The Holographic Principle – Spacetime as an Informational Projection

The Holographic Principle – Spacetime as an Informational Projection Alexander Grünberg* Independent Researcher, Germany Alumni, University of Heidelberg ORCID: 0009-0009-7034-2202 *Correspondence: [email protected] Abstract This paper formulates a theoretical framework interpreting spacetime as an informational projection. Building on holographic and thermodynamic principles, it proposes that spacetime geometry represents the macroscopic equilibrium configuration of an underlying informational network. Information is treated as a foundational physical quantity from which geometry and dynamics emerge. The model integrates insights from thermodynamic gravity, information geometry, and holographic duality to establish a unified conceptual basis for emergent spacetime. The Einstein tensor is interpreted as a measure of informational imbalance, while curvature quantifies deviations from informational equilibrium. By introducing a mapping between informational and geometric curvature on an informational manifold, the framework connects entropic, quantum, and geometric descriptions under a common informational ontology. This interpretation maintains consistency with established semiclassical results while providing a coherent ontological foundation for emergent-spacetime models. The paper offers a conceptual synthesis clarifying the informational basis of gravitational dynamics. Keywords Holographic principle; Informational ontology; Emergent spacetime; Information geometry; Entropic gravity; Quantum thermodynamics. 1 Introduction The present work extends prior thermodynamic and entropic approaches to gravity [6–8] by introducing a geometrically structured informational ontology of spacetime. Unlike previous interpretations that treat information as a metaphor for entropy production or energy flux, the framework defines it as a physically instantiated pattern of correlations among quantum degrees of freedom, embedded within an information-geometric manifold that renders these relations explicit. Conceptually, the framework builds upon established correspondences between thermodynamic, geometric, and informational formalisms, but aims to formalize the link between informational flux—quantified as entropy flow—and geometric curvature using an informational metric on a statistical manifold derived from Fisher information and Kullback– Leibler divergence. This provides a unified interpretive structure that situates classical curvature, energy, and entanglement within a common informational domain. This approach is neither purely philosophical nor merely analogical; it provides operational definitions of informational quantities that may, in principle, connect measurable entropy gradients and information flows in quantum systems or analog-gravity experiments. The holographic principle, originally proposed by ’t Hooft and refined by Susskind and Maldacena, asserts that the information content of a spatial region – its degrees of freedom or entropy content – is encoded on its boundary [1–3]. It is rooted in black-hole thermodynamics, where entropy scales with horizon area rather than volume [4, 5], and was given concrete form through the AdS/CFT correspondence. Yet, despite its technical successes, the ontological status of holography – whether it describes a physical mechanism or merely a dual description – remains unsettled: if geometry and dynamics are emergent, from what underlying informational structure do they arise, and under which constraints? Recent developments in spacetime–information duality, including work on flat-space holography and cosmological extensions [17], have extended holographic reasoning beyond AdS contexts, supporting the view that spacetime structure may reflect an underlying information-theoretic organization. Recent developments intensify the information-centric view – quantum entanglement appears to build spacetime connectivity (ER = EPR, entanglement wedge, RT/HRT) [11–13, 19]; tensornetwork models model bulk geometry from boundary correlations [14, 20]; and informationgeometric and complexity-based approaches relate curvature to informational change [15, 16, 22, 23]. Foundational thermodynamic derivations of gravitational dynamics based on the Clausius relation (Jacobson; Padmanabhan) and entropic gravity proposals (Verlinde) reinforce this trend [5, 7, 8]. However, what remains missing is a coherent ontological account that explains why informational organization should yield stable geometric laws and how Einstein’s equations can be read as macroscopic informational balance conditions rather than primitive geometric postulates. This paper develops a conceptual framework that interprets spacetime as an informational projection – the macroscopic manifestation of an underlying informational equilibrium between boundary and bulk degrees of freedom. The contribution is threefold: (C1) Synthesis: It