This project presents a conceptual and mathematical investigation into the relationship between uncertainty, distinguishability, and the ontological persistence of physical variables. Rather than treating uncertainty as a mechanism that alters or destroys underlying system states, the work develops a formal framework in which uncertainty acts as an obscuring layer that limits epistemic access while leaving fundamental structure intact. Using tools from information theory, stochastic dynamics, and quantum state evolution, the study introduces a Persistence Criterion that distinguishes between genuine ontological change and mere loss of distinguishability. The framework is applied across classical noise models, feedback-controlled systems, and quantum decoherence processes to demonstrate that contraction of information measures does not imply elimination of underlying states. The project aims to clarify common interpretational confusions in physics and complex systems, particularly in contexts involving strong noise, coarse-graining, and measurement limits. It is intended as a foundations-oriented contribution, with relevance to physical modeling, control theory, and the philosophy of uncertainty.
This project presents a conceptual and mathematical investigation into the relationship between uncertainty, distinguishability, and the ontological persistence of physical variables. Rather than treating uncertainty as a mechanism that alters or destroys underlying system states, the work develops a formal framework in which uncertainty acts as an obscuring layer that limits epistemic access while leaving fundamental structure intact. Using tools from information theory, stochastic dynamics, and quantum state evolution, the study introduces a Persistence Criterion that distinguishes between genuine ontological change and mere loss of distinguishability. The framework is applied across classical noise models, feedback-controlled systems, and quantum decoherence processes to demonstrate that contraction of information measures does not imply elimination of underlying states. The project aims to clarify common interpretational confusions in physics and complex systems, particularly in contexts involving strong noise, coarse-graining, and measurement limits. It is intended as a foundations-oriented contribution, with relevance to physical modeling, control theory, and the philosophy of uncertainty.
This preprint introduces the Persistence Criterion (PC), a conceptual and mathematical framework for distinguishing epistemic obscuration from ontological elimination in physical theories. The central claim is that uncertainty, noise, decoherence, or coarse-graining reduce empirical distinguishability of states or observables without implying that the underlying theoretical structures cease to exist. The framework is developed across classical estimation theory, stochastic dynamical systems, and quantum theory. In the classical domain, noisy observation models and information-theoretic metrics are used to show how distinguishability contracts while state variables persist, consistent with standard treatments in estimation theory and statistical physics (e.g., Fisher information and Bayesian filtering). For dynamical systems, stochastic differential equations and Fokker–Planck dynamics illustrate how deterministic generators remain structurally present despite diffusion-dominated behavior, aligning with established results in open-system dynamics and control theory. In the quantum domain, the Persistence Criterion is formulated using density operators, completely positive trace-preserving (CPTP) maps, and the algebraic (C*-algebraic) formulation of quantum mechanics. Decoherence is treated as an obscuring process acting on states via CPTP channels, while the underlying observable algebra remains invariant. This formulation draws on standard results from quantum information theory and algebraic quantum mechanics, emphasizing that loss of coherence or distinguishability does not entail annihilation of observables or dynamical structure (Holevo, 2011; Nielsen & Chuang, 2010; Breuer & Petruccione, 2002). The Persistence Criterion is interpretation-neutral and consistent with quantum no-go theorems, including Bell, Kochen–Specker, and PBR-type results, as it makes no assumption of value definiteness or hidden variables. Instead, it functions as a criterion of ontological coherence, identifying and excluding a specific interpretational error: the conflation of indistinguishability with non-existence. The work is aligned with non-eliminative structural realism and contemporary discussions of decoherence and ontology in quantum foundations (Ladyman & Ross, 2007; Wallace, 2012; Ruetsche, 2018). No new physical dynamics or empirical predictions are proposed. The contribution is conceptual and formal: clarifying how existing mathematical frameworks already encode persistence under uncertainty, and providing a principled interpretational constraint applicable across classical and quantum theories.
