Space-time superpositions as fluctuating geometries

TL;DR

This paper develops a covariant framework for describing superpositions of black holes and quantum fluctuations in spacetime, revealing quantum corrections to gravity and new bounds on fluctuations in the weak-field limit.

Contribution

It introduces a covariant formulation of superposed black hole geometries incorporating quantum fluctuations, extending previous models to include quantum corrections in weak-field gravity.

Findings

Quantum corrections to Newton's potential in semiclassical states.

New bounds on quantum fluctuations derived from covariance conditions.

Framework enables predictions of quantum effects in gravity for observational tests.

Abstract

Superpositions of black holes can be described geometrically using a combined canonical formulation for space-time and quantum states. A previously introduced black-hole model that includes quantum fluctuations of metric components is shown here to give full access to the corresponding space-time geometry of weak-field gravity in terms of suitable line elements with quantum corrections. These results can be interpreted as providing covariant formulations of the gravitational force implied by a distribution of black holes in superposition. They can also be understood as a distribution of quantum matter constituents in superposition for a single black hole. A detailed analysis in the weak-field limit reveals quantum corrections to Newton's potential in generic semiclassical states, as well as new bounds on quantum fluctuations, implied by the covariance condition, rather than the usual uncertainty principle. These results provide additional control on quantum effects in Newton's potential that can be used in a broad range of predictions to be compared with observations.