Constraining non-commutative space-time from GW150914

TL;DR

This paper uses gravitational wave data from GW150914 to set the most stringent limit to date on the non-commutative scale of space-time, constraining quantum fuzziness at near-Planckian levels.

Contribution

It introduces a novel method to bound non-commutative space-time effects using gravitational wave phase corrections, improving previous constraints by 15 orders of magnitude.

Findings

The non-commutative correction appears at 2nd order in post-Newtonian expansion.

The bound on the non-commutative scale is less than one order of magnitude above the Planck scale.

This method surpasses previous particle physics constraints by about 15 orders of magnitude.

Abstract

The gravitational wave signal GW150914, recently detected by LIGO and Virgo collaborations, is used to place a bound on the scale of quantum fuzziness of non-commutative space-time. We show that the leading non-commutative correction to the phase of the gravitational waves produced by a binary system appears at the 2nd order of the post- Newtonian expansion. This correction is proportional to $\Lambda^2 \equiv |\theta^{0i}|^2/(l_P t_P)^2$, where $\theta^{\mu \nu}$ is the antisymmetric tensor of non-commutativity. To comply with GW150914 data, we find that $\sqrt{\Lambda} \lesssim 6$, namely less than one order of magnitude above the Planck scale. This is the most stringent bound on non-commutative scale, exceeding the previous constraints from particle physics processes by $\sim 15$ orders of magnitude.