Dynamics of Quantum State Reduction via Critical Interaction Action Threshold: A Threshold-Activated Collapse Framework

We propose a threshold-based physical framework for quantum state reduction in which wave function collapse occurs when the accumulated interaction action between a quantum system and a measurement environment exceeds a critical threshold of order Planck's reduced constant (Ac~). The model introduces a nonlinear collapse boundary governed by invariant accumulated interaction action, predicting a sigmoidal collapse law. We demonstrate compatibility with Born-rule statistics and show that the Diósi-Penrose gravitational collapse timescale emerges as a special case in the static gravitational Hamiltonian limit. The theory predicts experimentally distinguishable deviations from exponential decoherence.