Relativistic Optics, Mechanical Reduction of Classical GR Tests, and Substrate Non-linear Saturation Limits (Paper 5)

AbstractThis paper presents a deterministic optical-mechanical reduction of General Relativity (GR)phenomenology to the continuum mechanics of an inhomogeneous elastic substrate (FieldDynamics, Document #0). The postulation of 4D pseudo-Riemannian spacetime curvature iseliminated. We demonstrate that: (1) Gravitational Potential as a Pressure Gradient: Spaceis strictly Euclidean (R3). Gravitational attraction represents a radial hydrostatic pressure drainof an incompressible elastic monolith (ρ0 ≈ 4.30 × 1018 kg/m3, μ0 ≈ 3.865 × 1035 Pa) towardcavitation density deficits (ρin ≡ 0). Newton’s constant is reduced from substrate parametersas G = P0VpRp/m2p, where P0 ≈ 1.90 × 10−3 Pa is the global cosmological background pressureand Vp = 2π2R3p/Λ2 ≈ 1.167 × 10−46 m3 is the exact toroidal cavity volume of the proton(matching Paper 1). This yields G ≈ 6.67 × 10−11 m3/(kg · s2) and GM ≈ 1.326 × 1020 m3/s2(0.05% divergence from astronomy), predicting the cosmological evolution G(P0). (2) First-Order Effects (Clock Dilation / GPS, Factor 1): Ambient hydrostatic decompression neara mass decreases local shear stiffness: μ(r) = μ0(1 − 2GM /(c2r)). For stationary atomicclocks, this strictly derives the first-principles frequency shift δν/ν = δc/c = ∆Φ/c2 withfactor 1, matching GPS/GLONASS satellite telemetry (+45.7 μs/day, 0.5% precision) and Pound–Rebka measurements. (3) Relativistic Optics (Factor 2): The refractive index n(r) ≈ 1 +2 GMc2r is accepted empirically based on 5 independent tests: solar light bending (θ ≈ 1.751′′,0.05%), Shapiro radar delay (∆t ≈ 218 μs, Cassini, 0.2%), Lunar Laser Ranging (LLR), Martianranging (Viking, MRO), and gravitational lensing. (4) Methodological Status of Factor 2: Weformally distinguish that while Factor 1 is derived from local elasticity μ(r), Factor 2 cannotbe derived from a scalar eikonal equation (which yields only 0.875′′). Flawed derivations(εrr + εθθ , longitudinal compressibility, ray path curvature) are explicitly rejected. Candidatemechanisms (θ-polarization of Cosserat media and wave viscosity ηwave) are classified as an**open variational problem**. (5) Gravitational Waves (LIGO, h ∼ 10−21): LIGO signalsare reduced to transverse quadrupolar shear waves of the elastic monolith without metricripples, matching h ∼ 10−21 under the condition Geff = G at cosmological pressure P0. (6)Substrate Saturation Limit (Breit–Wheeler): The acoustic power flux ceiling of the monolithis Πsat = μ0c ≈ 1.16 × 1040 W/cm2. Under the critical strain hypothesis εcrit = α, a laserthreshold Ilasersat ≈ 6.16 × 1035 W/cm2 is predicted, above which continuum acoustic lockingsuppresses e+e− pair production.