Quantum Statistics from Oscillatory Sampling: A Detection-Theoretic Derivation of the Born Rule

Abstract We derive the Born rule and quantum interference from an oscillatory field model using standard signal processing and detection theory. Physical particles are modeled as coherent patterns in an underlying oscillatory field, with measurement formalized as finite-window demodulation followed by threshold detection in noise. Key Results Born rule derived: Detection probability P ∝ |Ψ|² emerges as leading-order term in Taylor expansion Falsifiable predictions: Higher-order corrections O(|Ψ|&sup4;) provide testable deviations from standard QM Interference automatic: Arises from superposition of same-frequency components without additional postulates Uncertainty = aliasing: Heisenberg uncertainty relations are equivalent to the Gabor limit from signal processing Schrödinger from Klein-Gordon: Schrödinger equation emerges as non-relativistic envelope dynamics Scope Single-system detection statistics only. Multi-particle entanglement and Bell inequality violations require additional theoretical structure not claimed here. Links ASCRI: systems.ac/4/DP-2504 Research Lab: Dissensus AI Version update (February 2026): Expanded literature review with additional citations and substantive engagement with recent scholarship. v1.1.0 (2026-07-11): §9.2 sinc-law direction corrected; Simulation I/II compute totals stated; scope-disclosure items closed; working-paper number DAI-2517.