Abstract
Models of quantum gravity imply a fundamental revision of our description of position and momentum that manifests in modifications of the canonical commutation relations. Experimental tests of such modifications remain an outstanding challenge. These corrections scale with the mass of test particles, which motivates experiments using macroscopic composite particles. Here we consider a challenge to such tests, namely that quantum gravity corrections of canonical commutation relations are expected to be suppressed with increasing number of constituent particles. Since the precise scaling of this suppression is unknown, it needs to be bounded experimentally and explicitly incorporated into rigorous analyses of quantum gravity tests. We analyse this scaling based on data from past experiments involving macroscopic pendula, and provide tight bounds that exceed those of current experiments based on quantum mechanical oscillators. Furthermore, we discuss possible experiments that promise even stronger bounds thus bringing rigorous and well-controlled tests of quantum gravity closer to reality.
Highlights
Models of quantum gravity imply a fundamental revision of our description of position and momentum that manifests in modifications of the canonical commutation relations
To account for the unknown scaling law that governs the suppression of corrections to the canonical commutation relations with the number of particles, we define the parameter α such that the deformation is suppressed by Nα, i.e., 1⁄2x; p
Quantum gravity suggests corrections to the canonical commutation relations that are proportional to a parameter β0
Summary
Models of quantum gravity imply a fundamental revision of our description of position and momentum that manifests in modifications of the canonical commutation relations. Experimental tests of such modifications remain an outstanding challenge. One class of indirect tests of a minimal length scale is based on observations of photon arrival times from gamma-ray bursts in distant galaxies[2]. Such experiments, are hard to control as they rely on a wide range of hard to verify model assumptions. The underlying concept on which several such table-top experiments rely upon is the deformations of the canonical commutation relations of position and momentum as a consequence of a variety of formulations of quantum gravity[1,9,10,11,12]
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