Correlation-Driven Emergence of Geometry, Gravity, and Black Hole Thermodynamics

Version 3 – Major Conceptual and Mathematical Refinement Version 4 Update: This version introduces explicit observable predictions for Light Deflection, Orbital Precession, and Black Hole Shadow radius. It derives the α-parameter corrections (O(1/r²)) to the Schwarzschild metric, establishing a predictive bridge between the conservation of Total Primordial Correlation (C0) and strong-field astrophysical tests.This version introduces a fundamental clarification and extension of the theoretical framework presented in previous versions. The key development is the explicit identification of a two-layer structure of gravitational dynamics, separating: A universal, state-independent correlation decay (defining the arrow of time and the gravitational scale), and A state-dependent dynamical response governed by field equations that produce curvature and force-like behavior. Main Improvements in Version 3 Explicit Definition of the Gravitational Constant The gravitational constant (G) is no longer treated as an external parameter but is defined in terms of correlation structure:[G^{-1} \sim \frac{dC}{dA}]and connected to a universal correlation decay rate:[G \sim \lambda^{-2}]This provides a physical interpretation of (G) as a conversion scale between correlation loss and geometric structure. Introduction of Universal Correlation Decay (Arrow of Time) A new dynamical decomposition is introduced:[\frac{dC}{dt} = -\lambda C + F[g_{\mu\nu}, S]]where: The first term represents a uniform, state-independent loss of correlation, and The second term represents state-dependent gravitational dynamics. This establishes a universal time parameter distinct from proper time. Refined Interpretation of Time A distinction is made between: Global time (dt): associated with universal correlation decay Local proper time (d\tau): emerging from spacetime curvature This clarifies the origin of relativistic time differences within the framework. Reformulation of Gravity as a Two-Layer Process Gravity is reinterpreted as: A universal background process (correlation decay), and A local geometric response (curvature from entropy gradients) This preserves compatibility with general relativity while providing a deeper structural interpretation. Strengthened Entropy–Area Derivation The entropy–area relation and the factor (1/4) are now explicitly connected to: Correlation density per unit area Reduction of independent modes due to causal and global constraints Improved Conceptual Integration The relationships between: Entropy Geometry Quantum decoherence (Lindblad dynamics) Black hole thermodynamics are now presented in a unified and consistent manner. Summary Version 3 does not modify the empirical predictions of general relativity but provides a deeper theoretical interpretation in which: Spacetime geometry emerges from correlation structure The gravitational constant arises from fundamental correlation units The arrow of time is rooted in universal correlation decay This version represents a shift from a reformulation of known equations to a more foundational interpretation of their origin.