P-Adic Probability Theory and the Born Rule: Deriving Quantum Measurement from Ultrametric Information Geometry

QNFO Research Collective, Rowan Brad Quni-Gudzinas

Published Jul 12, 2026• 0 citations

Abstract

We derive the Born rule from p-adic probability theory, showing that quantum measurement probabilities emerge as ultrametric distance functions on the Bruhat-Tits tree. The squaring operation |ψ|² reflects the squared distance in p-adic metric, and Gleason's theorem acquires a geometric interpretation as the homogeneity of ultrametric balls. Companion to RTAQ v0.2.

DOI: 10.5281/zenodo.21327207

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