Emergent Schwarzschild Geometry from Lattice Field Medium Dynamics

We demonstrate that the Schwarzschild metric emerges from Lattice Field Medium (LFM) substrate dynamics because measurement apparatus, clocks and rulers, are themselves χ-dependent wave excitations.

A critical distinction exists between GOV-04 (quasi-static) and GOV-02 (wave equation): GOV-04 gives χ = χ₀ − Λ/r producing retrograde precession, but GOV-02 wave dynamics at equilibrium produce χ(r) = χ₀√(1 − rₛ/r) where rₛ = 2GM/c². Clock frequencies scale as ω ∝ χ, giving time dilation gₜₜ = −(1 − rₛ/r). Ruler sizes scale as λ ∝ 1/χ, giving spatial curvature gᵢⱼ = (1 + rₛ/r)δᵢⱼ. The combined metric is the Schwarzschild solution in isotropic coordinates—geometrically identical to standard Schwarzschild.

This resolves a critical objection that LFM, as a scalar field theory, cannot reproduce General Relativity's predictions. Unlike Nordström's scalar gravity (1913), which modifies only g₀₀ and predicts 1/3 of Mercury's perihelion precession, LFM produces full tensor-like phenomenology because both temporal and spatial measurements are substrate-dependent.

Key results:

• Mercury perihelion precession: 43.06 arcsec/century (0.14% from GR's 42.98)
• Gravitational light bending: 1.75 arcsec at solar limb (matches GR exactly)
• GOV-02 equilibrium χ-profile matches √(1-rₛ/r) with RMS residual 0.0118 (vs 0.0130 for linear fit)

The key insight: LFM is not a scalar field propagating through spacetime, it IS the computational substrate from which spacetime geometry emerges. This categorical distinction is what allows a scalar substrate to produce tensor-like phenomenology.