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.
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.
We propose a unified framework in which spacetime and gravity emerge from the structure of quantum correlations in a single universal wavefunction. In this approach, the full set of allowed correlation patterns of the quantum state is represented geometrically as a high-dimensional convex object, called the correlationhedron. By imposing additional structure on the correlationhedron (namely spherical topology, finite tessellation, and universal constant rotation), we obtain a specialized case dubbed the footballhedron, for its resemblance to a football (soccer ball in American English). Crucially, we show how the footballhedron's radius and angular frequency are linked directly to fundamental quantum information principles, and how this geometric structure is essential for deriving physical laws from the model. Under the footballhedron assumption, key features of relativistic spacetime physics naturally emerge. In particular, the universal correlation rotation speed (analogous to the speed of light) ensures Lorentz symmetry for all observers, while a suitable definition of an emergent metric from the correlation density leads directly to Einstein's field equations of gravity in the emergent spacetime. The finite tessellation assumption (an optional but natural extension) introduces intrinsic informational granularity, providing the theory with a fundamental ultraviolet cutoff at the Planck scale.
We develop a complete geometric framework in which each quantum particle possesses its own private spacetime—a world-block—constructed from Fermi–Walker coordinates. The intrinsic spatial metric on each proper-time slice is a dynamical field governed by an action with a universal stiffness constant A0. A single world-block exhibits kinematic non-locality: the metric perturbation at a point depends on the entire wavefunction through an integral relation, while maintaining dynamic locality via causal wave equations. This duality captures the essential non-locality of quantum mechanics without violating relativistic causality. When two particles interact, their world-blocks are stitched along a common boundary, forming a single compound world-block in ordinary four-dimensional spacetime. The stitching imposes local matching conditions that yield a non-separable strain field, providing a geometric account of quantum entanglement. Measurements correspond to fixing boundary conditions on one part of the compound block; the correlated outcome on the distant part is automatically determined by the shared global geometry, not by any superluminal signal. Thus, the apparent non-locality of EPR correlations is explained as a manifestation of geometric connectivity within a single 4D manifold, consistent with Bell’s theorem because the geometry itself is non-local. In the continuum limit of many overlapping blocks, coarse-graining restores an effective local description, and Newton’s law of universal gravitation emerges exactly, with Newton’s constant given by G = 3c4/(8πA0). The model offers a unified, deterministic, and fully relativistic foundation for quantum mechanics and gravity, without invoking extra dimensions or stochastic elements. Experimental signatures in ultrafast interferometry and possible connections to dark energy are discussed. The framework aligns with recent developments in emergent gravity and provides a concrete geometric realization of spacetime from quantum entanglement.
This paper develops a theoretical framework that seeks to unify the foundational principles of quantum mechanics, general relativity, and thermodynamics by extending spatial geometry to include a compactified fourth spatial dimension. The central proposal is that many counterintuitive features of quantum systems—such as wave function collapse, superposition, entanglement, tunneling, and decoherence—emerge as phenomena from the projection of four-dimensional quantum states into observable three-dimensional space. Within this formulation, apparent quantum randomness is reinterpreted as a consequence of observing only a lower-dimensional slice of a higher-dimensional structure. A key innovation of the framework is the introduction of a scalar degree of freedom, termed the entropion field, which governs decoherence and encodes the thermodynamic arrow of time. The entropion field couples directly to both quantum fields and spacetime curvature, leading to modified Einstein field equations and an entropic extension of quantum field dynamics. This mechanism provides a consistent account of classicality emerging from quantum substrates, links entropy growth to projection dynamics, and clarifies how spacetime geometry constrains quantum evolution. The theory is presented through a structured progression of conceptual foundations, mathematical formalism, physical interpretation, and predictive consequences. Particular emphasis is placed on testable deviations from standard theories, including altered interference signatures in 4D-projected systems, entropion-modulated decoherence rates, and revised mechanisms of tunneling and entanglement. Broader implications are explored for quantum information theory, cosmology, condensed matter, and computational theory. Collectively, these results establish a geometrically grounded unification scheme that integrates the three major pillars of modern physics into a consistent and falsifiable framework.
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.
This work presents a comprehensive theoretical formulation of Quantum Fractal Geometry (QFG), a framework in which spacetime is fundamentally resolution-dependent. The apparent distinction between quantum and classical physics emerges from a single geometric principle: observer resolution as a structural parameter. The paper develops the formal mathematical foundations of QFG, including the definition of resolution-dependent metrics, a projection operator governing information accessibility, and the derivation of key physical results. These include the emergence of the Born rule from projection covariance, the recovery of the Einstein field equations as an infrared limit, and the Schrödinger equation as a dual flow correspondence. The framework provides a unified geometric interpretation of entanglement, black hole entropy, and gravitational structure, and introduces the Curvature Texture Index (CTI) as a measurable prediction linking multiscale geometric structure to astrophysical observables. A companion empirical study tests the CTI prediction using observational data from supermassive black hole host galaxies. All predictions are formulated with explicit falsifiability criteria, enabling experimental validation or refutation.
ABSTRACT The emergence of quantum entanglement correlations across spatially separated measurement regions renders the interpretation of the relationship between quantum mechanics and relativistic causality a core problem in quantum foundations [Einstein et al., 1935; Bell, 1964]. In this study, two entangled particles are modeled not as two independent physical objects in Minkowski spacetime, but as a joint quantum state in configuration space. The relative space and time coordinates of the joint state are defined via: and the ideal space-time correlation limit assumed in the model is expressed as: This limit is not a general definition of quantum entanglement, but an idealized geometric assumption representing strong correlation in the relative coordinates of the joint state within the proposed model. In this approach, physical spacetime is treated as a geometric structure representing the projection of the joint quantum state onto observable spacetime coordinates. To ensure the projection is Lorentz-covariant, the light-like interval: is employed as the constitutive geometric condition of the model. This condition is accepted not as a mandatory Minkowski interval between physical measurement events, but as the mathematical postulate of the proposed projection geometry. The dynamic scale parameter of the model is grounded in total relativistic quantum energy instead of rest mass, establishing a dimensionless Planck-scaling factor defined as: To encompass both massive and massless systems, quantum energy density is defined via the energy density component of the stress-energy tensor relative to an observer. The required consistency condition for covariant energy-momentum conservation is derived in its general form. Furthermore, modeling the proposed geometric effect as a dimensionless metric perturbation yields a phenomenological first-order geometric phase correction defined as: where is the energy-dependent reduced wavelength. Under fixed and finite , the vanishing of the proposed correction in the low-energy regime relative to the Planck scale () demonstrates that the geometric effect added by the model to standard low-energy quantum mechanics becomes negligible. This study proposes a testable theoretical model aimed at explaining the spatiotemporal correlations of quantum entanglement within a Lorentz-covariant, energy-scaled, and phenomenological geometric framework.