Abstract

The Modified Einstein Field Interaction (MEFI) theory proposes a single tri-field ontology—Universal Frequency Resonance (UFR), compression field, and \(\Delta Q\) (quantum difference)—replacing particle-based, gravitational, and probabilistic quantum models. The core radial response equation is

\[ F_{\text{MEFI}}(r, t) = \left[\frac{k_r}{r^2} - \frac{k_c}{r^2(1+r)}\right] + \Delta Q\, f_{\text{UFR}}(t), \]

which unifies phenomena from atomic fluctuations to galactic coherence and biological resonance. Simulations demonstrate emergent stability (disks, arms, nodes) over > 100 Byr equivalents, resilient absorption of large \(\Delta Q\) events (minor coherence dips followed by recovery), and Phase D decoherence when compression overtakes expansion. Applications include a MEFI resonant periodic table (elements as frequency zones), hippocampal neuron resonance (\(\sim 81.92\ \text{Hz}\)), nuclear deformation reinterpretation (Pb-208), and compression-bubble engineering via structured \(\Delta Q\) channels. Findings suggest MEFI provides a scale-invariant, response-centric alternative to GR/QFT with falsifiable predictions.

Keywords: MEFI, resonance–compression, \(\Delta Q\) modulation, UFR, scale invariance, dynamic disorder, resonant periodic table, phase coherence

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1 Introduction

The current paradigm in physics is fragmented. General Relativity (GR) governs large-scale gravitational effects through spacetime curvature, Quantum Field Theory (QFT) describes particle interactions probabilistically, and the Standard Model catalogs fundamental excitations. Despite their successes, these frameworks fail to form a cohesive description of reality. Their reconciliation requires ad-hoc constructs such as dark matter, dark energy, and renormalization procedures that lack fundamental justification.

The Modified Einstein Field Interaction (MEFI) theory proposes a resonance–compression ontology in which all structure and dynamics emerge from interactions among three scalar fields. The Universal Frequency Resonance (UFR) field defines the stabilizing reference state, the compression field regulates localization and density, and \(\Delta Q\) quantifies deviation from equilibrium, driving change. This closed-loop model replaces forces, particles, curvature, and indeterminacy with resonance alignment and mismatch.

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2 Theoretical Framework

MEFI models reality as a tri-field system. The UFR field \(U(x,t)\) represents the universal coherence target. The compression field \(C(x,t)\) constrains resonance spatially. The \(\Delta Q\) field \(Q(x,t)\) quantifies deviation from equilibrium,

\[ Q(x,t) = \kappa\left(C(x,t) - C_{\text{eq}}[U(x,t)]\right), \]

where \(\kappa\) is a coupling constant.

The dynamics follow from a Lagrangian density \(L_{\text{MEFI}}\). The Euler–Lagrange equations are

\[ \alpha\,\Box U + \frac{dV_U}{dU} + 2\lambda C U + \mu Q = 0, \] \[ \beta\,\Box C + \frac{dV_C}{dC} + \lambda U^2 + \nu Q = 0, \] \[ \gamma\,\Box Q + \frac{dV_Q}{dQ} + \mu U + \nu C = 0, \]

where \(\Box\) denotes the d’Alembertian operator.

For spherically symmetric systems, the effective radial response reduces to

\[ F_{\text{MEFI}}(r,t) = \left[\frac{k_r}{r^2} - \frac{k_c}{r^2(1+r)}\right] + \Delta Q\, f_{\text{UFR}}(t), \quad \text{with } f_{\text{UFR}}(t) = \sin(\omega t). \]

Matter forms only within resonance bands where compression and expansion balance permits stable UFR alignment. Outside these bands, \(\Delta Q\) exceeds coherence thresholds, producing Phase D decoherence.

