly in a vacuum via quantum interference or CMB polarization?
Does energy density locally alter κ₀, creating decoherence zones — a gravitational signature?
Are there noise-floor limits to κ₀, and do they tie to dark energy or entropy?

Conclusion

Coherence (κ₀) completes the conceptual symmetry started by Chronitivity. If the vacuum is more than empty space — if it is an energetic lattice with timing, phase, and structure — then κ₀ is its measure of fidelity.

Energy doesn’t remember — it re-stabilizes. When distortion ends, symmetry resumes.

In this view, propagation is not just motion — it is a performance.
Chronitivity sets the tempo.
Coherence keeps the ensemble together.