We propose an operational framework in which spacetime geometry and gravitational dynamics emerge directly from quantum information correlations in many-body systems. Utilizing Multiscale Entanglement Renormalization Ansatz (MERA), we derive an effective metric based on mutual information, demonstrating that Einstein's field equations arise from a variational entropy principle, providing a theoretical link between entanglement density and the cosmological constant.
We propose an operational framework in which spacetime geometry and gravitational dynamics emerge directly from quantum information correlations in many-body systems. Utilizing Multiscale Entanglement Renormalization Ansatz (MERA), we derive an effective metric based on mutual information, demonstrating that Einstein's field equations arise from a variational entropy principle, providing a theoretical link between entanglement density and the cosmological constant.
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 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 show that the gradient of entanglement entropy across a holographic boundary, as described by the Ryu–Takayanagi formula, generates an effective force thatobeys Einstein’s field equations. By representing the entanglement structure of aquantum many-body system as a MERA tensor network, we demonstrate that thevariation of the entanglement entropy with respect to the boundary metric yieldsthe Einstein tensor. The result provides a constructive link between quantum information theory and classical gravity, in which spacetime curvature emerges asa thermodynamic consequence of entanglement renormalization. A testable prediction is derived: the entanglement-driven acceleration of a test particle near aholographic screen deviates from the Newtonian prediction by a factor proportionalto the mutual information density.
We present a fundamental unified framework based on information geometry, in which quantum mechanics, statistical thermodynamics, and general relativity emerge from a single information-theoretic ontology. Starting from three rigorous axioms that establish quantum information as the primary physical substrate, we construct the universal information action functional using the Bures–Fisher–Rao metric on the manifold of quantum density matrices. Full variational derivation yields a unified field equation that governs the evolution of quantum information and emergent spacetime geometry. In appropriate limiting regimes, we recover the Schrödinger equation, equilibrium statistical mechanics, and the Einstein field equations. This work provides the foundational layer of a complete theory of everything based on the principle: geometry is information.
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.
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.