# Indirect Probe of Quantum Gravity using Molecular Wave-packets

## TL;DR

This paper proposes an experimental approach to indirectly test quantum gravity effects by measuring the dispersion of large molecular wave-packets, which could reveal the existence of a minimal length scale in nature.

## Contribution

It introduces a method to test quantum gravity by analyzing wave-packet dispersion, linking minimal length scale effects to measurable quantum phenomena.

## Key findings

- Modified commutation relations affect wave-packet dispersion rates.
- Precise measurements of molecular wave broadening can indicate quantum gravity effects.
- Large molecules like C60 and C176 are suitable for such experiments.

## Abstract

The most obvious obstacle behind a direct test of Quantum Gravity (QG) is its energy scale ($10^{19}$ GeV), which remains well outside of any human made machine. The next best possible approach is to provide indirect tests on effective theories of QG which can be performed in a lower energy scale. This paper is aimed in this direction, and shows a promising path to test the existence of the fundamental minimal length scale of Nature by measuring the dispersion of free, large molecular wave-packets. The existence of the minimal length is believed to be the reason for a modified commutation relationship between the position and momentum operators and, 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 measurement on the broadening times of large molecular wave-packets (such as $C_{60}$, $C_{176}$ and large organic molecules) provide a promising path for an indirect test of quantum gravity, in a laboratory setting.