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

Luis Ratia

Published Apr 5, 2026• 0 citations

Abstract

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.

DOI: 10.5281/zenodo.19432288

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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.

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.

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.

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

A_{c}\sim\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.

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.

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.