Minimum Length from Quantum Mechanics and Classical General Relativity

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 lP. This suggests a Planck-size 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 lP. Our results imply a device independent limit on possible position measurements.