Gödel Holonomy and Aether Spin Fibers: Reinterpreting Closed Timelike Curves in Quantum Measurement Units

Gödel’s 1949 rotating-universe solution to Einstein’s field equations admits closed timelike curves (CTCs), typically interpreted as a purely geometric mechanism for “time travel” via spacetime loop closure. This paper develops a QMU-native Aether Physics Model (APM) reinterpretation that separates base-manifold closure in spacetime coordinates from physical recurrence of the full state. The full APM state is modeled as a fibered system\[\gamma(\tau)=\big(x^\mu(\tau),\Theta(\tau),\chi(\tau)\big),\]where $x^\mu$ is the spacetime trajectory, $\Theta$ is a chronophase acting as the frame index of the quantum movie (counting blocks of $F_q$-events), and $\chi$ is an internal Aether-unit spin-position (handedness) state. In this framework, a Gödel-type loop can close in $x^\mu$ while remaining non-recurrent in $(\Theta,\chi)$, dissolving backward-causation paradoxes by reclassifying CTCs as internal holonomy diagnostics rather than primitives of reverse time. A continuous $SU(2)$ transport is defined on the forward two-spin fiber $\mathcal{H}_{+}\cong\mathbb{C}^{2}$ with basis $\{|L_{+}\rangle,|R_{+}\rangle\}$. Matter is modeled as handed-localized (approximately confined to one of the two spin positions), while photons are modeled as bilateral excitations spanning both handed channels. Rotation enters only through the QMU-native dimensionless ratio\[\Omega_{\star}\equiv\frac{\Omega}{F_q},\]and the internal connection is fixed by a first-principles APM bridge: the fine-structure constant $\alpha$ is identified as the unique dimensionless conversion factor between the electrostatic charge quantum $e^{2}$ and the magnetic charge quantum ${e_\mathrm{emax}}^{2}$ via\[{e_\mathrm{emax}}^{2}=\frac{e^{2}}{8\pi\alpha}\qquad\Longleftrightarrow\qquad\alpha=\frac{e^{2}}{8\pi\,{e_\mathrm{emax}}^{2}}.\]With this identification, the handedness connection and holonomy are parameter-free at leading order, yielding an exact recurrence discriminator for handed-localized matter:\[\mathcal{H}(\Omega_{\star})^{N}=I\quad\Longleftrightarrow\quad\alpha\,\Omega_{\star}\,N=2k,\qquad k\in\mathbb{Z}.\]Thus, in a Gödel-type rotational environment, physical recurrence is quantized in discrete blocks of $F_q$-events, while photon-like states can persist under nontrivial holonomy because they are not handed-localized. The paper further presents a falsifiable four-spin extension $\mathcal{H}_{\mathrm{tot}}=\mathcal{H}_{+}\oplus\mathcal{H}_{-}$ (introducing a backward-sector fiber) and states explicit evidentiary requirements for any forward/back mixing. An appendix gives order-of-magnitude scaling for recurrence blocks under terrestrial rotation and engineered laboratory rotation environments, emphasizing a practical near-term test strategy: not to “wait for recurrence,” but to search for rotation-linked, loop-count-linked discrete structure in phase-sensitive observables consistent with the dimensionless control variable\[X\equiv \alpha\,\frac{\Omega}{F_q}\,N.\]The experimental objective is a falsifiable signature: data collapse and/or step-like structure versus $X$ (with special structure at $X=2k$), measurable with existing interferometric and precision-rotation platforms.