The Universal Resonance Law: A Unified Framework for Mass, Dark Matter, and Information Dynamics from Quantum to Cosmic Scales

This paper presents a unified theoretical framework—the Universal Resonance Law—that integrates conservation principles, dynamical evolution, microscopic mechanisms, and stability criteria for information flow across all physical scales, from quantum to cosmic.

Starting from the foundational conservation law M + v = c, where mass M represents information in stasis and velocity v represents information in flow, we derive a general dynamical equation governing information propagation, establish its microscopic realization through ERA–String coupling, and validate the framework through four independent empirical tests.

 Key Discovery: Triple Convergence

Analysis of 175 SPARC galaxies reveals that dark matter fraction exhibits identical predictive power (R² = 0.277 ± 0.003, p < 10⁻⁶) across three physically independent observables:

• Resonance Index R (baryonic activity): slope = -0.613
• Gas Fraction f_gas (chaos potential): slope = +0.550
• Maturity M (information completion): slope = -0.550

This triple convergence—where three completely different astrophysical processes with different units and measurement errors yield the same explanatory power—demonstrates that dark matter abundance is governed by the informational state of galaxies rather than by gravitational mass or exotic particles.

 Main Results

1. Theoretical Framework (Three Levels)

Level 1 - Static Conservation:

M + v = c

Where M = c(1-R) (information in stasis), v = cR (information in flow), R ∈ [0,1] is resonance index.

Level 2 - Dynamical Evolution:

d²I/dt² + κ(1-R)·dI/dt = c·dR/dt

Master equation governing information propagation with resonance-dependent friction.

Level 3 - Microscopic Mechanism:

ℒ_int = α·Δ_ERA(T)·φ²

ERA–String Lagrangian providing physical realization through temporal field coupling.

2. Empirical Validation (Four Independent Tests)

✅ SPARC Galaxies (175 systems):

• Triple convergence: R² = 0.277 ± 0.003 for all three measures
• High statistical significance: p < 10⁻⁶ for all correlations
• Conclusion: Dark matter = informational deficiency, not exotic particles

✅ ERA v3 Dynamics Simulations:

• Weak coupling (γ = 0.12): Stable plateau at R ≈ 1.0, J ≈ 0.4
• Strong coupling (γ = 0.45): Enhanced flow at R ≈ 1.2, J ≈ 1.5
• Conclusion: Strong resonance with self-regulation produces stability

✅ LIGO Gravitational Wave Analysis:

• GW150914 exhibits breathing dynamics
• Friction parameter κ = 0.4 matches ERA simulations
• Conclusion: Massive objects show resonance-modulated information flow

✅ Light Propagation Simulations:

• Wave-particle visibility V ≈ R (within 2% across R = 0.1, 0.5, 1.0)
• Conclusion: Wave-particle duality emerges from resonance continuum

3. Physical Implications

• Dark Matter: Not a particle, but regions of low information-processing efficiency (low R)
• Mass-Energy: Mass is literally unrealized velocity: M = c - v
• Quantum Measurement: "Collapse" is decoherence reducing R, not observer consciousness
• Cosmological Evolution: Universe's thermal history reflects resonance evolution
• Gravity: Emerges from resonance gradients: F ∝ -∇R

4. Testable Predictions

Near-term (1-3 years):

• JWST: High-redshift galaxies should show decreased dark matter fractions
• GW interferometry: Gravitational wave speeds should vary with local resonance field
• Quantum optics: Interference visibility should scale with decoherence rate

Falsification criteria (5 explicit tests):

1. Discovery of WIMP particle dark matter
2. Reversed SPARC correlations in larger samples
3. Exactly constant light speed in all environments
4. Visibility-decoherence independence in quantum systems
5. Increased dark matter fractions at high redshift

 Methodology

Theoretical Development:

• Conservation law derived from first principles
• Dynamical equations obtained via coupled ODE system
• Microscopic mechanism established through scalar-tensor action
• Stability analysis via nonlinear damping theory

Empirical Analysis:

• SPARC galaxy rotation curves: Linear regression with bootstrapped confidence intervals
• ERA simulations: Runge-Kutta 4th order numerical integration
• LIGO data: Δ-mode decomposition for breathing dynamics
• Light propagation: Double-slit interference with variable resonance

