Description This paper presents a novel mechanical derivation of Newton’s gravitational constant (G) by modeling the physical vacuum as a homogeneous, barotropic quantum condensate. While standard General Relativity treats G as a fundamental empirical constant, this research proposes that gravity emerges from the equilibrium between the vacuum's mechanical bulk modulus and geometric curvature. Core Theoretical Contributions: The Stiffness Matching Principle: We demonstrate that the mechanical stiffness of a dark-matter medium (K = ρm * c²) is identically equal to the Einstein–Hilbert (EH) prefactor. Empirical Consistency Check: The work verifies the identity G = (Λ * c⁴) / (8π * uν), where Λ is the cosmological constant and uν is the vacuum energy density. Gravity as Emergent Elasticity: By treating the Einstein–Hilbert action as the "stress-strain" equation for the universal medium, G is transformed from a bare parameter into a calculable property of the vacuum condensate. Methodology: The derivation provides a unique correlation between three established pillars of physics: Gross–Pitaevskii Equation: Used to define the hydrodynamic framework of the vacuum. Heat Kernel Expansion: Utilized in the Appendix to compute the one-loop induced gravity terms. Friedmann Cosmology: Applied to anchor the mechanical results to current observational data. Phenomenological Impact: This "Condensate Link Framework" offers potential resolutions to contemporary cosmological tensions, including the unexpectedly rapid growth of high-redshift galaxies observed by the James Webb Space Telescope (JWST) and the "cusp-core" problem in dark matter distribution. By linking gravitational strength to local field pressure, the model suggests a dynamic nature for G across different cosmological epochs.
Robin Skavberg (Tue,) studied this question.