Angular Momentum Framework: A First-Principles Derivation of Physical Law

We present a theoretical framework that derives physical constants, coupling strengths, and cosmological
parameters from three foundational principles: angular momentum conservation, energy minimization, and
cosmic equilibration. The framework contains zero fitting parameters—all predictions emerge directly from
the fundamental constants ℏ, c, G, kB , mp, me, TCMB and the mathematical constants π and ϕ (golden
ratio).
The framework introduces specific angular momentum σ0 = L/m as the organizing quantity, establishing
that physical systems at all scales are characterized by discrete σ0 values spanning 33 orders of magnitude
from the Planck scale (4.845 × 10−27 m2/s) to macroscopic structure (1.01 × 106 m2/s). From this hierarchy,
we derive a coupling potential U = −GL1L2/(σ2
0 r) that recovers Newton’s gravitational law as a special
case while extending naturally to regimes where Newtonian mechanics fails. A stationary photon field,
interpreted as the angular momentum ground state of the vacuum, provides the medium through which
gravitational and electromagnetic interactions propagate.
Key predictions with observational agreement include: the fine structure constant α = 1/137.074 (0.028%
agreement); cosmological matter fraction Ωm = 0.3152 (0.07%); MOND acceleration a0 = cH0/6 (1.7%);
Hubble tension ratio H0,local/H0,CMB = 12/11 (exact); spectral index ns = 0.9646 (0.07 σ); baryon-to-photon
ratio η = 6.05 × 10−10 (0.8%); flat galactic rotation curves without dark matter; the Bekenstein–Hawking
entropy factor 1/4; exactly three fermion generations; the Bell/CHSH parameter at the Tsirelson bound;
and a minimum black hole mass Mmin = 2.39 M⊕ as a novel testable prediction.
The framework resolves the Hubble tension through equilibration-selected degrees of freedom, produces
flat rotation curves from photon field dynamics, and replaces inflationary fine-tuning with a primordial
sphere model yielding geometric flatness, causal horizon unity, and CMB uniformity from first principles.
We specify eight explicit numerical falsification criteria with exact thresholds beyond which the framework
would be definitively refuted. All 32 quantitative predictions are derived, not fitted, and experimentally
accessible.