Quantum Gravity and String Theory

    

A Geometric Model of Quantum—Like Behavior: Spin, Measurement, and Probabilities from Pure Spatial Geometry

Authors: Tomasz Kobierzycki

We present a minimal geometric framework in which several quantum—like phenom-ena arise without introducing Hilbert spaces, operators, or probabilistic postulates.The only fundamental structure is a spatial Riemannian manifold (Σ, hij ) on whichspin states, measurement axes, and multi—particle configurations are represented asvectors of equal norm. Probabilities and correlations emerge from purely geometricrelations between these vectors, most importantly from their angular separation.A single geometric expression reproduces both single—particle Born probabilitiesand the − cos θ EPR correlation, depending only on how two geometric directionsare interpreted. Entanglement is reinterpreted as a constraint identifying whichpairs of vectors must be compared, rather than as a tensor—product structure. Theresulting model is deterministic at the level of geometry but yields quantum—likeprobabilistic predictions through normalization and symmetry arguments.

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[v1] 2025-12-07 02:06:49

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