Gravitational Lensing

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What Is It?

This experiment is a lensing analogue built from a relaxed lattice potential. A compact mass source is stamped into a two-dimensional field, then that field is relaxed by local updates until it becomes a smooth potential-like structure.

The relaxed field is converted into a refractive index map using the relation n(x) = 1 + α·φ(x). Rays then move through that index map. They bend toward regions of higher index, producing an optical analogue of gravitational lensing.

What It Tests

The experiment asks whether lensing-like behaviour can be produced from a locally generated field rather than from an analytic potential. The mass does not create a hard-coded 1/r function. It creates a source that is relaxed through neighbour updates.

The ray paths test the resulting effective geometry. If the field produces a coherent index gradient, rays bend around the source. If the gradient is weak or incoherent, the lensing effect collapses. That makes this a useful bridge between local field transport and emergent geometric behaviour.

How It Works

A local mass source is injected into a scalar field. The field is repeatedly relaxed by averaging against local neighbours with a small source injection and decay term. The outer boundary is clamped to zero, giving a finite bounded domain.

Once the refractive map is built, parallel rays are traced through it by midpoint-style integration. Each ray samples the local refractive index and its gradient from the grid. Its direction changes according to the transverse part of that gradient, which is the local optical steering term.

The pulse wavefront advances by equal optical path length rather than equal coordinate distance. Rays that pass through higher-index regions near the mass lag behind. The visible bowed wavefront is the Shapiro-delay analogue.

What Is Not Hard-Coded

• No analytic 1/r potential is imposed.
• No geodesic equation is solved.
• No metric tensor is provided to the renderer.
• No final bent ray path is painted into the animation.

The potential is produced by local relaxation. The rays respond to the local refractive index field. The wavefront lag comes from optical path length accumulated along each traced ray.

Why It Matters

This experiment is not a claim that general relativity has been reconstructed from CAELIX. It is a controlled optical analogue. Its value is that it makes delay and bending visible using a field produced by local lattice work rather than a pre-written continuum formula.

For CAELIX, that distinction matters. Lensing-style behaviour is only useful if the substrate has to do the work. Here the field, the refractive map and the ray delay remain inspectable at every stage, which makes the experiment a clear test of local-field-to-effective-geometry behaviour.