Abstract

We propose a geometric reformulation of measurement in Hyperhamiltonian Quantum Mechanics (HHQM), replacing the inverse-distance propensity by a complex transition amplitude defined on the state manifold. The amplitude depends on geodesic distance and a phase functional associated with the hyper quantum bundle, leading to a normalized Born-type probability rule. In a minimal bipartite setting, we show that interference between a small number of transition channels can produce joint probability distributions with nonclassical correlations. In particular, a simple two channel model yields a cosine correlator and attains the Tsirelson bound while preserving no-signaling.

The resulting structure suggests that Bell-type correlations in HHQM, if realized, arise from interference of geometric transition amplitudes rather than from spacetime dynamics. The explicit kernel constructed here should be regarded as an effective realization within this framework; a full derivation from the underlying bundle geometry remains an open problem.