Schr\"odinger's cat for de Sitter spacetime

TL;DR

This paper introduces a novel phenomenological framework for modeling quantum superpositions of spacetime geometries, specifically applied to de Sitter space, revealing scenarios where quantum spacetime effects mimic superpositions of trajectories.

Contribution

It proposes a new method to assign a Hilbert space to spacetime, enabling the study of superpositions of geometries and their operational indistinguishability from flat space trajectory superpositions.

Findings

Quantum spacetime effects can be indistinguishable from superpositions of trajectories in flat space.

The framework links field correlations to the distinguishability of quantum geometries.

Application to de Sitter space demonstrates potential for new quantum gravity insights.

Abstract

Quantum gravity is expected to contain descriptions of semiclassical spacetime geometries in quantum superpositions. To date, no framework for modelling such superpositions has been devised. Here, we provide a new phenomenological description for the response of quantum probes (i.e. Unruh-deWitt detectors) on a spacetime manifold in quantum superposition. By introducing an additional control degree of freedom, one can assign a Hilbert space to the spacetime, allowing it to exist in a superposition of spatial or curvature states. Applying this approach to static de Sitter space, we discover scenarios in which the effects produced by the quantum spacetime are operationally indistinguishable from those induced by superpositions of Rindler trajectories in Minkowski spacetime. The distinguishability of such quantum spacetimes from superpositions of trajectories in flat space reduces to the equivalence or non-equivalence of the field correlations between the superposed amplitudes.