This paper examines information stability and collapse across physical scales within the Representational Sufficiency Principle (RSP) framework established in "On the Foundations of Informational Physics" (Kozyra, 2026, Zenodo DOI: 10.5281/zenodo.17783127). I propose that collapse occurs when the minimal algorithmic description length of a state exceeds the maximal representational capacity of the bulk geometry. The criterion is K(ψ) > SBek, where K(ψ) denotes Kolmogorov complexity and SBek = Ac3/4Gℏ represents the holographic entropy bound. This renders collapse geometry-dependent, scale-dependent, and observer-independent. The framework preserves global unitarity through complexity redistribution and requires no modification to quantum mechanics. Three testable predictions follow: (1) calculable mesoscopic thresholds where coherence vanishes independent of environmental decoherence, (2) geometry-dependent collapse rates varying with gravitational potential, and (3) no requirement for non-unitary dynamics. The collapse threshold can be approached not only through particle mass but through controlled entanglement with auxiliary photonic degrees of freedom. This protocol may enable near-term experimental testing using levitated nanoparticles coupled to high-Q microwave cavities, with a calculable prediction for the critical photon number at which interference visibility should decrease independent of environmental decoherence. The criterion applies across scales: protein folding exhibits one-dimensional sequence information projecting onto three-dimensional geometry under configurational constraints; quantum measurement shows superposition collapse when representational capacity saturates; cosmological cycles preserve structural ordering through minimal encoding. The common mechanism is geometric constraint on representational capacity. A probabilistic analysis further demonstrates that life emergence under unbiased initial conditions is effectively impossible in a single cycle, and that cyclic informational heredity is structurally necessary to render it non-negligible — converting the classical improbability argument for design into an affirmative case for cosmic heredity. The framework connects measurement to established bounds from holographic entropy and algorithmic information theory. A unified variational derivation of these results alongside the Einstein field equations is developed in the companion paper "On the Unification of Informational Physics" (Kozyra, 2026, Zenodo DOI: 10.5281/zenodo.18666908).
This paper examines information stability and collapse across physical scales within the Representational Sufficiency Principle (RSP) framework established in "On the Foundations of Informational Physics" (Kozyra, 2026, Zenodo DOI: 10.5281/zenodo.17783127). I propose that collapse occurs when the minimal algorithmic description length of a state exceeds the maximal representational capacity of the bulk geometry. The criterion is K(ψ) > SBek, where K(ψ) denotes Kolmogorov complexity and SBek = Ac3/4Gℏ represents the holographic entropy bound. This renders collapse geometry-dependent, scale-dependent, and observer-independent. The framework preserves global unitarity through complexity redistribution and requires no modification to quantum mechanics. Three testable predictions follow: (1) calculable mesoscopic thresholds where coherence vanishes independent of environmental decoherence, (2) geometry-dependent collapse rates varying with gravitational potential, and (3) no requirement for non-unitary dynamics. The collapse threshold can be approached not only through particle mass but through controlled entanglement with auxiliary photonic degrees of freedom. This protocol may enable near-term experimental testing using levitated nanoparticles coupled to high-Q microwave cavities, with a calculable prediction for the critical photon number at which interference visibility should decrease independent of environmental decoherence. The criterion applies across scales: protein folding exhibits one-dimensional sequence information projecting onto three-dimensional geometry under configurational constraints; quantum measurement shows superposition collapse when representational capacity saturates; cosmological cycles preserve structural ordering through minimal encoding. The common mechanism is geometric constraint on representational capacity. A probabilistic analysis further demonstrates that life emergence under unbiased initial conditions is effectively impossible in a single cycle, and that cyclic informational heredity is structurally necessary to render it non-negligible — converting the classical improbability argument for design into an affirmative case for cosmic heredity. The framework connects measurement to established bounds from holographic entropy and algorithmic information theory. A unified variational derivation of these results alongside the Einstein field equations is developed in the companion paper "On the Unification of Informational Physics" (Kozyra, 2026, Zenodo DOI: 10.5281/zenodo.18666908).
Building on the frameworks established in On the Physical Consequences of Distinguishability and On the Stability and Collapse of Physical Information, this paper derives quantum state collapse and Einstein field equations from a single variational principle incorporating a holographic information constraint. Following Jacobson’s thermodynamic approach to gravity, I propose that representational capacity — quantified by the Bekenstein bound — constrains both geometric and quantum dynamics. The constraint is formalized using Kolmogorov complexity: quantum states satisfy K(ψ) ≤ Imax(g), where K(ψ) denotes the minimal algorithmic description length. Varying a total action under this constraint yields Einstein equations with an additional stress-energy contribution from information overflow, and a modified Schrödinger equation with a collapse term proportional to excess complexity. The collapse rate emerges as Γ = (c/R) · max(0, K(ψ) − Imax)/Imax, containing no free parameters. This framework suggests quantum collapse and gravitational curvature represent complementary responses to holographic saturation: energy excess induces curvature, information excess induces collapse. The approach makes testable predictions for interference visibility decay as a function of entanglement depth, distinguishable from existing objective collapse models.
