Spacetime structure and vacuum entanglement

TL;DR

This paper investigates how vacuum fluctuations and entanglement of a scalar field can reveal the global topology of spacetime, even when local geometry is identical, through detector correlations and entanglement harvesting.

Contribution

It demonstrates that vacuum entanglement and fluctuations can be used to distinguish different topologies of spacetime that share the same local geometry.

Findings

Detector correlations depend on spacetime topology.

Vacuum entanglement harvesting reveals topological features.

Preferred directions in topology influence detector measurements.

Abstract

We study the role that both vacuum fluctuations and vacuum entanglement of a scalar field play in identifying the spacetime topology, which is not prescribed from first principles---neither in general relativity or quantum gravity. We analyze how the entanglement and observable correlations acquired between two particle detectors are sensitive to the spatial topology of spacetime. We examine the detector's time evolution to all orders in perturbation theory and then study the phenomenon of vacuum entanglement harvesting in Minkowski spacetime and two flat topologically distinct spacetimes constructed from identifications of the Minkowski space. We show that, for instance, if the spatial topology induces a preferred direction, this direction may be inferred from the dependence of correlations between the two detectors on their orientation. We therefore show that vacuum fluctuations and vacuum entanglement harvesting makes it, in principle, possible to distinguish spacetimes with identical local geometry that differ only in their topology.