Quantum superpositions of Minkowski spacetime

TL;DR

This paper explores quantum superpositions of Minkowski spacetime with different periodic lengths, demonstrating how relativistic quantum matter detectors can reveal measurable effects, including discontinuous resonances at rational ratios.

Contribution

It introduces a model for spacetime superpositions involving different periodic lengths and analyzes their measurable effects using the Unruh-deWitt detector.

Findings

Detector response shows discontinuous resonances at rational length ratios

Quantum superpositions of spacetime can produce observable field-theoretic effects

The approach enables probing quantum gravitational effects in simplified models

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.