Gravity as a Multi-Layered Phenomenon: Entanglement, Entropy, and Curvature

! 1! Gravity as a Multi-Layered Phenomenon: Entanglement, Entropy, and Curvature Borros Arneth, Philipps University Marburg, Justus Liebig University Giessen, Germany, [email protected] Abstract The nature of gravity remains a central open question in theoretical physics. While general relativity interprets gravity as spacetime curvature, recent advances suggest that gravity may be emergent from deeper microscopic mechanisms involving quantum entanglement and entropy. In this manuscript, we propose a layered framework in which gravity is understood as a combined phenomenon: (i) a microscopic layer of entanglement between subspaces of a diagram Hilbert space, (ii) a statistical layer where entropy emerges as the coarse-grained measure of these correlations, and (iii) a macroscopic layer where curvature represents the effective geometric manifestation. This unified picture synthesizes insights from black hole thermodynamics, quantum information theory, holography, and emergent gravity models. We argue that the interplay between these layers provides a consistent pathway toward a quantum theory of gravity and suggests concrete experimental signatures. 1. Introduction Since Einstein’s formulation of general relativity, gravity has been regarded as a manifestation of spacetime curvature induced by energy and momentum [1]. However, growing evidence from black hole thermodynamics [2], the holographic principle [3,4], and entanglement-based approaches [5,6] suggests that gravity is not fundamental but emergent. This paradigm shift raises the possibility that gravity originates from microscopic information-theoretic and statistical structures rather than from geometry alone. Black hole entropy [2,7], the AdS/CFT correspondence [3,8], and recent tensor network reconstructions of holographic geometry [5,9] strongly support the idea that spacetime geometry is an emergent manifestation of quantum entanglement. In parallel, entropic gravity proposals argue that the gravitational force can be understood as an entropic effect associated with microscopic degrees of freedom [10,11]. Together, these developments indicate that gravity may be a multi-layered phenomenon in which ! 2! entanglement, entropy, and curvature are distinct but interconnected aspects of a single structure. In this work, we present a framework that unifies these insights into a layered description of gravity: (i) a microscopic layer where gravity originates from entanglement patterns between diagrammatic Hilbert space substructures [12], (ii) a statistical layer where entropy measures these correlations and drives emergent dynamics [10,13], and (iii) a macroscopic layer where the effective manifestation is spacetime curvature as described by Einstein’s equations [1,14]. 2. Microscopic Layer: Entanglement in Diagram Hilbert Space At the most fundamental level, gravity emerges from entanglement between subspaces of the Hilbert space describing matter and gauge fields. In holographic dualities, the Ryu– Takayanagi formula directly links entanglement entropy to minimal surfaces in spacetime [5]. Beyond holography, this principle extends to generic settings, where entanglement patterns define connectivity and locality [6,9]. We introduce a diagram Hilbert space [12,15], in which projective operators encode the correlations between fundamental degrees of freedom. In this microscopic layer, gravity is not yet geometry but rather a network of entangled projective subspaces. These correlations are the seeds of spacetime connectivity and ultimately dictate the emergence of causal structure. 3. Statistical Layer: Entropy as the Coarse-Grained Measure When entanglement is coarse-grained over large ensembles of degrees of freedom, it manifests as entropy. Black hole thermodynamics revealed that gravitational systems possess entropy proportional to horizon area [2,7,16]. This inspired Jacobson’s derivation of the Einstein equations as an equation of state [13], establishing a direct link between entropy and spacetime dynamics. In our layered framework, the statistical layer is where entropy acts as the bridge between microscopic entanglement and macroscopic curvature. The entropy quantifies information loss when microscopic correlations are traced out, providing the thermodynamic force that underlies gravitational interaction [10,11]. Thus, gravity in this layer appears as an entropic drive toward maximizing information distribution. ! 3! 4. Macroscopic Layer: Curvature as Effective Geometry At the largest scales, gravity manifests as spacetime curvature, as captured by Einstein’s field equations [1,14]. This macroscopic layer is the effective description accessible to experiments and astrophysical observations. From planetary orbits to gravitational waves, curvature provides a successful classical account of gravitational phenomena. However, in the layered picture, curvature is understood not as fundamental but as the geometric projection of underlying entropic and entanglement structures. Just as thermodynamics emerges from microscopic statistical mechanics, general relativity emerges from entanglement-driven entropy. The Einstein equations are thus effective equations of state for the underlying information-theoretic system [13,17]. 5. Unification and Phenomenological Implications The synthesis of entanglement, entropy, and curvature offers several key insights: 1. Black hole physics: Entanglement entropy at the microscopic level explains the Bekenstein–Hawking entropy law [2,7], while macroscopic curvature accounts for horizon geometry. 2. Cosmology: Entropic forces may account for dark energy or modified large-scale dynamics [11,18]. 3. Quantum gravity phenomenology: Entanglement-induced corrections to curvature could manifest as deviations in gravitational wave propagation or in the earlyuniverse power spectrum [19,20]. This multi-layered approach provides a conceptual roadmap toward unifying quantum field theory, thermodynamics, and general relativity under a single information-theoretic framework. 6. Conclusion We have argued that gravity should be understood as a combined phenomenon with three distinct but interconnected layers: entanglement at the microscopic level, entropy at the statistical level, and curvature at the macroscopic level. This synthesis bridges approaches from quantum information, statistical mechanics, and differential geometry. By framing gravity as an emergent projection of entanglement-generated entropy into ! 4! effective curvature, we unify several seemingly disparate perspectives on gravitational dynamics. Future work should explore experimental probes of entanglement-induced corrections and further develop operator-based formulations such as the diagram Hilbert space. References 1. A. Einstein, Annalen der Physik 49, 769 (1916). 2. J. D. Bekenstein, Phys. Rev. D 7, 2333 (1973). 3. G. ’t Hooft, Conf. Proc. C 930308, 284 (1993). 4. L. Susskind, J. Math. Phys. 36, 6377 (1995). 5. S. Ryu and T. Takayanagi, Phys. Rev. Lett. 96, 181602 (2006). 6. M. 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