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.
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.
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).
We propose a model in which proper time emerges from a finite local informationsampling capacity and wave-function collapse occurs when the informational content ofa quantum branch approaches the Bekenstein bound. Combining insights from entropicgravity, holographic entropy limits, and objective collapse models, we suggest that collapsecorresponds to stochastic pruning of branches approaching saturation of local informationcapacity. The collapse rate is derived from the gravitational self-energy of spatially separated branches, yielding a dimensionally consistent scaling relation with quadratic massdependence consistent with the Diósi–Penrose framework. The model predicts anomalousdecoherence in massive spatial superpositions and provides experimentally testable thresholds relevant to next-generation interferometers. This framework offers a unified perspectiverelating emergent time, collapse dynamics, and gravitational information boundsNote: Bekenstein bound proposed as suggestion of pruning trigger, not definitive mechanism. Other informational thresholds possible.
We propose a model in which proper time emerges from a finite local information samplingcapacity and wave-function collapse occurs when the informational content of a quantumbranch approaches the Bekenstein bound. Combining insights from entropic gravity, holographic entropy limits, and objective collapse models, we suggest that collapse correspondsto stochastic pruning of branches approaching saturation of local information capacity. Themodel predicts anomalous decoherence in massive spatial superpositions and provides experimentally testable thresholds relevant to next-generation interferometers. This frameworkoffers a unified perspective relating emergent time, collapse dynamics, and gravitationalinformation bounds.
This work presents an extended, mathematically complete formulation of the Information Geometry Unification Principle (IGUP), a foundational framework in which quantum mechanics, statistical thermodynamics, general relativity, and spacetime geometry emerge from a single information-theoretic ontology. We begin with rigorous axioms defining information as the primary physical substance, then systematically construct the Bures–Fisher–Rao metric on the manifold of quantum density matrices. We derive the universal information action functional and perform full variational derivations to obtain the unified field equations. We show explicitly how standard physical theories including the Schrödinger equation, Heisenberg picture, Liouville mechanics, classical thermodynamics, and Einstein field equations are recovered in appropriate limiting regimes. We further derive geometric expressions for entanglement, entropy, temperature, energy, and force. The theory resolves longstanding conceptual tensions between unitary quantum evolution and gravitational irreversibility, provides a natural resolution to the black hole information paradox, and yields eight concrete, experimentally testable predictions. This extended version includes full tensor calculus, covariant derivatives, curvature expansions, and limit theorems, amounting to a self-contained theory of everything based on Geometry=Information.
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).
We propose a model in which proper time emerges from a finite local information sampling rate and wavefunction collapse occurs when the informational contentof a quantum branch approaches the Bekenstein bound. Combining insights from entropic gravity, holographic entropy limits, and objective collapse models, we suggestthat collapse corresponds to stochastic pruning of branches approaching saturationof local information capacity. The model predicts anomalous decoherence in massivespatial superpositions and provides experimentally testable thresholds relevant to nextgeneration interferometers. This framework offers a unified perspective relating emergent time, collapse dynamics, and gravitational information bounds.