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Spin Network: Quantized Space in Loop Quantum Gravity

Interactive 3D spin-network simulator: build a Loop Quantum Gravity quantum tetrahedron, tune half-integer spin labels on its links, watch quantized area emerge from the LQG area operator, and run 1-to-4 Pachner moves to refine the spin foam.

Quantum Physics3DAdvanced60 FPS📱 Mobile-adapted

Loop Quantum Gravity replaces smooth spacetime with a combinatorial spin network — a graph of volume-quanta nodes joined by area-quanta links, each link labelled with a half-integer spin j. This simulator renders a real 3D quantum tetrahedron built from that graph and computes its area spectrum with the actual LQG area-operator eigenvalue formula, A_j = 8πγl_P²√(j(j+1)). Drag a link's spin and watch its area jump between the theory's discrete allowed values instead of varying smoothly, or run a 1→4 Pachner move to refine one node of volume into four, the same combinatorial step spin foam models sum over to define quantum gravitational dynamics.

⚙ Under the hood

Build and refine a 3D Loop Quantum Gravity spin network: tune half-integer spin labels on the links of a quantum tetrahedron, watch quantized area emerge from the real LQG area-operator formula, and run 1-to-4 Pachner moves to refine the spin foam.

loop quantum gravityspin networkspin foamquantum gravityarea quantizationAshtekar variables

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install