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