Fractal Resonance Collapse: Guided Wavefunction Collapse via Resonant Attractors

This paper advances the Fractal Resonance Collapse (FRC) framework, building on foundational concepts from Fractal Resonance Cognition (FRC 100.001) and its application to quantum chaos (FRC 100.002). We propose that quantum wavefunction collapse follows structured, non-random pathways guided by resonant attractor states in phase space, challenging the purely probabilistic outcomes of conventional quantum mechanics. By extending the Schrödinger equation with fractal resonance perturbations, we preserve quantum chaotic properties while enabling deterministic collapse trajectories. Numerical simulations using random matrix theory reveal eigenvalue spacing distributions that maintain level repulsion—a hallmark of quantum chaos—while exhibiting a controlled structure, with a slight Poisson-like shift due to resonance strength (σ = 0.1). Phase space simulations identify vortex attractors with a fractal dimension D = 1.94 ± 0.05, consistent with prior quantum chaos findings (D ≈ 1.90 ± 0.02) and distinct from unperturbed systems (D ≈ 1.2) and Feynman's fractal paths (D = 2). We propose experimental validation using Laguerre-Gaussian (LG) optical vortex beams, leveraging their applications in gravitational wave detection and quantum information processing. This work offers a potential resolution to the measurement problem by demonstrating how deterministic patterns emerge from quantum processes, bridging quantum foundations and experimental physics.