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.

预计量子引力将包含对量子叠加中半经典时空几何的描述。迄今为止，还没有设计出对这种叠加进行建模的框架。在这里，我们为量子探测器（即 Unruh-deWitt 探测器）在量子叠加时空流形上的响应提供了一种新的现象学描述。通过引入额外的控制自由度，人们可以将希尔伯特空间分配给时空，使其存在于空间或曲率状态的叠加中。将这种方法应用于静态德西特空间，我们发现了量子时空产生的效应与闵可夫斯基时空中林德勒轨迹叠加引起的效应在操作上无法区分的场景。