3D Quantum Field Theory: Mediator Field Lattice

This is the volumetric companion to the 2D virtual-particle exchange simulator: rather than tracing a single Feynman-diagram-style line between two particles, it renders the whole mediator field as a live 3D lattice sourced by both particles' Yukawa propagators, φ(x) = g·e⁻ᵐʳ¹/r₁ + g·e⁻ᵐʳ²/r₂. Each particle's motion is driven by numerically sampling the local field gradient at its own position — a genuine field-to-force measurement rather than a plugged-in formula. Tune the coupling g and the mediator's mass m and watch the field's visible bubble expand toward infinite range at m = 0 or collapse into a tight, exponentially screened shell as m grows, exactly as it does for the real photon versus the massive W/Z bosons.