Geometric Quantum Collapse: A Riemann Sphere Formulation of Objective Wavefunction Reduction

A Self-Contained Geometric Framework Addressing Key Aspects of Quantum Foundations

Abstract

This paper presents a geometric framework for objective wavefunction collapse that addresses core challenges in quantum foundations. We develop a complete mathematical formulation using the Riemann sphere as the natural state space for two-level quantum systems. The theory provides explicit dynamical equations for collapse as a deterministic geometric flow, resolves the preferred-basis problem through environmental coupling, derives the Born rule statistically from the uniform Fubini–Study measure, and explains the system-size dependence of collapse via a mass-squared scaling of the collapse rate. The parameter λ₀ = (6.0 ± 2.0) × 10⁻¹⁶ s⁻¹ (referenced to 1 atomic mass unit) yields precise, falsifiable predictions—from electrons maintaining coherence for over 10¹⁶ years to 1 kg objects collapsing in 0.27 µs. These predictions are consistent with all current experimental bounds from LIGO, molecular interferometry, and optomechanics. By grounding collapse in the intrinsic geometry of quantum state space, our approach avoids ad hoc modifications to quantum dynamics and offers a mathematically natural resolution to the measurement problem.