Spin Network: Quantized Space in Loop Quantum Gravity (2D)

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 2D simulator draws that graph directly, laid out as a quantum tetrahedron, 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, read off an illustrative node-volume estimate that correctly vanishes on any 3-valent node, 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.