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Continuous Subsystem Decoherence and Deterministic Outcome Selection in Quantum Measurement

Mario Martinez Correas

Published Sep 15, 2026• 0 citations
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Abstract

[EXPLORATORY DRAFT NOTICE] This record corresponds to a preliminary draft/approach within the conceptual development of this project. The rigorous, revised, and definitive mathematical formulation derived from this research is published in the main work: The Epistemological Interference: Why Physics Cannot Solve Its Own Frontier Problems Available in its most recent version here: https://doi.org/10.5281/zenodo.22876515

DOI
10.5281/zenodo.22776686

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[EXPLORATORY DRAFT NOTICE] This record corresponds to a preliminary draft/approach within the conceptual development of this project. The rigorous, revised, and definitive mathematical formulation derived from this research is published in the main work: The Epistemological Interference: Why Physics Cannot Solve Its Own Frontier Problems Available in its most recent version here: https://doi.org/10.5281/zenodo.22876515
The question of how probabilistic systems select individual outcomes remains conceptually open in several areas of physics and complex systems theory. Standard decoherence models successfully describe the emergence of classical behavior from quantum systems, yet they generally treat the selection of specific outcomes as statistically neutral once the probabilistic structure is fixed. The present work is motivated by the possibility that probabilistic selection processes may, under certain conditions, exhibit weak forms of context dependence without requiring any violation of standard probabilistic laws. Rather than proposing a replacement for established physical theory, the paper explores whether minimal and formally controlled modifications of probabilistic weighting could provide a useful phenomenological framework for describing such effects. The approach is intentionally conservative in scope. Its purpose is not to claim evidence for new physics, but to investigate whether concepts such as context, structural compatibility, and informational coupling can be represented within a mathematically bounded probabilistic setting. This preprint proposes a minimal framework for modeling context-dependent selection in probabilistic systems. While standard decoherence theory explains the emergence of classical behavior from quantum systems, it does not specify whether the selection of individual outcomes is entirely neutral or may be weakly influenced by additional constraints. The present work explores the possibility that probabilistic state selection could exhibit small context-dependent biases without modifying the underlying probabilistic structure. To formalize this idea, the model introduces a resonance function that weakly reweights baseline transition probabilities in a controlled and non-disruptive manner. A dynamic extension is considered in which probabilities and resonance co-evolve through simple feedback, damping, and context-dependent source terms. Analytical considerations and numerical simulations indicate that such systems can produce small but systematic and bounded deviations from baseline distributions. Under certain conditions, these deviations may stabilize, leading to attractor-like behavior. The framework is intended as an exploratory and phenomenological model, not as a modification of established physical theory. Its purpose is to provide a formal setting for investigating whether context, information, and structural compatibility can be represented within probabilistic state selection. A possible connection to underlying physical processes was considered in earlier work (https://doi.org/10.5281/zenodo.17246478). In the present paper, however, this line of interpretation is not pursued further and remains speculative. Keywords: decoherence; probability dynamics; attractors; resonance; complex systems; information theory Version note:This version presents a revised and clarified formulation of the proposed framework. In particular, the formal structure has been made more explicit by refining key derivation steps, clarifying the role of the resonance term, and tightening the interpretation of the model within its intended scope. No fundamental change to the core idea has been introduced. The revision primarily sharpens the probabilistic formulation, reduces ambiguity in the definition of the resonance function, and makes the exploratory and phenomenological status of the model more explicit.
Abstract The measurement problem has long been a fundamental challenge in quantum mechanics. The mainstream decoherence theory attributes the transition from quantum superposition to classical determinacy to the entanglement between the system and its environment. However, this theory still leaves several foundational issues unresolved: decoherence can only eliminate observable interference fringes but cannot explain why a single measurement yields only one definite outcome; nor can it fully account for the phenomena observed in recent attosecond tunneling experiments. The author first published the temporal relativity hypothesis on the Zenodo preprint platform on June 20, 2026[4]. This theory proposes that quantum superposition is not an intrinsic property of microscopic particles, but rather an apparent effect arising from the relative relationship between the temporal sampling frequency of the detection system and the evolution frequency of the quantum object. When the detector's temporal resolution frequency far exceeds the characteristic evolution frequency of the microscopic particle, the interference fringes from wavefunction superposition gradually disappear, and continuous classical trajectories become observable. On July 11, 2026, the author systematically proposed the qualitative three-stage criterion of temporal relativity within the original preprint framework (also published on Zenodo[8]): when the sampling frequency , the system exhibits classical determinacy; when , the system resides in a critical transition state; when , the system manifests as a quantum superposition state. The precise threshold corresponding to this ratio requires calibration through subsequent continuous attosecond imaging experiments, establishing a natural collaborative pathway between theory and experiment. The attosecond scanning tunneling experiment published by the University of Regensburg on July 3, 2026[3], is in strong agreement with the independent theoretical predictions and the experimentally designed predictions presented in the above preprint (June 20). Furthermore, after the publication of the author's Zenodo preprint on July 11, 2026[8], it was found that the experimental results from the Weizmann Institute of Science group in early 2026[5] are also highly isomorphic with the three-stage evolution predicted by this hypothesis. This paper is an advanced revision building upon two previous versions published by the author on the Zenodo preprint platform: the initial temporal relativity hypothesis incorporating the concept of "consciousness" was proposed on June 20, 2026[4]; the July 11, 2026 version[8] removed the consciousness concept and established a purely physical "detector temporal resolution frequency" qualitative framework with the explicit three-stage model; this version fully inherits the qualitative three-stage model while adding a complete unified mathematical framework—built upon the three pillars of the time-dependent Schrödinger equation, time-domain sampling boundary conditions, and critical phase criteria—upgrading the theory from a qualitative hypothesis to a complete mathematical system capable of quantitative computation and experimental data fitting.