This paper introduces a novel framework for analog gravity in which an effective (2+1)-dimensional Lorentzian spacetime emerges dynamically on the information geometry of a driven open quantum system. Unlike traditional fluid-based analogs, the spatial fabric is provided by the Quantum Fisher Information Metric (QFIM) over a control-parameter manifold, while laboratory time serves as the temporal axis. Using Keldysh nonequilibrium field theory, the study demonstrates that the Lorentzian signature and thus the existence of causal light cones-originates fundamentally from the thermodynamic passivity of the quantum state. This profound connection makes the causal structure a tunable, falsifiable property: driving the system into population inversion triggers a signature-breakdown transition that destroys the hyperbolicity of the emergent spacetime. Supported by exact derivations for a two-qubit model and concrete experimental protocols involving continuous homodyne detection and FPGA-based feedback, the research offers a fully measurable laboratory platform to explore the intersection of quantum information geometry, nonequilibrium thermodynamics, and emergent causal structure. By Gökay Yıldız gokay@krekpot.com
This paper introduces a novel framework for analog gravity in which an effective (2+1)-dimensional Lorentzian spacetime emerges dynamically on the information geometry of a driven open quantum system. Unlike traditional fluid-based analogs, the spatial fabric is provided by the Quantum Fisher Information Metric (QFIM) over a control-parameter manifold, while laboratory time serves as the temporal axis. Using Keldysh nonequilibrium field theory, the study demonstrates that the Lorentzian signature and thus the existence of causal light cones-originates fundamentally from the thermodynamic passivity of the quantum state. This profound connection makes the causal structure a tunable, falsifiable property: driving the system into population inversion triggers a signature-breakdown transition that destroys the hyperbolicity of the emergent spacetime. Supported by exact derivations for a two-qubit model and concrete experimental protocols involving continuous homodyne detection and FPGA-based feedback, the research offers a fully measurable laboratory platform to explore the intersection of quantum information geometry, nonequilibrium thermodynamics, and emergent causal structure. By Gökay Yıldız gokay@krekpot.com
This work proposes a theoretical framework in which entropy is treated as a geometric degree of freedom in an extended quantum state space. By introducing a resolution parameter defined as the inverse of von Neumann entropy, an informational metric is constructed on the space of density matrices. Within this framework, a causal structure emerges from a null condition on the metric, defining a light-cone-like boundary for the propagation of quantum correlations. Entanglement propagation is derived and shown to depend on entropy evolution, leading to a dynamical causal structure. In the near-equilibrium limit, the model reproduces a Lieb–Robinson-type bound with finite correlation speed. Connections to holography are established by interpreting entropy as a radial coordinate controlling scale, and an analogue of the Ryu–Takayanagi relation is derived, where entropy corresponds to the length of minimal curves in the informational geometry. Black hole horizons are interpreted as maximal entropy surfaces corresponding to a collapse of distinguishability in quantum state space. The framework suggests that spacetime geometry, causality, and gravitational behavior may emerge from entropy-weighted quantum information structure. This work is an independent theoretical exploration aimed at providing a unified perspective linking quantum information, geometry, and gravity.
The Emergent Spacetime program (Informational Geometry of Emergent Spacetime – IGES) has shown that the linearized Information Open-systems Flow (IOF) on the Bures manifold of density operators projects to a symmetric hyperbolic hydrodynamic system whose characteristic cone is exactly Lorentzian. This established that spacetime causal structure can emerge from quantum information degradation, but only in the tangent-space approximation. In this work, we address the principal remaining gap: we provide strong numerical evidence for a Nonlinear Emergent Causal Structure Scenario, supporting the conclusion that an effective hyperbolic causal cone acts as a dynamically stable attractor of the full, nonlinear IOF dynamics. We implement a complete numerical simulation of two coupled qubits with dephasing on a 1D lattice, evolving the exact IOF on the 15-dimensional Bures manifold. At each time step we extract the Bures Hessian of the information degradation functional, construct the dynamic spectral gap ∆(t), compute the nonlinear Schur complement Keff(t), and measure the instantaneous cone deviation δ(t) ≡ supk |ω 2 (t, k) − c 2 s(t)k 2 |. We find that: (1) the fast/slow mode separation persists globally; (2) the spectral gap remains strictly positive, ∆(t) ≥ ∆0 > 0; (3) the effective reduced generator Keff(t) remains symmetric in the Bures metric to machine precision; (4) the cone deviation δ(t) decays as e −∆t , falling below 10−4 after a few gap times. These results provide significant evidence that the emergent hyperbolic causal structure is not a linear artifact – the effective causal cone is a robust attractor of the full gradient flow. This nonlinear stability suggests compatibility with Jacobson-type thermodynamic gravity scenarios. The complete simulation code and diagnostic data are provided as supplemental material.
The series Time as Phase Flow (Papers I–IV) established that time is not fundamental but emerges from the geometric phase flow of quantum information, providing a unified account of dynamically generated cosmological constants, informational temporal viscosity, and the suppression of large-scale structure. Despite these successes, a fundamental mechanism explaining why a single, stable observable reality emerges from the space of quantum informational states has remained unresolved. In this work, we introduce the framework of Information-Geometric Spacetime (IGS), in which spacetime itself emerges from the geometry of quantum information, entanglement, and modular flow. Within IGS, we define an Actualization Operator that mediates between quantum informational states and observable spacetime geometry. Derived from first principles, the operator combines entropy-based suppression with modular evolution, governed by a universal geometric constant β = 1/(π√3) ≈ 0.1837 fixed by the geometry of causal diamonds and the associated modular Hamiltonian. We show that actualization preserves information conservation and quantum unitarity, acting as a structural filter that selectively stabilizes informational states capable of forming consistent geometric reality, in close analogy with decoherence-driven classical emergence. Under this mechanism, previously identified cosmological effects—most notably the suppression of the matter power spectrum and the S_8 tension—are reinterpreted as observational consequences of information actualization rather than modifications of gravity or exotic matter. This framework also offers a geometric reformulation of the quantum measurement problem, in which the observer is not an external agent but an emergent process associated with modular structure and entanglement thermodynamics. The theory yields testable predictions in controlled quantum systems and forthcoming cosmological surveys, providing a concrete pathway toward empirical tests of spacetime emergence from quantum information.