A recurring interpretive move in quantum physics treats the loss of observational distinguishability as equivalent to the loss of ontological structure. In this paper, I show that the formal structure of the theory does not support that move. I prove the Structural Persistence Theorem, which identifies precisely which algebraic invariants survive arbitrary completely positive trace-preserving (CPTP) maps. The invariants form a natural and complete set: the C*-algebra of observables A = B(H), its norm, commutation relations, and positivity structure. No CPTP process removes any observable from the algebra. State-space distinguishability contracts; algebraic structure does not. This partition — preserved structure versus contracted epistemic access — is the core formal result of the paper. I identify and formally diagnose a specific class of ontological overclaiming in the decoherence literature: instances where pointer-basis selection and suppression of off-diagonal density matrix elements are treated as eliminative of superposition. I show exactly where these inferences overreach the formalism and provide corrected formulations. I then demonstrate that this criterion places formal constraints on how the major quantum interpretations can consistently attribute ontological change. Many-Worlds and pilot-wave theory are fully consistent with the criterion. Copenhagen's physical-collapse reading carries an unspecified mechanism burden. GRW and CSL objective collapse models are PC-violating by deliberate design — which the framework clarifies rather than criticizes. Any empirical confirmation of GRW/CSL predictions would constitute direct evidence for PC-violation in nature. Two practical applications are discussed. In quantum error correction, the success of the fault-tolerance threshold theorem is indirect empirical evidence for the Persistence Criterion: decoherence degrades distinguishability but leaves the algebraic structure intact, which is precisely what makes error recovery possible. In effective field theory, the persistence of UV degrees of freedom under coarse-graining is consistent with the same structural partition. This work proposes no new experimental predictions. It clarifies what the existing formalism entails and does not entail — drawing a sharp, formal boundary between what the mathematics licenses and what must be supplied by interpretation.
his paper proposes persistence under stochastic interaction as a unifying physical constraint across quantum, gravitational, and macroscopic regimes. Rather than treating noise as a nuisance or generative force, it is framed as a universal selector that eliminates informational structures incapable of maintaining coherence under compression. Across quantum decoherence, gravitational coarse-graining, renormalization, and entropy production, stable laws emerge not through optimization or design, but through selective survival. Structures that persist do so because they tolerate loss, averaging, and repeated perturbation; those that cannot are eliminated. Physical law is therefore interpreted as residue rather than prescription. The framework formalizes persistence as an informational viability condition, independent of substrate or ontology, and integrates results from decoherence theory, renormalization group flow, and gravitational thermodynamics. It predicts abrupt regime transitions, scaling cliffs, hysteresis, and lawful failure modes rather than smooth unification. This work extends the Living Information Theory (LIT) program by positioning persistence as a primitive constraint shaping which physical regularities can exist at all.
This work is substantial because it does not merely reinterpret existing theories, but identifies a single physical principle that operates across domains that are usually treated as separate. Instead of introducing new particles, forces, or purely mathematical constructs, it focuses on a concrete mechanism: the accessibility of physical state transitions. At its core, the framework defines time not as a background parameter, but as the rate at which a system can undergo real, admissible changes. This leads to the Ikaezian accessibility factor, which measures how much of the universe’s total evolution a system can actually participate in. In this view, familiar effects such as time dilation are no longer abstract geometric consequences—they arise because constraints reduce the number of transitions a system can physically realize. The same principle extends naturally into quantum theory. Rather than treating all mathematically possible histories as equally viable, the framework introduces accessibility as a filter that determines which histories can contribute to reality. This provides a consistent way to interpret quantum behavior while also addressing issues such as divergences and unphysical configurations. What makes the work particularly significant is that it places both quantum mechanics and relativity within a shared structure. Kinematic effects, gravitational effects, and quantum selection are not treated as fundamentally different phenomena, but as different expressions of a single constraint: the limitation of accessible transitions. In this sense, the work does not attempt a unification through additional complexity, but through a reduction to a common mechanism. Finally, the framework is not purely philosophical. It leads to concrete constraints on physical behavior and suggests directions for empirical investigation, particularly in regimes where accessibility is strongly limited. Its contribution lies in reorganizing established results under a unified ontology, while preserving their empirical validity and clarifying their underlying cause.
This registration documents a completed theoretical study in fundamental physics and statistical mechanics. The work introduces a universal, model-independent stability criterion for the applicability of object-based descriptions in physical theories. Objecthood is treated not as an ontological primitive, but as an operationally defined regime characterized by (i) a separation of characteristic timescales and (ii) the capacity to support persistent internal records under coarse-grained observation. A dimensionless stability parameter is defined as the ratio between the exit time from a coarse-grained state and the intrinsic relaxation time of the system. The central result is the identification of a sharp threshold below which identity-based language (localization, persistence, re-identification) becomes physically uncontrolled, independently of microscopic dynamics. The registration serves to time-stamp and formally fix the theoretical formulation, definitions, assumptions, and conclusions presented in the associated preprint. No data collection, experimental intervention, or hypothesis testing is planned. The results are normative rather than predictive: they do not modify equations of motion but constrain the domain of physical validity of object-based descriptions across classical, quantum, and relativistic regimes. This registration is intended to establish priority and transparency for a foundational theoretical contribution at the interface of statistical mechanics, quantum foundations, and information theory.