Unified Resonance Model (URM): Toward a Process-First Theory of Everything

Author: Michael Simpson\
Date: September 2025\
Status: v1.1 Public Draft for Review

⚖️ Licensed under CC BY (Foundational, URM . 0 _|) and CC BY-NC-ND (URM Complete Documentation).

Preface

This document is released publicly to ensure the preservation and accessibility of the Unified Resonance Model (URM). It represents draft v1.1, a submission-ready version that integrates theoretical framework,
mathematical formalism, and experimental predictions.

By publishing openly, I establish a permanent public record of this work so that it is not lost and can be openly discussed, tested, and refined by the scientific community.

Abstract

We propose a process-first framework in which all interactions arise from coherence dynamics of a dimensionless phase field φ. A universal partition over phase steps Δφ yields three channels—transmit, resist, reflect— with environment coupling η, obeying the conservation law (T+B+R=1). A field-theoretic formulation with potential V(Δφ;η) and an amplitude lift A=cosΔφ + i√η·sinΔφ ensures unitarity and links naturally to quantum probabilities. An effective metric defined by coherence correlations makes spacetime emergent rather than fundamental, reproducing Newtonian gravity in the weak-field limit. URM provides
testable, falsifiable predictions: interferometer visibility, atomic clock drifts, light bending, neutrino anomalies, and CMB morphology. Geometry-first programs appear as limiting cases in the high-coherence regime.

1. Introduction

  • Motivation: unify quantum mechanics, gravitation, and cosmology under a single process law.\
  • Core novelty: φ-phase law is compact, scale-free, and experimentally falsifiable.\
  • Contrast: geometry-first approaches (string theory, amplituhedron) assume space as prior; URM derives space from coherence.\
  • Roadmap: axioms → amplitude lift → field theory → known physics → predictions → falsifiability → relation to other programs.

2. Core URM Law

2.1 φ-Phase Partition

T(Δφ) = cos²Δφ
B(Δφ;η) = η·sin²Δφ
R(Δφ;η) = (1-η)·sin²Δφ
T + B + R = 1
  • η: dimensionless environment/bath coupling, 0 ≤ η ≤ 1\
  • Scale-free recurrence: applies at atomic, mesoscopic, and cosmic
    levels

2.2 Amplitude Lift

A(Δφ;η) = cosΔφ + i√η·sinΔφ
A_total = ∏ A(Δφ_k;η_k)
P = |A_total|²

This ensures unitarity and recovers the Born rule.

3. Field-Theoretic Formulation

  • Candidate Lagrangian:\
    L = ½(∂μφ)(∂\^μφ) – V(Δφ;η), with V = λ[cos²Δφ + η sin²Δφ]\
  • Stress–energy tensor: Tμν = ∂μφ ∂νφ – gμν L\
  • Metric from coherence kernel: gμν from ∂μ∂ν’ G(x,x’)| (α,β > 0
    enforce Lorentz signature)

4. Recovering Known Physics

  • Newtonian limit: ∇²φ = κρ, mapped to Poisson equation.\
  • Einstein limit: weak-field curvature tensors (R₀₀, Rij) reproduce GR.\
  • Second law: decoherence rate Γdecoh = η⟨sin²Δφ⟩ → entropy
    increase dS/dt ≥ 0.

5. Predictions & Falsifiability

5.1 Criteria

URM is falsified if:\

  1. T+B+R ≠ 1 in scattering.\
  2. No η-dependence in interferometer visibility.\
  3. No clock drift beyond GR/QFT error bars.\
  4. CMB morphology inconsistent with resonance-sheet flatness.\
  5. Ring-laser gyros insensitive to coherence.\
  6. White-hole inversion excluded astrophysically.

5.2 Prediction Table

Observable Predicted Effect Current Feasible Test
(v0.1) Sensitivity

Interferometer ΔV ≈ 0.05–0.10 10⁻⁴ Cold-atom
visibility interferometers

Optical lattice Δf/f ~10⁻¹⁸–10⁻¹⁷ 10⁻¹⁹ Dual-clock
clocks comparisons

Solar light bending +0.0009″–0.0026″ 10⁻⁴″ VLBI campaigns

Ring-laser gyros Noise slope vs η 10⁻¹⁴ rad/s Bath-controlled tests

CMB low-ℓ alignments Anisotropy bias cosmic variance Planck/future surveys

Neutrino Env.-dependent shifts Ongoing DUNE/Hyper-K oscillations anomalies

6. Worked Examples

  • Interferometer: V(η) ≈ 1 – 2η⟨sin²Δφ⟩ → predicts 5–10% drop for
    η=0.05–0.1.\
  • Solar light bending: δθ_URM = δθ_GR[1+0.01η] → correction
    +0.0009″–0.0026″.

7. Relation to Other Programs

Theory Fundamental starting Experimental Current
point accessibility maturity

URM Coherence (φ-law) High (lab & cosmology) Early but testable

String Theory Geometry, extra Very low (Planck scale) High dimensions mathematics

LQG Quantized geometry Low (quantum gravity) Medium maturity

Amplituhedron Scattering polytopes Medium (amplitude fits) High mathematics

8. Discussion & Conclusion

URM reframes physics as coherence in motion.\
Strengths: simplicity, universality, testability.\
Limitations: embedding SM + cosmology needs work.\
Next steps: gauge-field emergence, cosmological dynamics, preregistered tests.

Conclusion: Unlike many ToE candidates, URM can be confirmed or falsified within the coming decade.

References (illustrative)

  1. Arkani-Hamed & Trnka, The Amplituhedron, JHEP 2014\
  2. Planck Collaboration, Planck 2018 results, A&A 641, A6 (2020)\
  3. Chou et al., Optical Clocks and Relativity, Science 329, 1630
    (2010)\
  4. Adelberger et al., Torsion Balance Tests of Gravity, Ann.
    Rev. Nucl. Part. Sci. 53 (2009)\
  5. Abe et al., Hyper-Kamiokande Design Report, PTEP (2018)\
  6. Schreiber et al., Ring Laser Gyroscopes, Rev. Sci. Instrum. 90
    (2019)\
  7. Clarke & Wilhelm, Superconducting quantum bits, Nature 453, 1031
    (2008)\
  8. Fomalont et al., VLBI deflection precision, ApJ 2009\
  9. Cronin et al., Atom interferometry precision methods, Rev. Mod.
    Phys. 2009\
  10. Nicholson et al., Systematic uncertainty in lattice clocks, Nat.
    Comm. 2015