Minimum Length from Quantum Mechanics and Classical General Relativity

TL;DR

This paper establishes fundamental limits on position measurements derived from quantum mechanics and classical general relativity, indicating a minimum length scale of the Planck length that constrains measurement precision.

Contribution

It introduces a fundamental limit on measurement accuracy based on the Planck length, applicable even to highly precise interferometers like LIGO.

Findings

Any probe must be larger than the Planck length

Interferometers are limited to precision on the order of the Planck length

Results imply a device-independent fundamental limit on position measurement accuracy

Abstract

We derive fundamental limits on measurements of position, arising from quantum mechanics and classical general relativity. First, we show that any primitive probe or target used in an experiment must be larger than the Planck length, $l_P$. This suggests a Planck-size {\it minimum ball} of uncertainty in any measurement. Next, we study interferometers (such as LIGO) whose precision is much finer than the size of any individual components and hence are not obviously limited by the minimum ball. Nevertheless, we deduce a fundamental limit on their accuracy of order $l_P$. Our results imply a {\it device independent} limit on possible position measurements.