Gravitational quantum speed limit

TL;DR

This paper explores how quantum speed limits are affected in superpositions of spherically symmetric masses within canonical quantum gravity, revealing potential improvements over traditional bounds and discussing measurement implications.

Contribution

It introduces a novel analysis of quantum speed limits in quantum gravity contexts, showing how superpositions can tighten these bounds compared to classical states.

Findings

Quantum speed limits can be improved by superposing spherically symmetric states.

Superpositions between states with different ADM energies and mass densities are feasible.

Implications for measuring quantum gravitational effects are discussed.

Abstract

While playing an important role in the foundations of quantum theory, Quantum Speed Limits (QSL) have no role in discussions about the search for quantum gravity. We fill this gap by analysing what QSL arises when superposing spherically symmetric masses in canonical quantum gravity. By this procedure, we find that the quantum mechanical Mandelstam-Tamm and Margolus-Levitin bounds can be improved by superposing a spherically symmetric, static and asymptotically flat spacetime between states with different ADM energies and mass densities. We discuss the feasibility and significance of measuring times via these superpositions.