According to several quantum gravity theories there is an effective minimal length beyond which space cannot be probed, possibly the Planck length. It has been suggested that this fundamental limit implies a generalised uncertainty principle (GUP) and corresponding 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. 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, which may be used to constrain the minimal length. We find how such experiments can be adjusted to provide significant improvements in such bounds, potentially surpassing those from sub-atomic measurements.
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