Scale invariance follows as

\[ \Delta Q_{\text{quantum}} = \left(\frac{\lambda_{\text{quantum}}}{\lambda_{\text{macro}}}\right)^{\alpha}\Delta Q_{\text{macro}}, \quad \alpha \approx 1.9 \text{ reflecting fractal compression behavior.} \]

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3 Notation and Symbol Definitions

For clarity and reproducibility, we summarize the primary symbols and fields used throughout the MEFI framework.

Symbol	Description
\(U(x,t)\)	Universal Frequency Resonance (UFR) field
\(C(x,t)\)	Compression field regulating localization and density
\(Q(x,t)\)	\(\Delta Q\) field representing deviation from equilibrium
\(\Delta Q\)	Quantum difference driving dynamical change
\(C_{\text{eq}}[U]\)	Equilibrium compression required for UFR alignment
\(k_r\)	Expansion coefficient (outward resonance tendency)
\(k_c\)	Compression coefficient (inward constraint)
\(f_{\text{UFR}}(t)\)	Time-dependent UFR modulation function
\(\omega\)	UFR angular frequency
\(r\)	Radial coordinate in spherically symmetric systems
\(\alpha\)	Fractal compression exponent (\(\approx 1.9\))
\(r(t)\)	Kuramoto phase coherence parameter
Phase D	Decoherence regime where compression dominates expansion

All quantities are scale-invariant unless explicitly stated. Mass, energy, and force are treated as emergent bookkeeping quantities rather than fundamental drivers.

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4 MEFI Resonant Periodic Table

In MEFI, elements correspond to resonance bands within the UFR spectrum rather than electron shells. Each element occupies a stable frequency interval characterized by compression phase and allowable \(\Delta Q\) variance. The element frequency is modeled as

\[ f_{\text{element}} = \frac{C\,Z}{R^2 H_f}, \]

where \(Z\) is atomic number and \(H_f\) a harmonic factor.

Representative cases include hydrogen (\(\sim 10^{15}\ \text{Hz}\)), carbon (\(\sim 2.3\times 10^{15}\ \text{Hz}\)), and high-\(Z\) elements (\(>10^{16}\ \text{Hz}\)). Bandwidth narrows monotonically with \(Z\), reflecting increasing compression dominance. Matter creation is restricted to these zones.

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5 Ultrafast Atomic Dynamics

Attosecond imaging reveals rapid atomic fluctuations with preserved order. In MEFI, these correspond to coherent \(\Delta Q\) surges interacting with UFR. Simulations of resonance chains show transient mean-squared displacement (MSD) spikes followed by rapid recovery:

\[ \text{MSD}=\frac{1}{N}\sum_i (x_i-x_0)^2. \]

The resulting “resonance breathing” reflects oscillatory modulation of the effective bandwidth, \(\delta\omega \propto \Delta Q\).

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6 Galaxy Formation and Long-Term Coherence

Galactic structures emerge from compression gradients and tangential \(\Delta Q\) torque. Low \(\Delta Q\) regimes yield ring-like shells, while higher values generate spiral arms through azimuthal phase drift. Coherence is quantified using the Kuramoto order parameter

\[ r(t)=\left|\frac{1}{N}\sum_{j=1}^{N} e^{i\phi_j(t)}\right|. \]

Simulations show baseline \(r(t)\approx 0.97\), with temporary dips of 3–6% during perturbations and full recovery over > 100 Byr equivalents.

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7 Biological and Neural Resonance

Biological systems operate near resonance criticality. MEFI predicts hippocampal pyramidal neuron resonance at

\[ f_{\text{MEFI}} \approx 81.92\ \text{Hz}, \]

consistent with theta–gamma coupling. Pathologies arise from persistent detuning and can be addressed via targeted \(\Delta Q\) damping and UFR reinforcement.

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8 Advanced Applications

Applications include resonance-stabilized nuclear configurations, compression-bubble lift systems, structured \(\Delta Q\) channels for traversal, resonance-based energy harvesting, and therapeutic modulation via adaptive biofeedback.

