Phase Coherence Simulator

Adjoint Phase Logic

Each edge carries a phase phi. When traversing:

Forward (U -> V, where U < V): apply +phi
Backward (U -> V, where U > V): apply -phi (adjoint)

This ensures gauge invariance around closed loops.

Coherence Factor

After N random walks, we compute the vector sum:

The coherence factor is:

R -> 1.0: All phases align (Global Monolith)
R -> 0.0: Phases cancel (decoherent)

Information Entropy as Geometry

When the Coherence Factor remains high, we measure the "elasticity" of the manifold—what Verlinde calls the "dark" gravitational force that emerges from the displacement of entropy.

This mirrors the Van Raamsdonk hypothesis: entanglement between quantum building blocks acts as the "glue" that creates the continuous experience of macroscopic space.

The Holographic Lens

The simulation demonstrates a Holographic principle. Even as the signal wanders across a complex lattice, the Adjoint Phase Logic acts as a holographic screen.

The global state (Mean Phase Shift) is encoded in the network's collective geometry, making it resistant to the thermal noise of the Lorentzian bath.

From Graphs to Particles

By deriving phase purely from connectivity, we confirm that matter is essentially a stable pocket of phase-locked information in an otherwise chaotic graph.

Particles are not things in space; they are the result of coherent information locking within the graph itself—the Spatial Electron.

Theoretical References

Entropic Gravity (Verlinde): Gravity as a consequence of information entropy.

It from Qubit (Wheeler/Van Raamsdonk): The universe emerges from underlying bits of quantum information.

Loop Quantum Gravity: Space as "spin networks" where geometry is discrete and emergent.