Quantum Rods and Clock in a Gravitational Universe

TL;DR

This paper explores how quantum fluctuations of reference systems like rods and clocks enable defining local observables in quantum gravity, addressing a fundamental puzzle about reconciling local measurements with dynamical spacetime.

Contribution

It demonstrates that quantum fluctuations of reference systems are essential for defining local operators in quantum gravity, providing a quantum realization of classical intuition.

Findings

Quantum fluctuations of rods and clocks are crucial for local observables.

The approach offers a way to reconcile local measurements with dynamical spacetime.

Addresses the puzzle of defining local operators in quantum gravity.

Abstract

Local operators are the basic observables in quantum field theory which encode the physics observed by a local experimentalist. However, when gravity is dynamical, diffeomorphism symmetries are gauged which apparently obstructs a sensible definition of local operators, as different locations in spacetime are connected by these gauged symmetries. This consideration brings in the puzzle of reconciling our empirical world with quantum gravity. Intuitively, this puzzle can be avoided using relatively defined observables when there exists a natural reference system such as a distribution of galaxies in our universe. Nevertheless, this intuition is classical as the rods and clock defined in this way may also have quantum fluctuations so it is not a priori clear if it can be realized in the quantum regime. In this letter, we provide an affirmative answer to this question. Interestingly, we notice that the quantum fluctuations of the reference system are in fact essential for the realization of the above intuition in the quantum regime.