Light Speed, Dimensional Breakthrough, and the Coupling Constant Hierarchy
SAE Physics Series — Four Forces Prequel

Writing Declaration: This paper was independently authored by Han Qin. All intellectual decisions, framework design, and editorial judgments were made by the author.

Abstract

Standard physics accepts the speed of light as an empirical constant and offers no structural explanation for the 34-order-of-magnitude gap between the electromagnetic and gravitational coupling constants. This paper derives both from SAE axioms.

The argument proceeds in three stages. First, the DD Breakthrough theorem: chaos (0DD) must develop (SAE axiom), creating distinction (1DD) and simultaneously defining c. Within each DD, the remainder develops until it reaches c, then breaks through to the next DD. Each breakthrough divides the remainder's potency by c. The characteristic quantity of (n+1)DD is E/c^n: energy E (1DD), momentum p = E/c (2DD), mass m = E/c² (3DD), and the pair-production parameter m/c = E/c³ (4DD, intelligible but not directly measurable). c is universal because all DDs share one spacetime, and finite because 4DD is only half of a dual structure.

Second, the DD Splitting theorem: a point (1DD) has no internal symmetry and cannot split. A line (2DD) embedded in higher-dimensional space has chirality — it can be wound left or right. Therefore 2DD splits symmetrically into left-handed and right-handed 3DD, which is the geometric origin of parity. Each 3DD has three spatial axes; each axis produces a dual 4DD (causality + reverse-causality) upon breakthrough. This yields 2 × 3 × 2 = 12 4DDs total. Our observable universe is one side of one dual pair within the left-handed 3DD.

Third, the Coupling Constant relation: the 12 4DDs span an internal Euclidean space R¹² with symmetry group SO(12) (66 generators). The 2DD splitting imparts a common phase to all dual-4DD planes; this SO(2) redundancy is quotiented out, yielding the coset space SO(12)/SO(2) of dimension 65. Normalized by the 4 spacetime dimensions, the internal complexity density is κ = 65/4 = 16.25. The postulate that κ determines the electromagnetic-gravitational coupling hierarchy predicts: α_G(M_Z) = α_em(M_Z)^{16.25}. Observation: |ln α_G(M_Z)| / |ln α_em(M_Z)| = 16.2572. Deviation: 0.044%, within experimental uncertainty.

Keywords: Self-as-an-End, speed of light, DD hierarchy, coupling constants, gauge symmetry, SO(12), gravitational coupling, electromagnetic coupling, DD Breakthrough theorem, DD Splitting theorem