The Dual-Field Interface Model (DFIM): Integrated Quantum Gravity, Information Recovery, and Cosmological Implications

The Dual-Field Interface Model (DFIM) proposes a reformulation of spacetime as a physical, high-tension membrane separating two fundamental 5D bulk fields: a positive bulk (observable matter) and a negative bulk (inverted reservoir). In this framework, gravity is derived as a "mechanical weld" (stiffness) created by matter density, while light is modeled as a surface ripple upon this interface. Version 3.5 introduces a fully covariant scalar-tensor formulation to preserve local Lorentz invariance while addressing major open problems in physics. The model resolves the Black Hole Information Paradox by deriving a non-singular Hawking temperature and ensuring unitarity via a continuous interface that follows the Page Curve during evaporation. Additionally, it offers a geometric resolution to the Hubble Tension by predicting non-uniform cosmic expansion governed by local density-dependent stiffness. Key Theoretical Advances in Version 3.5 1. Resolution of the Information Paradox Mechanical Dynamics: The model treats the event horizon as a "stiffness horizon" acting as a high-pass filter. It reflects low-frequency perturbations (echoes) but admits high-momentum infallers, preserving the Equivalence Principle for macroscopic objects (). Leakage Mechanism: Information recovery is governed by strain-rate dependent leakage modeled via non-adiabatic Landau-Zener transitions. This predicts high leakage during rapid formation (15–25%) and negligible leakage in stable, mature black holes. Unitarity: Explicit derivation of entropy evolution confirms that entanglement threads ("elastic links") purify radiation post-Page time, restoring unitarity. 2. Cosmological Implications & Hubble Tension Non-Uniform Expansion: The modified Friedmann equation introduces density-dependent stiffness terms. High-density regions (clusters) are "welded" rigid (recovering standard GR), while low-density voids possess a "loose" interface that expands faster due to kinetic relaxation. Resolution: This distinct behavior resolves the Hubble Tension geometrically: early-universe probes measure the stiffer background, while local void measurements probe the faster-expanding regimes. 3. Dark Matter as Stable Remnants PBH Stability: Primordial Black Holes (PBHs) do not evaporate completely but stabilize as "frozen knots" or saturated welds when the density reaches a critical saturation point (). These remnants (mass range to ) serve as stable cold dark matter candidates. Compilation Contents (Companion Notes & Extensions) Note 1 (Entanglement): Validates entanglement formation as "weld resonance" using recent attosecond delay measurements. Note 2 (Top-Down Cosmology): Aligns weld evolution with Hawking-Hertog’s quantum Darwinism. Notes 3 & 4 (Equivalence Principle): Formalizes the "soft breach" of the EP, deriving frequency-dependent horizon impedance. Note 5 (Solidity): Explains quantum emptiness and solidity via EM feedback stiffening. Note 6 (Higgs Integration): Derives particle mass from weld interactions, mapping tension modulation to Higgs-like potentials. Note 7 (Twistors): Integrates Twistor theory to explain non-locality as geometric projections. Note 8 (Migdal Effect): Correlates nuclear recoil lags with weld hysteresis to validate non-adiabatic leakage. Note 9 (Fine-Structure Constant): Proposes a geometric derivation of based on weld stability angles. Note 10 (Big Bang): Models the Big Bang as a primordial weld branching event ("Leaf Topology"). Note 11 (Superconducting Origins): Analogizes the dual fields to Type I/II superconductors and the weld to a Josephson junction. Extensions: Includes geometric derivations for modified metrics and an electromagnetic extension treating waves as membrane mediators. Keywords Quantum Gravity, Dual-Field Interface Model, Information Paradox, Black Hole Remnants, Dark Matter, Hubble Tension, Landau-Zener Transitions, Braneworld, Superconductivity Analogy.