Gravitational bar detectors set limits to Planck scale physics on macroscopic variables

Different approaches to quantum gravity, such as string theory and loop quantum gravity, as well as doubly special relativity and gedanken experiments in black holes physics \cite{maggiore1,scardigli,jizba}, all indicate the existence of a minimal measurable length of the order of the Planck length, $L_p =\sqrt{\hbar G/c^3} = 1.6 \times 10^{-35}$ m. This observation has motivated the proposal of generalized uncertainty relations, which imply changes in the energy spectrum of quantum systems. As a consequence, quantum gravitational effects could be revealed by experiments able to test deviations from standard quantum mechanics \cite{das,ali1,ali2}, such as those recently proposed on macroscopic mechanical oscillators \cite{pikovski}. Here we exploit the sub-millikelvin cooling of the normal modes of the ton-scale gravitational wave detector AURIGA, to place an upper limit for possible Planck scale modifications on the ground state energy of an oscillator. Our analysis, calls for the development of a satisfactory treatment of multi-particle states in the framework of quantum gravity models.