Double-Slit Detection as Physics: A Detector-Coupled Schrödinger Model in R-Theory

This paper presents a detector-coupled interpretation of the Schrödinger equation within R-Theory (Resonance Theory), reframing quantum mechanics as the evolution of coherence in an underlying zero field rather than as the motion of fundamental particles. Instead of treating particles as primary entities whose positions are revealed by measurement, R-Theory models reality as coherent resonant modes. Particle-like events emerge only when coherence couples locally to a material environment, forming what are termed resonance knots. Detection is therefore not an abstract postulate but a physical conversion process. The work proposes a minimal extension of the standard non-relativistic Schrödinger equation by introducing a local knot-formation rate Γ(x), interpreted as a property of detector material and configuration. This leads to an “R-Schrödinger” equation in which coherence loss represents the conversion of extended coherence into localized detection events. The familiar Born rule |Ψ|² is correspondingly refined into an event statistics rule p_click(x,t) = Γ(x) |Ψ(x,t)|², making detector participation explicit. Key contributions of this paper include: A clear operational definition of the zero field as a coherence substrate A reinterpretation of the wavefunction as coherence amplitude rather than particle probability An explicit physical role for detectors in knot formation A continuity equation with a conversion (sink) term linking coherence flow to detection Experimentally testable implications emphasizing detector-dependent statistics in interference experiments Mathematically, the framework aligns with known open-system and dissipative approaches, but conceptually reverses the hierarchy: detector coupling is treated as the mechanism that produces particle-like events, not as an external add-on to an otherwise complete theory. This paper is part of the R-Theory Phase Series and is intended as a conservative bridge between standard quantum mechanics and a resonance-based, phase-first ontology, with direct relevance to double-slit experiments, detector physics, and foundational questions about measurement.