The Entangled Substrate: Definitions, Regimes, and Consistency Requirements Bridging Vacuum Impedance to Displacement Gravity (Paper 3.5)

The Entangled Substrate: Definitions, Regimes, and Consistency Requirements Bridging Vacuum Impedance to Displacement Gravity Description This paper (“Paper 3.5”) serves as an integrative bridge within a larger research program that treats the physical vacuum as an active medium characterized by empirically fixed constants, including the free-space electromagnetic impedance Z₀ Building on earlier empirical and theoretical work, this manuscript consolidates definitions, assumptions, and regime distinctions required to connect two complementary descriptions of vacuum response: a low-acceleration (“stiff”) effective-field description motivated by galactic dynamics (Papers 1–3), and a high-acceleration (“liquid”) displacement-based hydrodynamic description that reproduces Newtonian gravity and its weak-field relativistic limits (Paper 4). Rather than introducing new fundamental fields, this paper clarifies how different effective variables arise through coarse-graining under the principle of least action and equilibrium constraints. In particular, it defines the role of emergent quantities (such as vacuum displacement) as regime-dependent descriptors, not independent degrees of freedom. The paper also establishes a consistent terminology and regime map, separating empirical inputs from model-dependent postulates and explicitly stating the conditions required for compatibility with: standard electromagnetism (Maxwell limit), Newtonian gravity and weak-field relativistic tests, and the operational no-signaling structure of quantum correlations. Entanglement and coherence. In this work, the term entanglement is used in an operational and structural sense, referring to the non-separability and coherence of degrees of freedom within a shared substrate. When quantum entanglement in the Bell-test sense is relevant, it is treated strictly within the standard no-signaling framework: correlations arise from shared boundary conditions and global constraints, not from superluminal communication or hidden signaling channels. The paper does not propose modifications to quantum statistics, but clarifies how coherence may be redistributed or effectively suppressed across regimes through interaction with environmental degrees of freedom. This work is intended as a reference “dictionary” paper that locks definitions and consistency requirements across the series, enabling falsifiable comparison with observational data while avoiding retrofitting or duplication of derivations presented elsewhere. Keywords Vacuum impedance; Emergent gravity; Galactic dynamics; Newtonian limit; Effective field theory; Coarse graining; Entanglement (operational); Principle of least action Related Works Paper 1: Empirical Evidence of Baryonic Thresholds (Zenodo: 10.5281/zenodo.18035640) Paper 2: Empirical Baryonic Surface-Density-Dependent Resonances (Zenodo: 10.5281/zenodo.18110723) Paper 3: The Impedance of Space: Emergent Galactic Dynamics (Zenodo: 10.5281/zenodo.18319014) Paper 4: The Impedance of Space II: Deriving Newtonian Gravity from Vacuum Hydrodynamics (Zenodo: 10.5281/zenodo.18354132) Notes This paper does not present new observational data. Its purpose is definitional, structural, and methodological, clarifying how multiple effective descriptions connect across acceleration regimes without modifying established experimental limits.This preprint is part of a multi-paper research program exploring vacuum impedance, emergent gravity, and regime-dependent behavior across galactic, stellar, and quantum scales. Paper 3.5 serves as a definitional and conceptual bridge within the series.