integrates black-hole thermodynamics, AdS/CFT, and quantum-information insights into a single interpretive ontology of spacetime, where information is ontologically primary [3–5, 11–16, 19–23]. (C2) Reinterpretation of dynamics: It recasts Einstein’s equations, in the spirit of Jacobson’s Clausius-relation approach, as constraints enforcing informational consistency, with δQ = T dS read as information flow across local causal horizons [5, 9]. (C3) Programmatic implications: It outlines empirically motivated directions – informational curvature and entropy flow – as candidates for formalization and future tests, connecting to contemporary work in information geometry and quantum error correction [12, 13, 15, 21, 22]. The framework is conceptual rather than derivational: no new fundamental field equations are proposed. Claims are interpretive and programmatic; they aim at clarifying ontology and motivating future quantitative formulation. The account is background-agnostic – not restricted to AdS – at the level of interpretation, while acknowledging that many rigorous tools currently exist within AdS/CFT. Where the paper extrapolates beyond proven dualities, it is explicitly labeled as interpretation. Information denotes physically instantiated, quantifiable degrees of freedom and their correlations – of the Shannon or von Neumann type – operationally grounded in quantuminformation theory rather than semantic or representational content [6–8, 15]. Projection refers to the mapping from boundary informational structure to effective bulk descriptors, such as metric and curvature, consistent with holographic bounds [3, 19]. Emergence indicates coarsegrained macroscopic order arising from microscopic correlations, without implying ontological entities beyond informational relations [7, 9, 16]. The present investigation addresses a foundational question rather than a phenomenological one: Can the geometric structure of spacetime be interpreted in terms of an informational equilibrium state? This question is explored in three logical steps: (i) reviewing established holographic and thermodynamic approaches to gravity, (ii) defining a minimal informationgeometric formalism linking curvature and entropy, and (iii) discussing the ontological implications of this identification. Each step is conceptually motivated and formally delimited to avoid conflating physical law with informational analogy. In contrast to purely formal readings of holography, the present account treats holography as an ontological principle: geometry represents the statistical regularities of informational organization, and gravitational dynamics act to stabilize informational coherence across scales. This position resonates with entanglement-built geometry [11–13, 19], network and compression-based views [14, 20], and information-geometric reconstructions [15, 16, 22, 23], while differing by elevating informational primacy and by articulating explicit programmatic variables, such as informational curvature and entropy flow. Section 2 provides the foundational theoretical background linking entropy, entanglement, and holography. Section 3 introduces the informational-projection framework and clarifies its conceptual assumptions and implications. Section 4 discusses the physical and philosophical consequences and outlines research directions toward quantitative formulation, and Section 5 concludes. 2 Theoretical Background The holographic principle originates from black-hole thermodynamics, in which Bekenstein and Hawking showed that the entropy 𝑆 of a black hole is proportional to the surface area 𝐴 of its event horizon rather than its volume [4, 5]. This relation is expressed as 𝑆 = 𝑘B𝐴 4𝐿P2, where 𝐿P denotes the Planck length. It implies that the maximal information capacity (in entropy units) of a spatial region scales with its boundary. ’t Hooft [1] and Susskind [2] generalized this result to all physical systems, proposing that the complete dynamical information of a volume can, in principle, be encoded on its boundary. Maldacena’s AdS/CFT correspondence [3] provided the first explicit realization of the holographic conjecture, establishing a duality between a gravitational theory in (𝑑 +1)- dimensional Anti-de Sitter space and a conformal field theory on its 𝑑-dimensional boundary. The correspondence showed that bulk geometry and gravitational dynamics can, in principle, be reconstructed from lower-dimensional quantum degrees of freedom. Extensions — such as the Ryu–Takayanagi formula [19] and its covariant generalization, the Hubeny–Rangamani– Takayanagi (HRT) prescription — quantify entanglement entropy in geometric terms, demonstrating that geometric connectivity is encoded in quantum entanglement structure. While these frameworks are well defined in asymptotically Anti-de Sitter (AdS) spacetimes, they do not directly generalize to cosmological (e.g., de Sitter) or non-conformal settings. The present study therefore