Temporal Wormholes From Temporal Quantum Correlations

Recent developments in quantum theory suggest a unified treatment of space and time, where spatial and temporal correlations can be regarded as equivalent. Specifically, spatial correlations between two systems at one time have been shown to correspond to temporal correlations of a single system at two times, via partial transposition. This formal equivalence implies a revised framework in which temporal correlations are also defined on a tensor product of Hilbert spaces. In this work, we extend these ideas to the AdS/CFT correspondence by proposing that the thermofield double state—traditionally understood as encoding spatial correlations between two CFTs—is equivalent to temporal correlations of a single CFT across two times. On the gravity side, this implies that temporal correlations correspond to one black hole at different times or two temporally separated black holes connected by an Einstein–Rosen bridge. We interpret this connection as a temporal wormhole and explore its properties, concluding that such wormholes are nontraversable. We further analyze the dual spacetime of these temporal wormholes in the context of BTZ black holes and demonstrate that interchanging space and time in the BTZ metric yields a spacetime analogous to static de Sitter space. This leads us to propose a novel link between the interior geometry of BTZ black holes and the dS/CFT correspondence, wherein quantum temporal correlations are dual to de Sitter spacetime. This framework may provide new insights into the nature of quantum gravity and spacetime structure.