Abstract
A minimal observable length is a common feature of theories that aim to merge quantum physics and gravity. Quantum mechanically, this concept is associated with a nonzero minimal uncertainty in position measurements, which is encoded in deformed commutation relations. In spite of increasing theoretical interest, the subject suffers from the complete lack of dedicated experiments and bounds to the deformation parameters have just been extrapolated from indirect measurements. As recently proposed, low-energy mechanical oscillators could allow to reveal the effect of a modified commutator. Here we analyze the free evolution of high-quality factor micro- and nano-oscillators, spanning a wide range of masses around the Planck mass mP (≈22 μg). The direct check against a model of deformed dynamics substantially lowers the previous limits on the parameters quantifying the commutator deformation.
Highlights
A minimal observable length is a common feature of theories that aim to merge quantum physics and gravity
Assuming that a deformed commutator between position and momentum governs the dynamics through standard Heisenberg equations, we obtain a reduction by many orders of magnitude of the previous upper limits to the parameters quantifying the commutator deformation
We remark that the measurements have been performed on state of the art oscillators, allowing low statistical uncertainty, low background noise, high-frequency stability, and the highest excitation amplitude allowed by each oscillator
Summary
A minimal observable length is a common feature of theories that aim to merge quantum physics and gravity. In the Heisenberg picture of quantum mechanics and assuming the validity of the commutator (2) for the coordinates of the centre-of-mass (c.m.), the time evolution of its position exhibits an additional third harmonic term and a dependence of the oscillation frequency on its amplitude.
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