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Energy-Action Threshold Model for Wave Function Collapse: A Nonlinear Dynamical Framework with Experimental Signatures.

Luis Ratia

Published Apr 11, 2026• 0 citations
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Abstract

We propose a phenomenological model for wave function collapse based on accumulated interaction action ($A$) between a quantum system and its environment. Collapse occurs when the action reaches a critical threshold of order $\hbar$, 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.

DOI
10.5281/zenodo.19522800

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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.
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.
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 (∆Edis) between a quantum system and an environment/apparatus. Replacing the abstract notion of "measurement" with a physical dissipation threshold (∆Edis · τcollapse ≥ ℏ/2), we demonstrate that phase coherence decay is directly coupled to environmental energy flux. The model is integrated with the Lindblad Master Equation and Stochastic Schrödinger Equations, incorporating Planck’s quantum of action (E = hν) as a discrete condition for state reduction. Numerical evaluations for an isolated electron, a fullerene (C60) molecule, and photoelectric emission confirm that the model naturally predicts macro-localization while preserving micro-scale quantum superposition, offering a thermodynamically consistent boundary for the quantum-classical transition.