Quantum gravity and time order

Title: Quantum gravity and time order

Abstract: Gravitational path integrals can be classified into two categories: those allowing superposition of time order and those that do not. This distinction is illustrated using different versions of 2D quantum Regge calculus. In the ordinary case, the Lorentzian path integral encompasses geometries that connect pairs of boundary points in both timelike directions. In contrast, when edge causal signature is fixed, as in fixed-topology triangulation models, such superposition of time order is excluded. Consequently, effects derived from superposition of time order could potentially distinguish and falsify theories of quantum gravity.

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• Original versions: Article v1.0