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Dynamics of Wave Packet Reduction via Ratia's Critical Action Threshold

Luis Ratia

Published Apr 4, 2026• 0 citations
Publisher

Abstract

This work proposes a physical mechanism for wave function collapse based on a critical action exchange threshold (A_c ≈ ħ). Unlike standard environmental decoherence models, this approach postulates a dynamic phase transition governed by the coupling energy g. Numerical simulations confirm a sigmoidal decay of interference visibility, providing a phenomenological basis for the measurement problem.

DOI
10.5281/zenodo.19417208

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This work proposes a physical mechanism for wave function collapse based on a critical action exchange threshold (A_c ≈ ħ). Unlike standard environmental decoherence models, this approach postulates a dynamic phase transition governed by the coupling energy g. Numerical simulations confirm a sigmoidal decay of interference visibility, providing a phenomenological basis for the measurement problem.
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We propose a phenomenological model for wave function collapse based on accumulated interaction action (AAA) between a quantum system and its environment. Collapse occurs when the action reaches a critical threshold of order ℏ\hbarℏ, producing a nonlinear sigmoidal transition in coherence. The framework extends open quantum system dynamics and predicts measurable deviations from standard exponential decoherence, such as a "logistic shoulder" in visibility curves. The model is testable in interferometric setups and provides a physically interpretable mechanism for quantum state reduction.
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∼ℏA_{c}\sim\hbarAc​∼ℏ). 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.
This work proposes a phenomenological extension to standard open quantum system dynamics in which the effective decoherence rate depends nonlinearly on the accumulated interaction action exchanged between a quantum system and its environment. Motivated by the hypothesis that quantum state reduction may involve a critical interaction scale of order Planck’s reduced constant, a threshold-activated decoherence ansatz is introduced that produces non-exponential suppression of coherence. Under finite-width stochastic broadening, the model yields sigmoidal-like transition behavior near the critical action scale. The framework is not presented as a fundamental derivation of wave function collapse, but rather as an exploratory phenomenological model intended to investigate whether threshold-based nonlinear decoherence may offer experimentally distinguishable predictions from conventional exponential decoherence. Analytical solutions, physical interpretation, and experimental implications are discussed.
Abstract: The transition from a quantum superposition to a definite classical state remains one of the foundational challenges in physics. We propose a dynamical, objective reduction model where wave function collapse is driven by the exchange and dissipation of energy (Δ�dis) between a quantum system and an observer/environment. Replacing the abstract notion of "measurement" with a physical dissipation threshold (Δ�dis⋅�collapse≥ℏ/2), we demonstrate that phase coherence decay is directly coupled to energy flux. The model is integrated with the Lindblad Master Equation and Stochastic Schrödinger Equations, incorporating Planck's quantum of action (�=ℎ�) as a discrete condition for state reduction. Numerical evaluations for an isolated electron and a C60 fullerene molecule confirm that the model naturally predicts macro-localization while preserving micro-scale quantum superposition, offering a thermodynamically consistent boundary for the quantum-classical transition.
This work proposes an objective collapse mechanism in which wave function reduction is triggered when the energy exchanged between a quantum system and a measurement apparatus exceeds a critical threshold Ec. The dynamics is described by an energy-dependent Lindblad master equation that preserves total energy while suppressing coherences above Ec. An interferometric test based on a Mach–Zehnder setup with tunable measurement strength is proposed, predicting a threshold-like loss of visibility. The critical energy can be related to a minimal mass change via E = mc^2, providing an operational link to Penrose–Diósi gravitational collapse scenarios.