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.

中文翻译：

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通过量子噪声测试广义不确定性原理

根据一些量子引力理论，存在一个有效的最小长度，超过该长度就无法探测空间，可能是“普朗克长度”。有人建议，这个基本限制意味着广义不确定性原理 (GUP) 和规范位置 - 动量换向关系的相应修改。这些修改后的关系中的一些也与任何物理理论可能假设的一般原则一致。在这里，我们研究了光机械系统的噪声行为，假设有一个普遍研究的改进换向器。根据最近在桌面光机械实验中对辐射压力噪声的观察以及 Advanced LIGO 的位置​​噪声谱，我们推导出了改进型换向器的界限，可用于限制最小长度。