We develop a covariant open-system framework in which spacetime curvature directly governs the decoherence of quantum fields on curved backgrounds. Starting from a geometric deformation of the matter wavefunctional and using standard microlocal assumptions, we derive a curvature-dependent Lindblad equation whose local decoherence rate is fixed by scalar curvature invariants through the influence of metric fluctuations. Within this setting we establish a general purity-decay theorem: the reduced state seen by any semiclassical observer undergoes monotonic purity loss, and complete mixing occurs precisely when the curvature-dependent effective rate diverges. To characterize the associated information flow, we construct a geometric entropy func- tional inspired by Perelman’s H-entropy and show that it obeys a monotonicity relation under the induced information-theoretic flow. Finally, we explain how the semiclassical appearance of information loss produced by curvature-driven decoherence is reconciled with global unitarity once nonperturbative gravitational saddles—replica wormholes and quantum extremal surfaces—are included. The resulting picture integrates curvature-induced deco- herence, geometric entropy production, and the unitary Page curve into a single coherent framework.
We develop a covariant open-system framework in which spacetime curvature directly governs the decoherence of quantum fields on curved backgrounds. Starting from a geometric deformation of the matter wavefunctional and using standard microlocal assumptions, we derive a curvature-dependent Lindblad equation whose local decoherence rate is fixed by scalar curvature invariants through the influence of metric fluctuations. Within this setting we establish a general purity-decay theorem: the reduced state seen by any semiclassical observer undergoes monotonic purity loss, and complete mixing occurs precisely when the curvature-dependent effective rate diverges. To characterize the associated information flow, we construct a geometric entropy func- tional inspired by Perelman’s H-entropy and show that it obeys a monotonicity relation under the induced information-theoretic flow. Finally, we explain how the semiclassical appearance of information loss produced by curvature-driven decoherence is reconciled with global unitarity once nonperturbative gravitational saddles—replica wormholes and quantum extremal surfaces—are included. The resulting picture integrates curvature-induced deco- herence, geometric entropy production, and the unitary Page curve into a single coherent framework.
This paper presents an observer-inclusive, semiclassical framework in which quantum measurement, the emergence of time, and spacetime curvature are unified through the dynamics of record formation. Measurement is modeled as a local, causal stabilization process driven by irreversible record creation within closed quantum systems, eliminating the need for external wavefunction collapse. Time is shown to emerge as a derived quantity proportional to record flux rather than as a fundamental background parameter. Regions of suppressed entropy production correspond to effective “timeless” steady states, while ordinary relativistic proper time is recovered in semiclassical regimes. The framework introduces a covariant, Planck-suppressed coupling between spacetime curvature and local record flow. Record density is defined on invariant causal diamonds using sandwiched Rényi mutual information to preserve Lorentz covariance and ultraviolet regularity. The energetic cost of record formation is compensated via Landauer’s principle, ensuring consistency with the Bianchi identities, null energy conditions, and the no-signaling theorem. The resulting theory is explicitly effective and semiclassical. It makes no claim to a fundamental quantum gravity completion, but provides a consistent, observer-inclusive description of measurement, time, and geometric response compatible with known physical constraints and open to experimental falsification.
This work analyzes the stability of probabilistic manifolds embedded in curved spacetime, extending earlier formulations in which gravity emerges from the localization of probability. By introducing an affine probabilistic connection that preserves normalization, the framework shows that curvature induces a natural correction to coherence transport on the underlying state manifold. The resulting curvature‑dependent coherence equation yields a stability criterion in which positive curvature enhances localization and suppresses divergence between probability configurations, while negative curvature drives decoherence growth. A generalized divergence metric and curvature‑modulated coherence gate unify gravitational localization, quantum coherence limits, and vacuum stability within a single geometric principle: the self‑consistency of probability under curvature. The analysis predicts curvature‑dependent decoherence rates, suppression of false‑vacuum tunneling in regions of positive curvature, and cosmological thresholds associated with coherence instability. This establishes a dynamic feedback loop between probability, coherence, and geometry, offering a unified interpretation of gravitational behavior and quantum stability.
