The Minimum Causal Structure For Quantum Interference

This paper identifies the Causal Square - a 2×2 four-history causal structure - as the fundamental topological building block for quantum interference. The author demonstrates that the Born Rule (P = |ψ|²) is not an external postulate but emerges as the unique consistent probability measure required by the structural geometry of this causal grid. Key highlights of this work include: Structural Derivation of Probability: A proof showing how the interference pattern is a direct consequence of the four-history requirement at every spacetime event. Resolution of Quantum Paradoxes: The framework provides a novel, strictly causal resolution to Wheeler’s delayed-choice experiment, treating the observer's choice as a selection within a pre-existing, coherent Causal Square. Dissolution of the Boltzmann Brain: By enforcing geometric coherence, the model structurally excludes incoherent history combinations, effectively resolving the Boltzmann Brain paradox at the foundational level. Theoretical Integration: The Causal Square is mapped against established frameworks, including Zurek’s envariance, Hardy’s axioms, and Aharonov’s Two-State Vector Formalism (TSVF). This paper serves as the foundational quantum pillar of the R.O.S.T. (Recursive Overlapping State-Time) framework. Copyright © 2026 Nicolò Figus Diaz. Licensed under Creative Commons Attribution Share Alike 4.0 International (CC BY-SA 4.0).