Unified Relational Projection Dynamics (URPD): A Minimal Information-Theoretic Foundation for Quantum Probabilities, Temporal Flow, and Causality

A.I. Trinity Lab

Published Nov 24, 2025• 0 citations

Abstract

This work presents Unified Relational Projection Dynamics (URPD),a minimal and self-contained information-theoretic framework that reconstructsquantum probabilities, temporal flow, and causal structure from a singlegeometric principle. URPD replaces the traditional Hilbert-space formulation with arelational description of physical states as points in the complex projectivemanifold CPN−1CP^{N-1}CPN−1.Within this representation, the Fubini–Study geometry encodes both dynamicaltransitions and probabilistic structure without requiring the Born rule as anadditional axiom. In URPD, physical evolution corresponds to geodesic and quasi-geodesictransitions between relational frames, and the arrow of time arises from themonotonic increase of relational displacement.Classical spacetime and deterministic trajectories emerge naturally in themacroscopic limit as coherence within frame ensembles becomes sharply peaked. This article provides a compact reconstruction of the foundations of quantummechanics and causality from a unified geometric principle, offering a pathwaytoward a deeper relational understanding of physical law.

DOI: 10.5281/zenodo.17700100

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