Gödelian Phases of Time: Emergent Rotation and Dimensionality from Quantum Temporal Correlations

<b>Gödelian Phases of Time </b>proposes that spacetime—and even its dimensionality and global rotation—emerge from patterns of quantum “echoes,” i.e. two‑time correlation functions of non‑commuting observables. By splitting these correlators into a symmetric part (defining an emergent metric) and an antisymmetric “vorticity” part, the framework shows how Gödel‑like rotating universes with closed causal loops can arise as informational phases. Dimensionality itself becomes an order parameter equal to the rank of the correlation matrix, allowing transitions between 3D, higher‑D, or lower‑D emergent spaces. A cosmological implication is that if our universe formed inside a rotating black hole, inherited informational vorticity could have seeded a primordial Gödel phase, potentially leaving observable imprints in large‑scale anisotropies.