New J. Phys. 22 (2020) 093073 https://doi.org/10.1088/1367-2630/abb43c PAPER Testing generalised uncertainty principles through quantum OPEN ACCESS noise RECEIVED 27 May 2020 Parth Girdhar∗ and Andrew C Doherty REVISED 25 August 2020 Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, Sydney, NSW 2006, Australia ∗ Author to whom any correspondence should be addressed. ACCEPTED FOR PUBLICATION 1 September 2020 E-mail:
[email protected] PUBLISHED Keywords: quantum gravity, optomechanics, LIGO, Planck scale, generalised uncertainty principle, radiation pressure noise 23 September 2020 Abstract Original content from this work may be used Motivated by several approaches to quantum gravity, there is a considerable literature on under the terms of the Creative Commons generalised uncertainty principles particularly through modification of the canonical Attribution 4.0 licence. position–momentum commutation relations. Some of these modified relations are also consistent Any further distribution with general principles that may be supposed of any physical theory. Such modified commutators of this work must maintain attribution to have significant observable consequences. Here we study the noisy behaviour of an the author(s) and the title of the work, journal optomechanical system assuming a certain commonly studied modified commutator. From recent citation and DOI. observations of radiation pressure noise in tabletop optomechanical experiments as well as the position noise spectrum of advanced LIGO we derive bounds on the modified commutator. We find how such experiments can be adjusted to provide significant improvements in such bounds, potentially surpassing those from sub-atomic measurements. 1. Introduction Quantum mechanics and the general theory of relativity have both been successful at explaining most of our observations of the Universe, the former is an accurate framework for predictions of phenomena at the microscopic scale while the latter explains gravity at the macroscopic scale.