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9 Cosmic Explanations

Dark matter effects arise from compression gradients, dark energy from unregulated expansion in low-compression regions, and inflation from early high-\(\Delta Q\) regimes. Extreme compression zones correspond to black hole horizons with information preserved as resonance waves. Entanglement, holography, and ER=EPR emerge naturally from UFR phase locking.

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10 Simulations and Findings

Across scales, MEFI simulations exhibit intrinsic resilience. Coherence dips remain small (2–6%) and recover fully. Matter formation consistently occurs only within resonance-stable zones.

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11 Falsifiability and Experimental Predictions

A central strength of MEFI is its explicit falsifiability. Because the framework reduces physical behavior to resonance alignment, compression balance, and \(\Delta Q\) modulation, it makes quantitative predictions that diverge from GR and QFT under specific conditions.

11.1 Ultrafast Atomic Experiments

MEFI predicts that attosecond-scale atomic motion will exhibit:

Coherent oscillatory displacement rather than stochastic diffusion
Rapid recovery of pair-distance distributions following perturbation
Harmonic sidebands proportional to \(\Delta Q\) amplitude

Failure to observe coherence recovery after controlled excitation would falsify the resonance-stabilization mechanism.

11.2 Biological and Neural Measurements

MEFI predicts:

Narrowband resonance plateaus in neural tissue near 80–90 Hz
Temporary coherence dips (2–6%) during high-stress events with full recovery
Pathological states corresponding to persistent \(\Delta Q\) detuning

Persistent incoherence without recovery would contradict the closed-loop tri-field model.

11.3 Cosmological Structure

At galactic scales, MEFI predicts:

Long-term structural coherence without unseen stabilizing matter
Quantized resonance shells detectable through phase-aligned stellar motion
Recovery from energetic perturbations without secular decay

Observed irreversible decoherence in isolated galaxies would invalidate the compression-driven binding mechanism.

These predictions are testable with existing ultrafast imaging, EEG/MEG, atomic clock arrays, and high-resolution galactic surveys.

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12 Discussion

MEFI replaces force-based ontology with resonance response, eliminating ad-hoc constructs while increasing predictive power. Its falsifiable predictions and compatibility with modern sensing and computation position it as a viable successor framework.

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References

S. Greenmyer, The MEFI Unified Field Framework, 2026.
S. Greenmyer, MEFI Scale Invariance and \(\Delta Q\) Analysis, 2026.
S. Greenmyer, Ultrafast Atomic Dynamics, 2025.
S. Greenmyer, Nuclear Structure in Pb-208, 2025.
S. Greenmyer, MEFI Transforms Chemistry, 2025.
S. Greenmyer, Fractal MEFI-Based Framework, 2026.
S. Greenmyer, LiDAR Resonance Phenotyping, undated.
S. Greenmyer and L. Resonance, Hippocampal Neuron Resonance, undated.
S. Greenmyer, Antigravity and Wormholes, 2025.

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Appendix A: Linear Stability Analysis and Phase D Criterion

To characterize stability, we linearize the tri-field system around equilibrium:

\[ U = U_0 + \delta U,\quad C = C_0 + \delta C,\quad Q = 0 + \delta Q. \]

Substituting into the Euler–Lagrange equations and retaining first-order terms yields the coupled system:

\[ \partial_t^2 \begin{pmatrix} \delta U\\ \delta C\\ \delta Q \end{pmatrix} = M \begin{pmatrix} \delta U\\ \delta C\\ \delta Q \end{pmatrix}, \]

where \(M\) is the resonance-compression coupling matrix.

Stability requires all eigenvalues \(\lambda_i\) of \(M\) to satisfy:

\[ \Re(\lambda_i) < 0. \]

Phase D decoherence occurs when compression dominates expansion such that:

\[ k_c > k_r + \Delta Q_{\text{crit}}, \]

causing one or more eigenvalues to cross into \(\Re(\lambda_i) > 0\), leading to runaway detuning and loss of phase coherence. This criterion defines a sharp boundary between matter-supporting and decoherent regimes and is independent of scale.

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