Limitation to Quantum Measurements of Spacetime Distances

TL;DR

This paper investigates the fundamental limits of quantum measurements of spacetime distances, revealing a length-dependent minimum error and its implications for quantum decoherence and metric uncertainty.

Contribution

It demonstrates that the minimum measurement error scales with the one-third power of the length, challenging previous assumptions and linking measurement uncertainty to decoherence effects.

Findings

Minimum error in length measurement scales as length^(1/3)

Quantum decoherence occurs for particles heavier than the Planck mass

Uncertainty in energy-momentum measurements is also established

Abstract

Inspired by the work of Wheeler among others, we have studied the problem of quantum measurements of space-time distances by applying the general principles of quantum mechanics as well as those of general relativity. Contrary to the folklore, the minimum error in the measurement of a length is shown to be proportional to the one-third power of the length itself. This uncertainty in space-time measurements implies an uncertainty of the space-time metric and yields quantum decoherence for particles heavier than the Planck mass. There is also a corresponding minimum error in energy-momentum measurements.