Vector-Network Idealism: A Relational Graph-Theoretic Framework for Emergent Spacetime and Quantum Observation
Vector Network Idealism (VNI) v1.4: A Relational Quantum-Informational Field Theory of Emerging Spacetime and Gravitation Overview: Vector Network Idealism (VNI) v1.4 represents a major theoretical milestone in the VNI framework, formally establishing 3+1-dimensional Riemannian spacetime and Einsteinian gravitation as an emergent macroscopic hydrodynamic limit of discrete quantum state updates. Operating on an underlying infinite-dimensional Hilbert substrate (H_infinity), version 1.4 delivers a closed, self-consistent field theory that bridges microscopic quantum information processing with continuous general relativity. Key Architectural Updates in Version 1.4: Information-Geometric Metric Emergence: Continuous spacetime metric components g_μν are derived directly from quantum state distinguishability via the Quantum Fisher Information Metric (QFIM) and the Belkin-Niyogi spectral convergence theorem applied to normalized graph Laplacians. Unified Field Action and Modified Field Equations: A master minimally coupled scalar-tensor action functional is established, incorporating spacetime curvature, physical matter fields, and the dynamic relational entropy scalar field χ(x). Variation of the action yields modified gravitational field equations driven by the relational stress-energy tensor T_μν^SPR. Parameter-Free Coupling Proof: By matching the relational field action to the gravitational stiffness of spacetime in Planck units, the coupling constant γ is uniquely proven to be identically Einstein's gravitational constant (8πG/c⁴), eliminating arbitrary free parameters from the theory. Dynamic Conservation and Coarse-Graining: Establishes covariant energy-information conservation laws, defining the exchange vector Q_ν that governs continuous energy transfer between physical matter and the cosmic environmental logbook L_cosmic. Microscopic node density matrix updates are rigorously mapped to macroscopic fields via local thermodynamic coarse-graining over 4-volume elements. Black Hole Physics and Singularity Resolution: Reconstructs the Bekenstein-Hawking area-entropy law from first principles at event horizon boundaries. Resolves classical central singularities by demonstrating that energy exchange halts gravitational collapse at a finite, non-singular Planckian Quantum Core (r_core ~ l_P), preserving quantum unitarity throughout the evolution cycle. Testable Empirical Predictions: Outlines concrete observational tests that distinguish VNI v1.4 from standard general relativity and pure quantum mechanics. These include internal-state-dependent atom-interferometry dephasing signatures for structural isomers (Δϕ_VNI), discrete Planckian execution tick noise floors (~10^-44 seconds), and CDM-free galactic rotation curves driven by scalar entropy gradients. Document Contents: This release includes the complete, publication-ready preprint manuscript formatted in standard academic LaTeX, featuring the Master VNI v1.4 Lexicon, structural execution schematics, extreme regime derivations, and observational signatures. Generative AI (Gemini) was used as a collaborative sounding board, a mathematical stress tester, and copy editor.