  We advocate a novel perspective on the phenomenology of a framework with
spacetime noncommutativity which is of established relevance for string theory.
Our analysis applies to cases in which the noncommutativity parameters are
arranged according to the criteria of "light-like noncommutativity" and
ultraviolet supersymmetry is assumed, so that the implications of the
characteristic mechanism of ultraviolet/infrared mixing are relatively soft. We
also observe that an analogous case of soft ultraviolet-infrared mixing is
present in a previously-proposed Loop-quantum-gravity-inspired description of
quantum spacetime. And we show that soft ultraviolet-infrared mixing produces
an anomaly for the nonrelativistic de Broglie relation $\lambda v = h/m$, with
correction term governed by a single (but particle-dependent) parameter $\chi$.
We test this hypothesis by comparing a determination of the fine structure
constant that relies on the de Broglie relation for nonrelativistic neutrons to
other independent determinations of the fine structure constant, and we obtain
an estimate of $\chi$ that differs from 0 with four-standard-deviation
significance.
