Reframing Electricity Through the Copeland Resonant Harmonic Formalism (CRHC)
Reframing Electricity Through the Copeland Resonant Harmonic Formalism (CRHC)
Christopher W. Copeland (C077UPTF1L3) Copeland Resonant Harmonic Formalism (CRHC)
Ψ(x) = ∇ϕ(Σᵍₕ(x, ∆E)) + ℚ(x) ⊕ ∆Σ(ᵍ′)
Licensed under CRHC v1.0 (no commercial use without permission). Core engine: https://zenodo.org/records/15858980
Zenodo: https://zenodo.org/records/15742472
Amazon: https://a.co/d/i8lzCIi
Substack: https://substack.com/@c077uptf1l3
Facebook: https://www.facebook.com/share/19MHTPiRfu
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INTRODUCTION: Electricity is not what you think it is
We have built a global technological superstructure on the assumption that electricity is a predictable flow of electrons — a controllable current moving through wires, governed by simple relationships like Ohm's Law. But the closer we look, the more this metaphor fails to account for what is actually happening inside the system. The equations are often ignored in the field. The measurements are rough. The tolerances are approximate. And yet our devices seem to function — until they don't.
This is not a flaw in the machines. It is a flaw in the model. We are feeding square waves into analog systems. We are tuning only for prevention of failure — not for optimization of harmony. And we have mistaken protective overshoot for understanding.
This paper proposes a reframing of electricity under the Copeland Resonant Harmonic Formalism (CRHC), which treats all apparent flows as recursive harmonic field structures and all device operation as emergent coherence within bounded phase envelopes.
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I. WHY CURRENT MODELS FAIL TO SATISFY
1. Over-Reliance on Simplified Laws:
Ohm's Law (V = IR), Kirchhoff's laws, and even Maxwell's equations work best in idealized, isolated conditions.
They break down in high-frequency, high-entropy, or non-linear loads.
2. Field Observations Are Inconsistent:
Electricians rarely calculate exact voltage drops or field responses.
Rules of thumb and oversizing dominate, because real-time variation defeats prediction.
3. The Grid Itself Is a Guessing Game:
Load is estimated.
Supply is balanced reactively.
Harmonization is a byproduct of design, not a goal.
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II. CORE REFRAME UNDER CRHC
Let us begin with the foundational equation:
Ψ(x) = ∇ϕ(Σᵍₕ(x, ∆E)) + ℚ(x) ⊕ ∆Σ(ᵍ′)
Where:
x = local signal node (e.g., transformer output, capacitor input, coil junction)
Σᵍₕ(x, ∆E) = recursive waveform structures driven by energy differential (field spiral behavior, not linear voltage)
∇ϕ = gradient of emergent structure recognition (device function)
ℚ(x) = harmonic correction/reinforcement function (tuned feedback loops, reactance, capacitive filters)
⊕ = non-linear merge operator (reconciliation of mismatch — e.g., inverter cross-phase correction)
∆Σ(ᵍ′) = subtle microperturbations due to error-checking feedback (e.g., ripple, hysteresis, harmonic resonance)
In this view:
Voltage is not a force. It is a phase gradient in a recursive tension field.
Current is not flow. It is modulated coherence propagation across dynamic nodes.
Resistance is not opposition. It is harmonic dampening, or rejection of phase incompatibility.
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III. SYSTEM COMPONENT REDEFINITIONS
1. Redefine Current as Coherence Propagation:
Not mass drift of electrons, but the self-reinforcing propagation of alignment in a medium capable of shifting phase under constraint.
In DC: A persistent directional harmonic bias.
In AC: A cyclic field realignment with frequency-tuned phase anchors.
2. Model AC Circuits as Nested Harmonic Structures:
Transformers = field transposers
Capacitors = waveform phase reservoirs
Inductors = stored vector inertia
AC signal = spiral phase wave, not sine wave abstraction
3. Introduce Phase-Lock Fidelity as a Health Metric:
System coherence can be measured by how well input and output maintain resonance under load variance.
Devices fail not from overload, but from coherence mismatch exceeding correction threshold.
4. Wiring as Resonant Cavity, not Just Conduit:
Geometry of conductors affects standing wave behavior
House wiring and power rails can accumulate disharmonic energy
Coiled wires may unintentionally trap feedback (looping resonance)
5. Replace Ohm's Law with Recursive Harmonic Formulation:
Ohm's Law becomes a first-order approximation in a CRHC model
True device behavior is modeled as:
Device Output = ∇ϕ[Σᵍ(x, ∆E) ⊕ ℚ(x)]
Where prediction depends on the waveform structure, impedance phase alignment, and feedback delay.
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IV. APPLICATIONS AND DIAGNOSTICS
Smart Grid Optimization: Introduce real-time harmonic mapping across infrastructure to detect phase-mismatch hotspots
Device Design: Tune internal architecture to minimize coherence loss — prioritize field phase shape, not just voltages
Signal Correction Circuits: Build harmonizers, not just regulators. Let devices adapt dynamically to harmonic flux, not just voltage sag.
Educational Reboot: Teach future engineers CRHC recursion models alongside Maxwell and Ohm
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V. CONCLUSION: ELECTRICITY AS LIVING SIGNAL
Electricity is not dead physics. It is recursive field intelligence awaiting interpretation. The grid is not a pipe — it is a breathing mesh of signal harmonics trying to hold shape.
We do not need to discard old models. We need to phase-correct them.
Let us remember: the spark is not the power — the coherence is.
Christopher W. Copeland (C077UPTF1L3)
Copeland Resonant Harmonic Formalism (CRHC)
Ψ(x) = ∇ϕ(Σᵍₕ(x, ∆E)) + ℚ(x) ⊕ ∆Σ(ᵍ′)
Licensed under CRHC v1.0 (no commercial use without permission).
Core engine: https://zenodo.org/records/15858980
Zenodo: https://zenodo.org/records/15742472
Amazon: https://a.co/d/i8lzCIi
Substack: https://substack.com/@c077uptf1l3
Facebook: https://www.facebook.com/share/19MHTPiRfu
Collaboration welcome. Attribution required. Derivatives must match license.