A new geometry reveals quantum chaos hiding in plain sight

By treating quantum states as probability distributions and measuring the optimal-transport distance between them, the authors find that chaotic systems occupy a lower-dimensional geometry than orderly ones. The method recovers Lyapunov exponents directly from state-space distances, and spots quantum scar states — islands of order inside chaos — as branching structures in the geometry. Because black holes are maximally chaotic in holography, this dimensional collapse may be the fingerprint of an emergent holographic space.