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

Luis Ratia

Published Apr 10, 2026• 0 citations
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Abstract

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 ($A_{c}\sim\hbar$). 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.

DOI
10.5281/zenodo.19496913

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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.
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.
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.
We present a unified formulation of the Ratia Postulate for wave function collapse, integrating twosuccessive theoretical frameworks developed by the author. In the first formulation (Ratia, 2026a),collapse was governed by a critical energy threshold E exchanged between a quantum system S ₙand a measurement apparatus M. Analysis of that model revealed that E lacked a natural ₙfundamental anchor. This limitation motivated a conceptual refinement: the second formulation(Ratia, 2026b) replaces E with a critical ₙ action threshold A ≈ , directly grounding the collapse ₙ ℏcondition in the fundamental quantum of action. The present work demonstrates that the energyformulation is recovered as a special case of the action formulation in the limit of constantinteraction Hamiltonian, establishes the causal chain energy → action → collapse, and integratesthe numerical simulation results (DOI: 10.5281/zenodo.19371738) confirming a sigmoidal visibilitydecay. Three independent estimates of the corresponding energy scale are preserved asexperimental predictions. The model is compared with decoherence theory, GRW spontaneouscollapse, and the Diósi–Penrose gravitational framework.
This paper proposes a speculative framework for a quantum collapse threshold based onirreversible action. Once the cumulative environmental action crosses a universal threshold:S = (e x h), quantum superpositions irreversibly transition into classical outcomes. This collapse threshold is motivated by thermodynamic principles: Euler’s number e describes the natural scale of irreversible entropy growth, and Planck’s constant h sets the fundamental quantum of action. This theory aims to prompt further discussion on the informational and thermodynamic underpinnings of quantum measurement. I derive a novel parameter-free and falsifiable law for quantum state reduction, which both predicts the Page curve and preserves the Born rule. This model provides a unified, testable framework connecting quantum measurement, thermodynamics, and information theory.
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.