This work constitutes Part VIII of Temporal Information Dynamics (TID) within the Scalar Temporal Field Ontology (STFO). Building on the geometric, thermodynamic, and quantum-informational foundations established in Parts I–VII, this installment develops the τ-adjoint formalism that governs non-Hermitian, dissipative, and information-nonconserving quantum evolution in the presence of temporal curvature and τ-noise. Where Part VII introduced τ-modified Schrödinger dynamics, decoherence kernels, τ-Lindblad evolution, and entanglement flow, Part VIII extends the framework by constructing: • the τ-adjoint operator associated with the effective disformal metric• a formally complete non-Hermitian τ-Hamiltonian governing open-system evolution• τ-dependent quantum continuity relations, including probability flux deformation• a temporal adjoint propagator and τ-corrected Green’s functions• the τ-antiunitary map connecting reversed temporal flow to geometric curvature• a unified treatment of τ-dissipation, decay channels, and information leakage• experimental predictions in interferometry, quantum optics, quantum hardware, and metrology This completes the quantum-dynamical layer of Temporal Information Dynamics. The τ-adjoint construction reveals how temporal geometry—through gradients, curvature, and fluctuations—induces non-Hermitian corrections, anisotropic decay rates, direction-dependent decoherence, and modified causal structure. As in Parts I–VII, all results are derived directly from the scalar temporal field τ(x), without phenomenological assumptions. Together with the previous installments, Part VIII advances TID into a complete, falsifiable, and fully geometric framework linking quantum evolution, information theory, decoherence, entanglement, channel capacities, Fisher information, and non-Hermitian dynamics, all unified by the scalar temporal field τ. Author: Cale Scott HoweProgram: Scalar Temporal Field Ontology (STFO)Contact: calescotthowe@gmail.com
Part VII of the Temporal Information Dynamics (TID) series develops the full quantum-information layer of the Scalar Temporal Field Ontology (STFO), where time is a physical scalar field τ(x) and information evolves along its integral curves. This work extends Parts I–VI by deriving the complete quantum dynamics implied by τ-geometry: the τ-modified Schrödinger equation governing intrinsic temporal evolution, the temporal decoherence kernel generated by fluctuations δτ, a covariant τ-Lindblad master equation for open quantum systems, directional entanglement flow induced by ∇μτ, τ-dependent deformations of the quantum Fisher metric, modified quantum-channel capacities, coherence lengths, and error exponents, τ-corrected propagators, Green’s functions, and canonical commutators, and a fully geometric τ-weighted path-integral formulation. Across all levels—Hamiltonian, thermodynamic, geometric, and quantum—information flow becomes a direct probe of τ-gradients and temporal curvature. The resulting framework is testable in atom interferometry, optical and microwave clock networks, spin-echo experiments, and quantum computing hardware. This paper completes the quantum-information pillar of STFO and unifies classical information flow, thermodynamic irreversibility, geometric curvature, and quantum coherence into one continuous, falsifiable theory of temporal dynamics.
We develop a mathematically rigorous theory of quantum measurement within Entanglement-Weighted Operator Gravity (EWOG), in which spacetime geometry is an operator-valued entity weighted by quantum entanglement. We show that quantum measurement corresponds to a localized, transient fluctuation of spacetime curvature induced by rapid redistribution of entanglement. We prove that competing measurement outcomes correspond to competing semiclassical geometries whose stability is governed by curvature variance. Minimization of curvature fluctuations leads uniquely to probability weights proportional to ∣ψ∣2, yielding the Born rule as an emergent geometric law rather than an axiom. This framework unifies quantum measurement, decoherence, and classical spacetime emergence within a single gravitational-informational principle. We further derive the spectral density of measurement-induced curvature fluctuations and establish experimental bounds on their detectability.
Abstract We develop a novel framework connecting quantum mechanics with gravitational geometry through a deformation of probability amplitudes. Inspired by Rohit Dhormare’s geometric formulation of probability under gravitational fields, we reinterpret the influence of curvature on probability not within classical settings, but in the domain of quantum amplitudes. We propose a quantum probabilistic manifold where space-time curvature induces topological and metric deformations on Hilbert space projections, affecting interference, measurement outcomes, and entropy. This formulation offers new pathways for understanding quantum gravity, decoherence, and information localization.