  Motivated by several approaches to quantum gravity, there is a considerable
literature on generalised uncertainty principles particularly through
modification of the canonical position-momentum commutation relations. Some of
these modified relations are also consistent with general principles that may
be supposed of any physical theory. Such modified commutators have significant
observable consequences. Here we study the noisy behaviour of an optomechanical
system assuming a certain commonly studied modified commutator. From recent
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.
