A Unified Geometric Theory of Matter, Gravity, and Forces

Author: Glenn Millar, 

Date: December 2025
 

DOCUMENT STRUCTURE

Page Count Estimate: ~80 pages (standard preprint format)
This work is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License. 

To view a copy of this license, visit - https://creativecommons.org/licenses/by-nc/4.0/)

ABSTRACT

We present the Single Bulk Framework (SBF), a phenomenological framework proposing that the observable universe is a discrete, critical-state granular vacuum at the jamming transition (coordination number $Z \approx 14.4$). By treating spacetime as a dynamic material governed by Random Close Packing (RCP) and Self-Organized Criticality (SOC), we derive the known forces and particles as mechanical stress modes of the vacuum substrate.

METHODOLOGICAL PREFACE: HOW TO READ THIS FRAMEWORK

To prevent common category errors in the assessment of this work, we explicitly distinguish the Analytical Foundations from the Phenomenological ones.

1. The Rigorous Foundation (Appendix H & E): This framework is not a numerological exercise. As demonstrated in Appendix H, the Standard Model Lagrangian density ($\mathcal{L}_{SM}$) is rigorously derived as the continuum elastic limit of the discrete Fundamental Granular Function ($F_{\text{Planck}}$). The known forces are not assumed; they are recovered as the inevitable stress modes of a Cosserat solid.

2. The Heuristic Phenomenology (Lepton Masses): While the field dynamics are derived ab initio, the specific mass eigenvalues ($M \propto Z^{N-3}$) currently occupy a "Keplerian" stage—phenomenological scaling laws that fit the data with high precision, pending a full "Newtonian" derivation from lattice eigenmodes.

3. The Verification Suite (Appendix A): The provided Python code is a verification tool. Run it and see for yourself.

"The chosen structural and visual formatting prioritizes Pedagogical Clarity to aid cross-disciplinary comprehension, a necessity given the framework's reliance on non-standard concepts (e.g., Cosserat Continua, Dilatancy)."

Quantitative Successes:

• Lepton Mass Hierarchy: The Muon ($0.28\%$ error) and Tau ($0.46\%$ error) masses are derived via topological knot scaling on the contact network ($M_N \propto Z^{N-3}$).

• Fine Structure Constant: $\alpha^{-1} \approx 138.2$ ($0.88\%$ error) is derived from torsional stress scaling in the void network ($\alpha^{-1} \approx \frac{2}{3}Z^2$).

• Dark Energy: The cosmological constant emerges from geometric frustration ($Z=12$ vs $Z \approx 14.4$) and holographic scaling, naturally resolving the $10^{120}$ magnitude discrepancy.

• Neutrino Masses: $\Sigma m_{\nu} < 0.12$ eV with mixing angles $\theta_{12} \approx 35.3^{\circ}$, $\theta_{23} \approx 45^{\circ}$, and $\theta_{13} \approx 8.2^{\circ}$, derived strictly from void geometry.

• Lagrangian Derivation: We prove that the Standard Model Lagrangian density ($\mathcal{L}_{SM}$) emerges naturally as the continuum elastic limit of the discrete Fundamental Granular Function ($F_{\text{Planck}}$). Consequently, General Relativity and Gauge Theory are recovered as the low-energy effective theories of the vacuum substrate, valid strictly below the granular yield stress ($Y < 0$).

Unified Force Structure:

• Gravity: Refractive dilatancy (vacuum expansion under stress).

• Strong Force: Tensile confinement via 1D force chains (linear potential).

• Weak Force: Topological shear transitions ($W/Z$ bosons as metastable defects).

• Electromagnetism: Conceptually unified via the void network. The electric field is identified as static torsion ($\nabla^2\Theta=0$), while the magnetic field is void vorticity. The Lorentz force emerges as the Magnus effect on topological knots moving through the swirling granular vacuum medium. 

• • Lagrangian Derivation: We prove that the Standard Model Lagrangian density ($\mathcal{L}_{SM}$) emerges naturally as the continuum elastic limit of the discrete Fundamental Granular Function ($F_{\text{Planck}}$). Consequently, General Relativity and Gauge Theory are recovered as the low-energy effective theories of the vacuum substrate, valid strictly below the granular yield stress ($Y < 0$). knots

Falsification Criteria:

We propose decisive tests for the next decade:

1. LiteBIRD (2032): Detection of a CMB B-mode sawtooth signature at multipoles $\ell=4, 6$.

2. LIGO (Ongoing): Detection of gravitational wave echoes at $\Delta t = 2R_s/c$ from crystalline black hole cores.

3. Dwarf Galaxies (Immediate): Absence of the 20 GeV gamma-ray excess, verifying vacuum resonance over WIMP annihilation.

"If you model reality as a Planck grain substrate at the Bernal limit of 14.4, then the rest of physics is inevitable." - G.

FOREWORD: BEYOND THE EFFECTIVE FIELD LIMIT

Quantum Field Theory (QFT) is the most successful effective theory in the history of science, yet it is mathematically distinct from the substrate it describes. Its infinities and renormalization requirements suggest it is a statistical description of a deeper, discrete reality—a "fluid mechanics" of spacetime that smooths over the underlying molecular granularity.

The Single Bulk Framework (SBF) proposes that QFT is the low-energy elastic limit of a granular vacuum at the jamming transition ($Z \approx 14.4$). We assert that the continuous Lagrangian density $\mathcal{L}$ is not the fundamental axiom of reality, but the emergent statistical result of the discrete Fundamental Granular Function ($F_{\text{Planck}}$).

Where QFT necessitates renormalization to manage divergences at the Planck scale, SBF introduces a natural mechanical cutoff: the Yield Stress of the vacuum lattice. This framework offers a UV Completion of the Standard Model, extending physics beyond the elastic limit ($Y < 0$) into the plastic regime ($Y \ge 0$)—the domain of singularities, horizons, and topological decay. This is not a rejection of QFT, but a derivation of its mechanical origin.