treats AdS/CFT as an existence proof of the holographic principle rather than as a universal law. It uses its informational structure — specifically boundary encoding and the entanglement-geometry correspondence — as conceptual scaffolding for an ontology that is not restricted to AdS symmetry. Jacobson’s derivation of Einstein’s equations from the Clausius relation δ𝑄 = 𝑇 𝑑𝑆 [6] interprets spacetime curvature as the macroscopic response to local energy–entropy exchange across causal horizons. Padmanabhan [7] and Verlinde [8] extended this reasoning by describing gravity as an entropic–statistical phenomenon emerging from coarse-grained microscopic degrees of freedom. These approaches converge on the view that gravitational dynamics act to enforce informational balance — a correspondence between thermodynamic flux and spacetime curvature. The recurring feature of these derivations is that spacetime dynamics emerges from variational or extremal principles involving entropy or information flux. This recurrent role of informational quantities suggests that geometry represents not a fundamental entity but the statistical equilibrium configuration of an underlying informational substrate. The next section formalizes this idea through the introduction of a minimal mathematical structure capable of representing such informational curvature. In contemporary theoretical physics, information refers to quantifiable correlations among physical degrees of freedom — typically Shannon or von Neumann entropy — embedded in Hilbert space structure [6, 15]. Entropy measures informational uncertainty, while entanglement quantifies the degree of non-factorizability — that is, the extent of quantum correlation — between subsystems. Tensor-network models such as the multi-scale entanglement renormalization ansatz (MERA) reproduce holographic scaling by encoding coarse-graining as renormalization in entanglement space [14, 20]. Quantum error correction formulations [12, 13, 21] clarify how local bulk operators emerge from redundant boundary encodings, ensuring stability against information loss. Finally, information-geometric approaches [15, 22] treat curvature on statistical manifolds as a measure of informational change, thus providing a formal bridge between thermodynamics and geometry — and the mathematical template developed in the next section. In this framework, information denotes physically instantiated correlations among degrees of freedom, whereas entropy quantifies the statistical uncertainty or distributional spread of those correlations. The two are conceptually related but not interchangeable: information represents structure, entropy its statistical measure. Collectively, these developments suggest that the fundamental variables of spacetime can be understood as informational rather than geometric in origin: curvature, energy, and causal structure emerge from the large-scale organization of underlying correlations [23, 27]. Gravity, in this interpretation, arises as a macroscopic manifestation of informational gradients that tend to restore informational equilibrium. Within this informational reading, geometry is not an independent ontological layer but an emergent descriptor of informational coherence. The informational relations themselves are physical, not merely epistemic—they correspond to operationally measurable correlations. Ontologically, this moves beyond substance metaphysics toward a structuralist view in which informational relations constitute reality [10, 25, 26]. Epistemically, observation and inference occur within the same informational network—both are physical processes of correlation extraction, not external to it [25, 34]. The present framework is methodologically related to entropic approaches that derive physical dynamics from informational principles, such as Jaynes’s entropic inference, Frieden’s Extreme Physical Information, and Caticha’s entropic dynamics. In contrast to these primarily inferential models, however, the present account adopts an ontological stance: informational relations are not merely epistemic constraints on knowledge but constitute the physical structure from which spacetime geometry itself emerges. Assumptions and Boundaries For conceptual clarity and methodological transparency, the framework operates under the following explicit assumptions and boundaries: (A1) The holographic bound 𝑆 ≤ 𝐴/4𝐿𝑃 2 is treated as an informational limiting principle constraining the maximal information density per boundary area, rather than as a purely thermodynamic relation. (A2) All references to “emergence” refer to the coarse-graining of physically instantiated informational structure. (A3) Statements extending beyond rigorously established dualities are explicitly marked as interpretive. (A4) Dimensional quantities are expressed in Planck units unless otherwise stated. These premises delineate the conceptual domain for the framework developed in Section 3, which interprets spacetime as an informational-equilibrium projection of such relations. 