Reflective Holonomy as an Operational Interface Between General Relativity and Quantum Measurement

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Abstract

We develop a fully covariant, operational link between general relativity and quantum measurement based on reflective holonomy : the spatial rotation induced in an apparatus rest frame when its tetrad is transported around a spacetime loop and projected onto the stabilizer of the apparatus four-velocity. This rotation determines the realized measurement basis in interferometric and Bell-type experiments. Shot-to-shot fluctuations in reflective holonomy—arising from spacetime curvature, platform dynamics, or control jitter—produce random-unitary basis noise that suppresses Ramsey visibility and Bell–CHSH values when not recorded, yet is fully reversible through per-shot logging and inversion. The framework requires no modification of either general relativity or quantum mechanics and yields a falsifiable prediction: complete logging and inversion must restore quantum-limited performance, with any residual deviation signaling non-holonomic physics. From first principles we derive (i) the holonomy-to-quantum-channel map, (ii) its Lindblad limit characterized by a dephasing rate proportional to the variance growth of the holonomy, (iii) closed-form expressions for Ramsey and CHSH contrasts, and (iv) a minimal small-loop variance law linking curvature to basis noise. Analytical and numerical studies show that several longstanding experimental anomalies—including anomalously low CHSH values exhibiting the characteristic three-damped–one-stable correlator pattern, and Ramsey contrast losses exceeding intrinsic decoherence—are precisely accounted for by untracked holonomy fluctuations and vanish under inversion, while no-signalling and Tsirelson’s bound remain preserved. We formulate a one-parameter Operational Unification Test : determine the holonomy-noise parameter from Ramsey data, predict CHSH values with no additional parameters, and confirm full recovery after inversion. Irreducible residuals isolate physics that cannot be attributed to reflective holonomy.

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