Quantum superpositions of Minkowski spacetime

Abstract

Within any anticipated unifying theory of quantum gravity, it should be meaningful to combine the fundamental notions of quantum superposition and spacetime to obtain so-called "spacetime superpositions": that is, quantum superpositions of different spacetimes not related by a global coordinate transformation. Here we consider the quantum-gravitational effects produced by superpositions of periodically identified Minkowski spacetime (i.e.\ Minkowski spacetime with a periodic boundary condition) with different characteristic lengths. By coupling relativistic quantum matter to fields on such a spacetime background (which we model using the Unruh-deWitt particle detector model), we are able to show how one can in-principle "measure" the field-theoretic effects produced by such a spacetime. We show that the detector's response exhibits discontinuous resonances at rational ratios of the superposed periodic length scale.