3 Conceptual Framework: Informational Ontology of Spacetime Building on the assumptions outlined above, the present framework develops an informational ontology of spacetime. It rests on the premise that the physical universe can be described as a network of quantifiable relations of information rather than as a continuum of substances or fields. Each physical system corresponds to a structured ensemble of correlations constrained by thermodynamic and quantum principles. The central hypothesis is that spacetime geometry emerges as the macroscopic equilibrium state of an informational network that maximizes consistency among its boundary correlations. The model generalizes Jacobson’s thermodynamic interpretation of Einstein’s equations [6] and Padmanabhan’s emergent-gravity picture [7] by treating the relation 𝛿𝑄 = 𝑇 𝑑𝑆 as an instance of informational flux rather than of energy transfer alone. In this reading, the Einstein tensor 𝐺μν quantifies deviations from informational equilibrium. Local curvature corresponds to a gradient of informational imbalance; flat spacetime represents maximal informational uniformity. The holographic entropy bound 𝑆 ≤ 𝐴/4𝐿P 2 [4, 19] thereby functions as a constraint on information density, not merely as a thermodynamic limit. This interpretation preserves compatibility with established semiclassical results while offering a unifying informational language. Three informational quantities underlie the framework: – Informational density ρI: the entropy per unit (Planck) area on a boundary surface, dimensionless in Planck units; – Informational flux ΦI: the rate at which boundary information changes with respect to local causal flow, measured per unit area and time; – Informational curvature ℛℐ: a measure of deviation from uniform informational distribution, formally analogous to the geometric scalar curvature. The corresponding information-geometric tensor is 𝑅μν (𝐼) [22, 32], and dimensionally [ℛℐ]= 𝐿−2. Informational manifold and dimensional consistency Mathematically, the informational structure is represented as a statistical manifold ℳℐ endowed with a Fisher information metric. To quantify informational distances between probability distributions, we adopt the framework of information geometry, in which the Fisher information defines a natural Riemannian metric on the space of statistical states. Parameterization and Fisher Metric. Let 𝑝(𝑥|𝜃)𝜃∈𝛩 be a smooth statistical model with parameter manifold 𝛩 ⊂ ℝⁿ. The Fisher information metric on 𝛩 is defined as 𝑔𝑖𝑗 (𝐼)(𝜃)= 𝐸𝑥∼𝑝(⋅|𝜃)[∂𝑖log𝑝(𝑥|𝜃) 𝜕𝑗log𝑝(𝑥|𝜃)] = 𝜕𝑖𝜕𝑗𝐷KL(𝑝(⋅|𝜃)||𝑝(⋅|𝜃′))|𝜃′=𝜃. (1) The associated Levi-Civita connection induces the information-geometric Ricci tensor 𝑅𝑖𝑗 (𝐼)(𝜃) and scalar curvature ℛ𝐼(𝜃)= 𝑔(𝐼) 𝑖𝑗 𝑅𝑖𝑗 (𝐼). In equilibrium, ℛℐ→ 0 corresponds to vanishing informational gradients, reproducing the geometric condition of flat spacetime, whereas deviations generate nonvanishing curvature, in analogy to thermodynamic imbalance. This mapping provides an explicit correspondence between informational and geometric curvature, forming the mathematical foundation for the projection formalism introduced in the next subsection. Since the Fisher metric is defined on a dimensionless parameter manifold, physical dimensions enter only through the bridge length ℓ𝐼, introduced to ensure dimensional consistency with spacetime curvature. This formal structure provides the informational substrate upon which the subsequent balance and projection relations are defined. Notation Although primarily conceptual, the informational framework can in principle be subjected to empirical or computational scrutiny. Possible empirical anchors include analog gravity systems, black-hole thermodynamics, and quantum-simulation platforms which emulate entanglement geometry. In such contexts, measurable correlations between information flow and curvature— interpreted through entropic scaling laws—could provide indirect tests of the informationalprojection hypothesis. Informational curvature κI could, in principle, be operationally approximated through entropy–area scaling in quantum-simulation systems, where entanglement correlates with geometric distance. A key implication is that the informational curvature ℛℐ may serve as a testable invariant in analog or simulated quantum-gravitational systems, e.g., in tensor-network models or opticallattice simulators. Mapping the mutual-information structure to emergent curvature tensors provides a concrete route toward empirical operationalization, aligning with the foundational yet empirically oriented scope of Foundations of Physics [36]. Interdisciplinary and Programmatic Outlook – Formalization: Develop rigorous and dimensionally consistent definitions of informational curvature, entropy flux, and equilibrium stability using information-geometry and complexity theory [22, 23, 32]. – Simulation and