The quantum Zeno effect (QZE) predicts that frequent measurement of an unstable quantum system suppresses its decay by repeatedly collapsing the wavefunction back to the undecayed state. However, experimentally confirmed results show that the QZE is fundamentally unattainable for radioactive or radiative decay, because the measurement rates required would destroy the system. We identify a distinct but phenomenologically analogous mechanism within the Stochastic Rupture (SR) framework: informational isolation. In SR, collapse occurs when the local von Neumann entropy approaches the Bousso-bounded informational capacity, SvN → η IBousso. A system that is informationally isolated from its environment — such as a single atom in vacuum, or a system inside a Casimir cavity with suppressed vacuum modes — has a reduced local saturation fraction I, and therefore a suppressed collapse rate. This is decay suppression without measurement, without observer, and without the destructive back-action that kills the standard QZE for radioactive systems. Unlike CSL and Diósi–Penrose, which predict measurable heating of diffuse cosmological matter at rates incompatible with Lyman-α forest and CMB temperature constraints, the SR mechanism is structurally silent in low-saturation environments: the collapse rate vanishes identically when I ≪ 1, independently of particle number or system mass. Informational isolation is thus not merely an analogue of the quantum Zeno effect — it is the same threshold geometry that resolves the cosmological heating problem of competing collapse models, and constitutes a necessary condition for any objective collapse theory to survive cosmological scrutiny. We derive the SR prediction for the suppression factor as a function of environmental mode density and identify two distinct regimes. In the low-saturation regime (I ≪ 1) accessible to current cavity QED, SR reduces exactly to Purcell physics and is not experimentally distinguishable from standard quantum optics. The genuinely SR-specific signature emerges only in the high-saturation regime (I → η), where the runaway factor (1 − I/η)−1 amplifies environmental modulation nonlinearly. This regime is accessible only at macroscopic mass scales (~109 –1010 amu, the MAQRO regime), where the SR discriminator combines with the σ x −2 scaling signature distinguishing SR from CSL and DP. The Casimir-cavity proposal is therefore reframed as a conceptual benchmark rather than a near-term experiment.
The Quantum Measurement Problem — the absence of any physical mechanism by which deterministic, unitary Schrödinger evolution transitions into a discrete, probabilistic classical outcome — remains the central open problem in the foundations of quantum mechanics. While environmental decoherence explains the suppression of quantum interference, it does not explain why or when a single outcome is realized. This paper resolves the measurement problem within the Algorithmic Theory of Reality (ATR). By treating the universe as a finite-bandwidth information-processing architecture, we demonstrate that wavefunction collapse is not a mystical observer effect, but a mandatory thermodynamic memory-management protocol. Key Results: The Collapse Threshold: We prove that when a microscopic superposition entangles with a macroscopic apparatus, the entanglement entropy grows until the local Bennett-Landauer processing cost exceeds the local holographic energy budget. This forces a non-unitary state truncation. Quantitative Timescale: The derived threshold yields a quantitative collapse timescale (τc) that mathematically matches the experimentally observed decoherence time. Derivation of the Born Rule: Given pointer-state orthogonality (from decoherence), we rigorously derive the Born Rule (pi = |ci|2) by formulating the forced state truncation as a constrained thermodynamic optimization problem that minimizes the Kullback-Leibler divergence (algorithmic information loss). Scale Unification: The exact same Bennett-Landauer limit that dictates the macroscopic boundaries of the universe (Dark Energy) and galaxies (the MOND scale) is shown to govern the microscopic limits of quantum coherence. The ATR framework mathematically determines when collapse must occur, with what statistics, and in which basis, reducing the single-outcome problem to a single, structurally necessary axiom (the Lüders update). Supplementary Material: The algebraic derivation of the Born Rule (via KL-divergence minimization and Lagrange multipliers), the exponential growth of entanglement entropy, and Monte Carlo statistical validations are independently reproducible via the companion computational verification script, available at: https://github.com/srdrymn/atr-verify-wavefunction-collapse
Collapse, Selection, and the Geometry of Information A Variational and Schrödinger Bridge Foundation for Quantum Measurement Quantum theory explains the evolution of possibilities with extraordinary precision, yet the emergence of definite outcomes remains conceptually unresolved. Why does one outcome appear rather than another? Decoherence explains the suppression of interference and the emergence of preferred bases, but not the mechanism by which multiplicity gives way to singularity. Collapse models introduce stochastic modifications of dynamics, yet the structural principle governing outcome selection remains obscure. Collapse, Selection, and the Geometry of Information proposes a new framework for approaching this longstanding problem. Drawing upon Schrödinger bridge theory, entropy-regularized optimal transport, concentration