Testing the generalized uncertainty principle with macroscopic mechanical oscillators and pendulums

Abstract

Recent progress in observing and manipulating mechanical oscillators at quantum regime provides new opportunities of studying fundamental physics, for example to search for low energy signatures of quantum gravity. For example, it was recently proposed that such devices can be used to test quantum gravity effects, by detecting the change in the [x,p] commutation relation that could result from quantum gravity corrections. We show that such a correction results in a dependence of a resonant frequency of a mechanical oscillator on its amplitude, which is known as amplitudefrequency effect. By implementing of this new method we measure amplitude-frequency effect for 0.3 kg ultra high-Q sapphire split-bar mechanical resonator and for ∼ 10 −5 kg quartz bulk acoustic wave resonator. Our experiments with sapphire resonator have established the upper limit on quantum gravity correction constant of β0 to not exceed 5.2 × 10 6 , which is factor of 6 better than previously measured. The reasonable estimates of β0 from experiments with quartz resonators yields β0 < 4×10 4 . The data sets of 1936 measurement of physical pendulum period by Atkinson [1] could potentially lead to significantly stronger limitations on β01. Yet, due to the lack of proper pendulum frequency stability measurement in these experiments the exact upper bound on β0 can not be reliably established. Moreover, pendulum based systems only allow to test a specific form of the modified commutator that depends on the mean value of momentum. The electro-mechanical oscillators to the contrary enable testing of any form of generalized uncertainty principle directly due to a much higher stability and higher degree of control.

On quantum gravity tests with composite particles

“…Similarly, from ref. 8 we obtain α > −0.25. Note that these bounds are significantly worse than those obtained in the present work using the data from 26 .…”

“…While the precise value of α is unknown, it is commonly accepted that it needs to be positive 19,20 . We shall see that the best bounds that can be calculated from recent experiments based on micro-and nano-scale quantum harmonic oscillators 5,8 are in fact negative for β 0 = 1 (and in fact any β 0 < 10 6 ).…”

“…Furthermore, the precision of such experiments is difficult to extend due to limitations on the distance to observable gamma-ray bursts and the maximal energy of the gamma-rays. This motivates the quest for highly controlled table-top experiments to test for Planck scale physics [3][4][5][6][7][8] .…”

Probing quantum gravity effects with quantum mechanical oscillators

“…In this regime, the effect of quantum fluctuations on the expectation value dynamics cannot be neglected anymore and the result of the experiment would provide novel useful hints for the development of a theory able to consider gravitational phenomena within a consistent quantum treatment. Due to the novel quantum regime, even if the bounds on the deformation parameter that can be achieved are probably not as good as those of references [48,49], the results acquire a particular interest.…”

“…The strength of such effects depends on the deformation parameter β 0 . Experiments proposed in reference [48] were realized by the same authors exploiting macroscopic nano-and microoscillators with masses ranging from 10 −11 to 10 −5 kg, and more recently by Bushev et al [49] with a sub-kilogram sapphire oscillator. These experiments have lowered previous limits on β 0 by several orders of magnitude.…”