Testing: Explore analog realizations on tensor-network and quantumsimulation platforms to test scaling relations between entanglement and emergent curvature [20, 21]. – Cosmological Extension: Relate informational-balance dynamics to large-scale structure formation and entropic cosmology [31]. – Philosophical Integration: Examine implications for a naturalized metaphysics of information and the relational foundations of lawfulness [10, 34]. These directions delineate a research program rather than a completed theory. By identifying information as the ontological core and equilibrium as the organizing principle, the framework unites quantum information theory, gravitational thermodynamics, and the philosophy of science under a single conceptual horizon. Its success will ultimately depend on formally and empirically articulating information as geometry—a task now within reach of both theory and experiment. 5 Conclusions This study reinterprets the holographic principle [1–3] within a formally defined informational ontology of spacetime. By embedding thermodynamic and entanglement concepts in an explicit information-geometric manifold [14, 15, 32], the framework establishes a minimal mathematical structure that expresses Einsteinian geometry as an informational balance condition [5–9]. Unlike previous heuristic treatments, the present approach specifies how informational density, flux, and curvature are interrelated through the Fisher metric and the Kullback–Leibler divergence [14, 15, 32], thereby establishing a bridge between thermodynamics, quantum information, and geometric structure [17, 19–21, 35]. While primarily programmatic, the model provides a mathematically coherent foundation for future derivations of testable invariants— such as informational curvature or entropy-flux measures—that may be explored in analoggravity and quantum-simulation environments [20, 21, 27, 36]. The informational-projection model unifies thermodynamics, entanglement theory, and geometry through a shared set of informational descriptors: density ρI, flux ΦI, and curvature κI. Together, these variables form a conceptual triad that can be formally embedded in information-geometric metrics, for example as 𝑅I ∼ ∂2𝐷KL. By linking curvature to informational divergence, the framework motivates a mathematically rigorous reformulation of gravitational equilibrium in purely informational terms [15, 22, 32]. Ontologically, information is treated as the primitive structure from which physical regularities emerge. Geometry, energy, and causality arise as statistical patterns of informational coherence, while physical law expresses the constraints that maintain that coherence [10, 25, 26, 34]. Epistemically, observation and theoretical representation are embedded within the same informational network; there is no privileged external standpoint beyond it. This stance grounds the framework in structural-relational realism, according to which reality consists in the total relational order of information physically instantiated in quantum correlations. Future work should – formalize informational curvature and entropy flow within generic curved spacetimes [22, 27, 32]; – develop computational models and quantum-simulation analogs for testing entanglement– curvature correlations [20, 21, 33]; and – integrate informational and cosmological dynamics to explore whether large-scale structure formation can be understood as a process of global entropy maximization [31]. Philosophically, continued investigation of the informational foundations of physical law may help clarify how ontology, epistemology, and computation are interconnected within a unified conception of nature. In conclusion, this framework reframes the holographic principle as an informational equilibrium condition underlying spacetime geometry. It provides a coherent bridge between thermodynamics, quantum information, and gravitation, while remaining open to formalization and empirical validation. Whether spacetime is indeed an emergent manifestation of informational order remains a question for future theory and experiment—but one that can now be posed with conceptual precision and testable intent. Declarations Conflict of Interest The author declares that there are no conflicts of interest regarding the publication of this paper. Funding This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. Data Availability No new data were created or analyzed in this study. Data sharing is not applicable to this article. Acknowledgments The author gratefully acknowledges the broader scientific community for open-access research and discussions that have inspired this work. Author Contribution The author confirms sole responsibility for the study conception, theoretical development, and manuscript preparation. References [1] ’t Hooft, G. Dimensional reduction in quantum gravity. arXiv:gr-qc/9310026 (1993). [2] Susskind, L. 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