Paper T14: A Classical Derivation of the Born Rule from Angular Coherence Filtering Probability as Real-Valued Path Volume in a Rotational Lattice

This paper presents a classical, geometric derivation of the Born Rule—the rule inquantum mechanics that relates the probability of an outcome to the square of a wave-function’s amplitude. In Holosphere Theory, particles such as electrons are modelednot as probability waves, but as angular phase structures moving through a rotatinglattice of discrete, gyroscope-like units called Holospheres. These angular paths mustpreserve rotational continuity in order to propagate, and most mathematically possiblepaths are filtered out by this structural constraint. The paths that remain determinewhich outcomes are physically possible. We show that the probability of a measurementoutcome is proportional to the number of angular phase paths that survive filteringand end in that outcome. This leads to a natural volume-based formula for proba-bility in real angular space. We then show that this is mathematically equivalent tothe standard Born Rule, but derived entirely from classical mechanics. No complexwavefunctions, randomness, or collapse assumptions are needed. Quantum probabilityemerges from geometry alone.