inequalities, and threshold phenomena in high-dimensional probability, the book develops a variational account of measurement in which selection emerges through constrained probabilistic evolution rather than through ad hoc dynamical interruption. At the center of the argument lies a simple but far-reaching shift in perspective: the measurement problem is reframed not primarily as a problem of collapse, but as a problem of selection. Within this framework, admissible measurement outcomes are represented as endpoint distributions connected by entropy-minimizing stochastic bridges. In the small-noise regime, concentration phenomena and large-deviation structure produce exponential stabilization of particular channels, yielding effective outcome definiteness without modification of unitary quantum evolution. The book integrates ideas from quantum foundations, stochastic processes, optimal transport, and information geometry into a unified conceptual architecture. Along the way, it explores the relation between decoherence and variational structure, the geometry of path space, threshold mechanisms in probabilistic systems, and the emergence of macroscopic stability from high-dimensional stochastic dynamics. Neither purely technical textbook nor purely philosophical meditation, this work occupies a rare middle ground: mathematically informed, conceptually ambitious, and written in continuous narrative prose accessible to advanced readers in physics, mathematics, and philosophy of science. Ultimately, the book argues that the transition from possibility to actuality may be inseparable from the geometry of probability itself.
Description This work proposes an information-theoretic framework for describing the quantum–classical transition during cosmological inflation through open quantum system dynamics and entanglement evolution. The study introduces a normalized Quantum Persistence Function (QPF) as a scale-invariant diagnostic measure of residual quantum coherence, formulated in representation-independent form using reduced density matrix purity and entropy growth. The framework connects microscopic decoherence processes with macroscopic cosmological observables by applying spin–boson open-system dynamics to inflationary perturbations. Classical emergence is interpreted as a dynamical suppression of quantum coherence driven by entanglement entropy growth between cosmological modes rather than by simple interference cancellation. Observational constraints from primordial Gaussianity bounds are used to derive an efficiency condition for decoherence during reheating, expressed as a lower bound on the decoherence functional. The results show that classicalization occurs well below holographic entropy saturation limits, suggesting that cosmological classical emergence is governed primarily by dynamical information redistribution rather than fundamental information capacity thresholds. This work is deposited on Zenodo as an open scientific preprint to encourage constructive discussion and feedback from the scientific community. KEYWORDS: Quantum classical transition; decoherence theory; inflationary cosmology; open quantum systems; entanglement entropy; cosmological perturbations; quantum persistence function; information theory in physics; primordial fluctuations; classical emergence dynamics
Version: v1.0 DESCRIPTION: We introduce Coherence Field Dynamics (CFD), a theoretical framework that extends holographic quantum gravity by promoting quantum coherence — the off-diagonal density matrix elements — to an independent geometric degree of freedom. While standard holographic frameworks (AdS/CFT, Ryu-Takayanagi) encode bulk geometry through entanglement entropy alone, CFD posits that coherence parameterizes effective bulk depth, complementary to entanglement's encoding of connectivity. The coherence field φ(p,γ) satisfies a wave equation in information-geometric parameter space, generating a Lorentzian metric that degenerates at a critical decoherence threshold γ_c. The framework predicts the existence of such a threshold from geometric stability analysis; its specific numerical value is system-dependent. Connections are established between information geometry, MERA tensor networks, and holographic entropy. The variational principle coupling coherence to an effective gravitational action is presented as an analogue gravity model (c and G are effective parameters), not a claim about physical 4D spacetime. Key results: Theoretical framework: coherence field equation, information-geometric metric, variational principle, and five testable predictionsCompanion experimental work demonstrates a fidelity threshold at γ ≈ 0.535 on IonQ Forte-1 (F = 0.988 baseline, collapse to F ≈ 0 under dephasing) and consistency with the dephasing response on Pasqal FRESNEL_CAN1 QPU (noise ratio 1.13×). These results are consistent with CFD's predicted critical behavior, though they do not uniquely distinguish CFD from standard noise models. The specific threshold value (0.535) is determined by the experimental circuit geometry, not derived from CFD aloneFour predictions remain open and experimentally accessible on current NISQ hardware: coherence-depth complementarity, MERA-decoherence correspondence, coherence-modulated entropy scaling, and hardware demonstration of non-trivial reversibilityThis paper presents the theoretical framework. The detailed experimental protocols and hardware data are reported in the companion publication "Cross-Platform Noise Thresholds in Quantum Teleportation: Trapped-Ion and Neutral-Atom Architectures" (see Related Identifiers).