On the Precision of a Length Measurement

TL;DR

This paper explores the fundamental limits on length measurement precision imposed by quantum mechanics and general relativity, demonstrating the existence of a minimal measurable length scale, the Planck length.

Contribution

It establishes that no device can measure lengths shorter than the Planck length due to combined quantum and gravitational constraints.

Findings

Existence of a minimal length scale (Planck length)

Operational limits on length measurement precision

Quantum-gravity principles imply spacetime discreteness

Abstract

We show that quantum mechanics and general relativity imply the existence of a minimal length. To be more precise, we show that no operational device subject to quantum mechanics, general relativity and causality could exclude the discreteness of spacetime on lengths shorter than the Planck length. We then consider the fundamental limit coming from quantum mechanics, general relativity and causality on the precision of the measurement of a length.