Reconsidering the relation between "matter wave interference" and "wave-particle duality"

Interference of more and more massive objects provides a spectacular confirmation of quantum theory. It is usually regarded as support for "wave-particle duality" and in an extension of this duality even as support for "complementarity". We first give an outline of the historical development of these notions. Already here it becomes evident that they are hard to define rigorously, i.e. have mainly a heuristic function. Then we discuss recent interference experiments of large and complex molecules which seem to support this heuristic function of "duality". However, we show that in these experiments the diffraction of a {\em delocalized} center-of-mass wave function depends on the interaction of the {\em localized} structure of the molecule with the diffraction element. Thus, the molecules display "dual features" at the same time, which contradicts the usual understanding of wave-particle duality. We conclude that the notion of "wave-particle duality" deserves no place in modern quantum physics.