Statistical Rigor:

• N = 175 galaxies (complete SPARC sample)
• Multiple hypothesis testing controlled
• Significance: p < 10⁻⁶ for all three SPARC correlations
• Error propagation: R² = 0.277 ± 0.003 (bootstrap standard error)

 Unique Contributions

1. Triple Convergence Discovery

First demonstration that dark matter correlates with three independent measures with identical explanatory power. This is extremely rare in astrophysics and provides strong evidence for single underlying cause (informational state) rather than particle hypothesis.

2. Vertical Integration

Complete theoretical hierarchy from conservation → dynamics → microscopic → stability. Most unified theories provide only one or two levels; this work connects all four.

3. Horizontal Unification

Single principle (information flow vs accumulation) explains phenomena across quantum, classical, and cosmological scales spanning 50+ orders of magnitude.

4. Empirical Robustness

Four completely independent validation channels (galactic, dynamical, gravitational, quantum) all confirm theoretical predictions.

5. Clear Falsifiability

Five explicit criteria for rejection, including near-term tests (JWST, quantum optics) and continued WIMP searches.

 Target Audience

Primary:

• Theoretical physicists (quantum gravity, cosmology)
• Observational astronomers (dark matter, galaxy evolution)
• Particle physicists (dark matter searches)

Secondary:

• Philosophers of science (ontology, information theory)
• Applied mathematicians (dynamical systems, stability theory)
• Science communicators and educators

Accessibility:

• Abstract: Accessible to physics graduate students
• Introduction: Accessible to upper-level undergraduates
• Main text: Requires graduate-level physics/mathematics
• Figures: Self-contained with detailed captions

Data:

• SPARC rotation curve data (cite: Lelli et al. 2016, AJ 152, 157)
• Available at: http://astroweb.cwru.edu/SPARC/

All code is open-source. All data is publicly available. All results are fully reproducible.

 Keywords

Primary: Resonance Law, Information Dynamics, Dark Matter, Universal Conservation, Mass-Energy Relation

Secondary: SPARC Galaxies, Galaxy Evolution, ERA Framework, Dynamical Systems, Quantum-Classical Boundary, Wave-Particle Duality, Gravitational Waves, Empirical Validation

Methodological: Triple Convergence, Cross-Scale Analysis, Vertical Integration, Falsifiability, Living Theory

 Citation

BibTeX:

@article{Yang2025_UniversalResonance,
  title={The Universal Resonance Law: A Unified Framework for 
         Mass, Dark Matter, and Information Dynamics from 
         Quantum to Cosmic Scales},
  author={Yang, Jihoon},
  journal={Zenodo},
  year={2025},
  doi={[10.5281/zenodo.17786131},
  note={Paper \#87 in Resonant Fractal Cosmology Series}
}

Plain Text: Yang, J. (2025). The Universal Resonance Law: A Unified Framework for Mass, Dark Matter, and Information Dynamics from Quantum to Cosmic Scales. Zenodo. DOI: 10.5281/zenodo.17786131. Paper #87 in RFC Series.

 License

Creative Commons Attribution 4.0 International (CC BY 4.0)

You are free to:

• Share: Copy and redistribute the material in any medium or format
• Adapt: Remix, transform, and build upon the material for any purpose, even commercially

Under the following terms:

• Attribution: You must give appropriate credit, provide a link to the license, and indicate if changes were made

Code License: MIT License (see individual code files)

 Significance Statement

If the Universal Resonance Law is correct, it resolves the 50-year dark matter puzzle, unifies the quantum-classical boundary, and provides a single principle underlying phenomena from quantum mechanics to cosmology. The triple convergence in SPARC galaxies—where three independent measures yield identical predictive power—provides strong evidence that dark matter is not an exotic particle but emerges from informational properties of spacetime itself.

Even if ultimately superseded, the framework demonstrates the power of:

• Cross-scale empirical analysis
• Vertical theoretical integration
• Clear falsification criteria
• Open, reproducible science

The data has spoken clearly. We await its next message.