Entanglement Entropy: Unifying the Quantum Origins of Gravity, Mass, Time, and Cosmic Structure

We present an emergent/entropic gravity framework in which quantum entanglement entropy Sent generates spacetime curvature and derives Newton’s constant G from first principles. A single scalar field encodes vacuum entanglement deficits, linking mass–information equivalence to galactic dynamics (flat rotation curves, Baryonic Tully–Fisher). We fix G de novo via a wedge-sharing constant gshare≈7.4 gshare motivated by group-field/tensor constructions and transport geometry, then validate units, normalizations, and the electron 1-bit anchor with analytic derivations and numerics. This deposit includes: the main paper, a microscopic supplement (GFT/tensor underpinnings), rigorous derivations/validations, a concise de-novo G note, and a plain-language foundation of gshare with a reproducible script. File 1 — Entanglement Entropy: Unifying the Quantum Origins of Gravity, Mass, Time, and Cosmic Structure This paper introduces a single real scalar field, Sent(x), that encodes local deficits of vacuum entanglement and whose gradients produce gravitational phenomena. Mass is identified with information via a universal conversion constant κm\kappa_mκm (kg/bit), with the electron providing the calibration point and operational anchor (one bit in the free-fermion baseline). On galactic scales, solutions of the entanglement–Poisson limit reproduce flat rotation curves and the Baryonic Tully–Fisher scaling, without invoking particulate dark matter. Black holes appear as maximal-deficit configurations, linking the field-theoretic picture to the Bekenstein–Hawking area law and clarifying the role of horizons as entanglement boundaries. The framework also sketches how temporal order and the “many pasts” structure of histories can emerge from coarse-grained entanglement flow, connecting information geometry to causal structure. Across these domains, a single constant κm\kappa_mκm ties particle masses to large-scale dynamics. File 2 — Supplement: Group Field / Tensor Underpinnings of the Entropic Scalar EFT This supplement develops microscopic underpinnings for the macroscopic Sent field using group-field/tensor-network constructions. It shows how spin-network–like degrees of freedom, coarse-grained over layers, yield an area-law capacity corrected by diffusive channel sharing, thereby motivating the universal +1/2+1/2+1/2 “sharing” exponent in the renormalization of κm\kappa_mκm. The coarse-graining flow explains how a continuum scalar description and its effective coupling κ=1/κm\kappa = 1/\kappa_mκ=1/κm emerge from discrete information carriers, while a geometric sharing factor gshare enters the normalization. The same microstructure clarifies why horizons extremize entanglement deficits and how macroscopic curvature responds to microscopic connectivity. Conceptually, the construction links “many pasts” to sums over entanglement graphs, with classical spacetimes arising as typical coarse-grained phases. The result is a concrete bridge from group-field/tensor microdynamics to the effective entanglement-scalar EFT used phenomenologically. File 3 — Derivations and Numerical Validations for the Entropic Scalar EFT This technical companion fixes the covariant action, equations of motion, and stress–energy for Sent, and establishes units and normalizations unambiguously. A top-down derivation of κm\kappa_mκm runs from the Planck scale to the electron’s Compton scale with total exponent 5/2 5/2 5/2 (area law +2+2+2 plus channel-sharing +1/2+1/2+1/2), producing a no-fit prediction that matches the electron calibration at the ∼0.1% level. The nontrivial +1/2+1/2+1/2 sharing exponent is validated independently by outward-biased random-walk numerics and a layered random-tensor network. Sent is defined operationally as a vacuum-subtracted von Neumann entropy; a free Dirac excitation yields a universal 111-bit baseline, while interacting toy models (Gross–Neveu; mini-Yukawa) demonstrate that interaction-generated mass shifts track interaction-generated entanglement in the weak-coupling regime. In the static limit, solving the disk Green’s function gives ΔS(R)∝[1+ln⁡(R/Rd)]\Delta S(R) \propto [1+\ln(R/R_d)]ΔS(R)∝[1+ln(R/Rd)] and, via a linearized entropic force law, recovers the Baryonic Tully–Fisher relation with the correct slope and a physically set zero-point. Together, these results make the framework tightly constrained and reproducible from definition to prediction. File 4 — Entanglement–Scalar Derivation of G (De Novo G) This note shows how Newton’s constant G is fixed without gravitational data once a single, dimensionless wedge-sharing constant gshare is specified in the entanglement-scalar EFT (“Chinitz EFT”). The logic is minimal: identify mass with information via κm\kappa_mκm using the electron as an operational anchor (one bit in the free-fermion baseline), propagate that calibration through the EFT’s coarse-graining to macroscales, and read off G. With gshare ⁣≈ ⁣7.4 (the value justified independently in File 5), the prediction for G matches CODATA at high precision, tying together the microscopic information-mass relation and macroscopic gravity with no astrophysical fits. The derivation is fully reproducible: a short Python appendix computes the forward map gshare ⁣→ ⁣G and the inverse G ⁣→ ⁣gshare from constants only. The result strengthens the program’s core claim—gravity emerges as entanglement-mediated response—by exhibiting a concrete de-novo determination of G from informational first principles. File 5 — Theoretical Foundations of the Wedge-Sharing Constant g_share File 5 explains, in plain terms, how we pin down the “wedge-sharing” constant that normalizes the theory. The idea is simple: each step of information flow is limited to a cone on the sphere (that sets a baseline amount of spread), and real transport has some memory from one step to the next (that boosts the baseline by a fixed multiplier). The file shows how to get both pieces cleanly and reproducibly: the cone baseline comes from a closed-form geometric calculation (no simulation), and the memory is estimated once from a standard nearest-neighbor graph on the sphere and then clipped by a conservative geometric cap so we can’t overstate it. With a ~62° cone and moderate memory, the product lands naturally at about 7.4—well inside conservative upper limits and with the right behavior in all edge cases (it shrinks to zero for a vanishing cone and grows smoothly as the cone widens or memory increases). A short script at the end computes everything and scans cone sizes so anyone can verify where ~7.4 appears.