Probing a Gravitational Cat State

TL;DR

This paper explores the quantum superposition of a mass in gravity, called a gravitational cat state, analyzing its force fluctuations and proposing measurement methods, thereby offering a testbed for quantum gravity theories.

Contribution

It introduces a simple model of a gravitational two-state system and examines its measurable force fluctuations using classical and quantum probes, grounded in standard quantum mechanics and classical gravity.

Findings

Mass density fluctuations are significant and comparable to the mean.

Classical probes detect non-Markovian force fluctuations.

Quantum probes may exhibit Rabi oscillations in strong coupling regimes.

Abstract

We investigate the nature of a gravitational two-state system (G2S) in the simplest setup in Newtonian gravity. In a quantum description of matter a single motionless massive particle can in principle be in a superposition state of two spatially-separated locations. This superposition state in gravity, or gravitational cat state, would lead to fluctuations in the Newtonian force exerted on a nearby test particle. The central quantity of importance for this inquiry is the energy density correlation. This corresponds to the noise kernel in stochastic gravity theory, evaluated in the weak field nonrelativistic limit. In this limit, quantum fluctuations of the stress energy tensor manifest as the fluctuations of the Newtonian force. We describe the properties of such a G2S system and present two ways of measuring the cat state for the Newtonian force, one by way of a classical probe, the other a quantum harmonic oscillator. Our findings include: (i) mass density fluctuations persist even in single particle systems, and they are of the same order of magnitude as the mean; (ii) a classical probe generically records a non-Markovian fluctuating force; (iii) a quantum probe interacting with the G2S system may undergo Rabi oscillations in a strong coupling regime. This simple prototypical gravitational quantum system could provide a robust testing ground to compare predictions from alternative quantum theories, since the results reported here are based on standard quantum mechanics and classical gravity.