Probing Quantum Gravity with Large Molecular Wave-packets

One of the biggest obstacles behind a direct test of Quantum Gravity (QG) is its energy scale (10¹⁹ GeV), which remains well outside of the capabilities of any human made machine. The next best possible approach to probe QG is to provide indirect tests on some effective theories, which can be performed in a lower energy scale; this paper is aimed in this direction and shows a promising path to test the minimal length scale of Nature using the dispersion of free, large molecular wave-packets. The existence of the minimal length is believed to be the reason for a modified commutation relation between the position and momentum operators; in this paper, we show that such a modification of the commutator has a profound effect on the dispersion rate of free wave-packets, and precise measurements on the broadening times of large molecular wave-packets (such as the C₆₀ and C₁₇₆ buckyballs, as well as larger organic molecules) provide a promising path for an indirect test of quantum gravity in a laboratory setting.