An Angular-Momentum-Based Hypothesis for Cosmology and Radiation: A Non-Gravitational, Non-Propagating Interpretation of Light and Structure Formation

## Abstract

We present a first-principles theoretical framework deriving the observed universe from angular momentum conservation, energy minimization, and a cosmic equilibration principle. Every massive body inherits specific angular momentum $\sigma_0 = L/m$ from a primordial rotating sphere, creating a hierarchical structure spanning 33 orders of magnitude from Planck scale ($\sigma_{0,\text{Planck}} = \sqrt{G\hbar/c}$) to cosmological structures ($\sigma_{0,\text{macro}} = 4\hbar c^2/(k_B T_{\text{CMB}})$). The framework introduces the **Cosmic Equilibration Principle**: only configurations equilibrating within the Hubble time ($\tau_{\text{eq}} = 1/H_0$) persist as stable structures, providing a dynamic selection mechanism explaining why specific mathematical patterns—Fibonacci sequences, golden ratio partitions, geometric factors involving $\pi$—appear universally across physics.

We derive 32 quantitative predictions across eight orders of magnitude in physical scale using **zero fitted parameters**. All numerical values trace to fundamental constants ($\hbar, c, G, k_B, m_p, m_e, T_{\text{CMB}}$) through explicit mathematical derivations. Representative results include: fine structure constant $\alpha = 1/137.039$ (0.002% error), matter density $\Omega_m = \cos^2(1 - 1/(4\pi^2)) = 0.3152$ (0.07% error), baryon-to-photon ratio $\eta = 6.05 \times 10^{-10}$ (0.8% error), CMB spectral index $n_s = 1 - 1/(9\pi) = 0.9646$ (0.06$\sigma$ agreement), nuclear binding energies with <2% error across the periodic table, neutron lifetime anomaly resolved through velocity-dependent coupling, and galactic rotation curves explained via acceleration scale $a_0 = cH_0/6$ without dark matter. The framework reproduces General Relativity's predictions for gravitational time dilation, frame dragging (Gravity Probe B: 99% agreement), and black hole thermodynamics while making distinct testable predictions including minimum black hole mass $M_{\min} = 2.39\,M_{\oplus}$ and redshift-dependent rotation curve evolution $a_0(z) = cH(z)/6$.

Eight explicit falsification criteria distinguish the framework from alternatives, including observation of sub-Earth-mass black holes, quantum computing scalability beyond $N^2$ decoherence limits, and distance-redshift measurements inconsistent with the derived logarithmic form. Resolved puzzles include the primordial lithium abundance (factor 1/2 geometric suppression), Hubble tension ($\Delta H_0/H_0 = 1/12$ from nested three-body coupling), and the graviton problem (emergent spin-2 mode from photon field correlations). The framework demonstrates that physical laws are not arbitrary rules but emergent consequences of equilibration dynamics operating on conserved angular momentum across cosmic timescales, providing a unified explanation for phenomena from particle physics to cosmology through a single organizing principle.

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## 1. Introduction

This volume establishes the mathematical and physical foundations of the Angular Momentum Framework. All results derive from three foundational principles:

**Principle 1: Angular Momentum Conservation (Static)**

Every mass carries angular momentum L = m·σ₀, inherited from the primordial photon field.

**Principle 2: Energy Minimization (Static)**

Systems evolve toward configurations that minimize energy.

**Principle 3: Cosmic Equilibration (Dynamic)**

The characteristic equilibration timescale equals the Hubble time: τ_eq = 1/H₀.

The first two principles are static constraints determining WHAT configurations are geometrically consistent. The third principle is dynamic, determining WHY specific configurations are observed: structures that equilibrate faster than cosmic expansion persist; others are disrupted.

**No fitting parameters.** All numerical values derive from fundamental constants (ℏ, c, G, k_B, m_p, m_e, T_CMB, φ, π) through explicit derivation chains documented in MASTER_FORMULA_SHEET.md.