Rotational Lorentz Contraction as the Geometric Origin of the Anomalous Magnetic Moment: A Structural Correspondence with the Muon Lifetime Problem (Structural Clarification Note)

47 Structural Clarification Note This paper demonstrates that the anomalous magnetic moment of the electron (ae) and the muon atmospheric lifetime extension are two manifestations of the same relativistic length-extension mechanism. The connection is made within the 0-Sphere Model of the electron, a geometric and thermodynamic framework developed continuously since 2018. — Core Result — Both phenomena are governed by a single identity of special relativity: ΔL = |γL − 1| · L0 In the muon case, v ≈ 0.9994c gives γL ≈ 29; the proper path length L0 ≈ 660 m is extended to ~19 km, allowing the muon to reach the ground. In the electron case, the internal orbital arc 2πr is contracted by the Lorentz factor of the Zitterbewegung velocity vZB ≈ 0.04c, and the fractional shortening is precisely ae. The velocity magnitude differs by a factor of ~25; the algebraic structure is identical. — Key Contributions — g = 2 from Thomas precession: Sinusoidal internal oscillation yields a double-angle angular velocity Ω ∝ sin(2ωt), geometrically necessitating g = 2 without any quantum-mechanical input. Geometric origin of ae: The deviation from g = 2 is identified with rotational Lorentz contraction of the internal orbital arc — the same mechanism underlying the Ehrenfest paradox (Einstein 1912). Inverse calculation: From the measured ae(exp), an RMS-corrected inverse formula yields vZB ≈ 0.04047c and confirms γL = 1 + ae. Open forward chain: Deriving vZB from Thomas precession independently of the measured ae remains the central open task; its completion would elevate the structural correspondence to a confirmed physical equivalence. Three occurrences of 1/2: The factor 1/2 in the Thomas angular velocity, the geometric centroid constraint, and the spin quantum number s = 1/2 as a topological invariant are identified as three expressions of the same underlying double-angle structure. — Relation to the 0-Sphere Model Series — This is a Structural Clarification Note (Paper #47 in the series). The inverse calculation yielding vZB ≈ 0.04c was originally introduced in: Paper #10 — Redefining Electron Spin and Anomalous Magnetic Moment Through Harmonic Oscillation and Lorentz Contraction (2023) — 10.5281/zenodo.17764997 The present paper makes the structural analogy with the muon lifetime experiment explicit and self-contained, adding no new theoretical claims beyond those in Paper #10. It includes a side-by-side comparison figure (TikZ) and a unified property table. The announced future work — a Berry-phase and fiber-bundle treatment of the dual-frame structure within which γL = 1 + ae appears as the bridge equation — builds on: Paper #38 — Electron Interference from Internal Geometry: Two-Kernel SU(2) Structure, Quartic Energy Flow, and an Intrinsic Visibility Limit (2026) — 10.5281/zenodo.18718174 — Primary References in This Work — # Title (abbreviated) DOI 1 A Model of an Electron Including Two Perfect Black Bodies 10.5281/zenodo.16759284 10 Redefining Electron Spin and AMM Through Harmonic Oscillation 10.5281/zenodo.17764997 13 Unified Spin Dynamics: From Pseudovector Nature to Relativistic Constraints 10.5281/zenodo.17765079 14 Bridging QM and GR: AMM and Geodetic Precession 10.5281/zenodo.17765097 15 Spin-Induced Inertial Resistance in Electrons 10.5281/zenodo.17765121 19 Spin as a Real Vector: Geometric Origin of U(1) and SU(2) Periodicity 10.5281/zenodo.17765238 — Series Context — The 0-Sphere Model is an ongoing research programme (2018–present) that derives spin, anomalous magnetic moment, Zitterbewegung, and emergent spacetime from the geometry and thermodynamics of a two-kernel electron model. All papers in the series are archived on Zenodo: Zenodo search: Hanamura, Satoshi