What the Fine‑Structure Constant Is: Theorem‑Content and Declared‑Anchor
Year: 2026
Type: preprint
Abstract: A century of attempts to derive the fine‑structure constant has produced numerology, anthropic reasoning, renormalisation‑group narratives, and asymptotic‑safety programmes, all competing on the question of how α is obtained. This paper argues that a logically prior question has been under‑investigated: what kind of object α is, such that some routes to it must fail. Inside an axiomatic geometric framework (ZQCM) whose remaining parameters are first‑principles outputs, a complete audit of the derivability of α was conducted under a pre‑registered protocol (Zhao, 2026b). The audit yields a composite answer. The numerical content of αskel−1=137.00132 is theorem‑content, carried by a proven spectral contact theorem. The selection of its anchor is declared, carried by a cross‑category bridge postulate. The underivability of the constant admits four layered characterisations — phenomenological, ontological, procedural, and structural — each with numbered criteria and a documented negative ledger. An enhancement line reconstructs a licensed version of the hadronic vacuum‑polarisation weight from the living axioms (not the lost appendix itself), and the structural layer identifies α as the unique dimensionless cross‑departmental quantity in the framework's output space. The paper closes with the framework's falsifiability structure, its relation to the century of explanations, and an honest ledger of its own outstanding tensions.
Author: Zhao, Qian
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212251968
Cites:
Cited by:
Related to: