Constraining noncommutative spacetime from GW150914

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 noncommutative space-time. We show that the leading noncommutative correction to the phase of the gravitational waves produced by a binary system appears at the second order of the post-Newtonian expansion. This correction is proportional to Lambda(2) vertical bar theta(0i)vertical bar(2)/(l(P)t(P))(2), where theta(mu nu) is the antisymmetric tensor of noncommutativity. To comply with GW150914 data, we find that root Lambda less than or similar to 3.5, namely at the order of the Planck scale. This is the most stringent bound on the noncommutative scale, exceeding the previous constraints from particle physics processes by similar to 15 orders of magnitude.