We present a geometric framework that provides a pathway toward resolving quantum measurement through thermodynamic entropy mechanics within causal diamond structures. Entropy mechanics demonstrates that quantum measurement represents the conversion of coherent entropy states (accessible quantum information) into decoherent entropy states (thermodynamically inaccessible information) at precise spacetime boundaries defined by light cone intersections. The universal Quantum-Thermodynamic Entropy Partition (QTEP) ratio Scoh/|Sdecoh| ≈ 2.257 emerges from von Neumann entropy analysis and is characterized by the fundamental information processing rate γ governing all quantum-to-classical transitions without requiring additional empirical input beyond standard quantum mechanics. We add definition to fundamental information units: ebits (entanglement bits) and obits (observational bits), resolving dimensional inconsistencies between thermodynamic entropy and discrete information content. Crucially, causal diamond geometry - the intersection of future and past light cones - provides calculable spacetime boundaries where entropy conversion occurs, with the universal rate γ serving as the fundamental geodesic parameter governing all timelike paths. This architecture features holographic screens of area A(p, q) encoding information and 4-volumes V(p, q) constraining processing capacity. Entropy mechanics offers a substantive refutation of the Many Worlds Interpretation by demonstrating that quantum measurement creates definite outcomes through negentropy generation rather than reality multiplication. The single causal diamond structure provides sufficient geometric and thermodynamic resources for complete energy and information conservation. Gravity emerges as bulk manifestation of information processing optimization on holographic screens, while black holes represent extreme coherent entropy organizations. This framework provides concrete, testable predictions grounded in geometric andthermodynamic principles, with the fundamental insight that quantum measurement dynamics are intrinsically connected to spacetime structure through the universal information processing rate γ governing timelike geodesics.
We propose a unified geometric framework in which space and time emerge as observer-dependent projections of quantum correlations embedded in the universal wavefunction. In this approach, we formulate six axioms (including a duality between entanglement and time) that establish a correspondence between correlation structures and effective spacetime geometry. We introduce the "correlationhedron", a convex geometric object representing the set of all permissible correlation vectors of a given state, and show how different observer "slicings" (modeled by projection maps) yield distinct emergent spacetimes from this object. An emergent metric is defined on each observer's spacetime via the second derivative of a correlation density (analogous to a Fisher information metric), linking gradients in quantum entanglement to curvature. This paper establishes the conceptual foundations of this approach as the first in a planned series of investigations. We illustrate the framework with conceptual and quantitative examples, including an explicit calculation of the emergent geometry for a two- qubit system in both separable and entangled states. Connections to holography (AdS/CFT) (Maldacena1998, Ryu2006), tensor networks (Swingle2012), and relational quantum approaches (Rovelli1996) are discussed, along with experimental signatures (such as curvature variations with entanglement) that could support the theory. Finally, we outline the limitations of the framework, particularly regarding dynamics and observer-dependent causality, to guide future investigations. This kinematic framework establishes the conceptual skeleton of emergent spacetime; detailed constructions, proofs of smoothness, and dynamical laws will appear in forthcoming work.
Abstract We propose physical distinguishability as the fundamental primitive underlying quantum mechanics, general relativity, and thermodynamics. A state is defined operationally: two states are physically distinct if a physical interaction or measurement can reveal a difference between them. From this single principle, the distinguishability divergence D generates a smooth state space endowed with a Riemannian metric , a geometric velocity, an accessibility scale Λ, an accessibility ratio , and a geometric time . The framework provides a unified geometric description of the three major domains of physics. Quantum mechanics emerges through the Fubini–Study geometry of projective Hilbert space, thermodynamics through Fisher–Rao and Ruppeiner information geometry, and general relativity through the geometry of geodesic deviation. The threshold condition A=1acquires a universal physical meaning and appears in all three realizations as the boundary between physically accessible and inaccessible evolution. Variational formulations of both the Einstein and Schrödinger equations are constructed within the same geometric framework. The Lorentzian signature of spacetime emerges from a single sign reversal associated with the geometric-time direction, while the coupling constant of the distinguishability action is connected to the observed vacuum energy density. The framework further predicts a characteristic vacuum distinguishability scale ≈8.8×10^(-5) m, corresponding to an energy scale≈2.25" " meV. The theory is tested experimentally on IBM Quantum superconducting processors. Across one-qubit, two-qubit, 127-qubit, and 156-qubit experiments performed on three independent Heron-generation backends, excitation probabilities collapse onto universal curves when parameterized by endpoint Fubini–Study distinguishability. Protocols with identical laboratory control parameters but different endpoint distinguishabilities produce excitation probabilities differing by up to a factor of 3.8, while protocols with identical distinguishability produce identical outcomes across independent processors. Cross-backend transfer errors remain below 1%, providing direct experimental support for endpoint distinguishability as a universal physical variable. Taken together, the theoretical construction, variational formulations, vacuum-sector predictions, and large-scale quantum-processor experiments support distinguishability geometry as a unified and experimentally testable foundation for physical dynamics.