The fact is that, beside the two quantum rules for energy and angular momentum, there is a third analogous rule for the linear momentum, established by W. Duane in 1923. Though this rule is generally accepted, there is no trace of recognition in the literature that it yields a consistent unitary particle explanation of all those phenomena of diffraction and coherence, e.g., of the two-slit experiment, which allegedly can be accounted for only by the fiction of a dual nature of matter, with transmutation of particles into waves and back into particles again. The usual method of solving this dilemma has admittedly been that of “refining the language of physics,” beginning with replacing the physical idea of a forth and back transformation by the term “dual manifestation,” thereby shunning any “real” constitution of matter, which then requires a specially adjusted philosophy of knowledge. In contrast, the quantum rule for the linear momentum solves the apparent contradictions in a physical manner without alternating manifestations. It introduces a great simplification which should also influence the method of teaching the theory. The purpose of the present article is to give due credit to the American pioneer of quantum mechanics, W. Duane, whose contribution to solving the duality paradox is a shining example of the scientific method, in contrast to the purely semantic approach in vogue for more than a generation.