Crystalline lattice binding • Chaotic atomic wobble averaging into stable macroscopic directional pull
While the previous sections describe the microscopic cause, this simulation demonstrates the macroscopic effect. By binding atoms into crystalline lattices, we see how the chaotic atomic wobble averages out into a stable, directional pull between macroscopic bodies.
1. The "Slab" Integral: This simulation projects a 3D volumetric interaction onto a 2D plane. To maintain physical fidelity, we do not use the point-particle law (1/r2) nor the infinite line law (1/r). Instead, we model the particles as Finite Cylindrical Slices (Slabs) of thickness L.
The force law is derived by integrating the 3D gravitational stress over the finite z-axis thickness of the slab:
In the simulation regime where particle separation (r) is comparable to the slice thickness (L), the effective power law of this integral is F ∝ 1/r1.5. This guarantees that potential energy U(r) ∝ -1/r0.5 is strictly conserved within this dimensionality.
2. Discrete Time as a Proxy: Like the first simulation, this engine utilizes discrete time steps. In standard physics engines, integration error is viewed as a flaw to be corrected to simulate instantaneous action-at-a-distance (infinite signal speed). In the CMFT framework, these discrete steps act as a deliberate proxy for delayed momentum transfer. By allowing the 'error' of discrete updates to persist, we capture the physical consequences of the finite speed of light (c), where momentum phase accumulation creates the emergent directional bias we perceive as gravity. Discrete time steps are utilized as a deliberate proxy for Phase Accumulation to demonstrate the robustness of the drift emergence.