You missed my point. What one observes in experiment can not be explained by a wave theory or a particle theory alone, or in shorter (but uninformative) phrasin

You missed my point. What one observes in experiment can not be explained by a wave theory or a particle theory alone, or in shorter (but uninformative) phrasing you can say that there is "wave particle duality". But what is the theory that actually works? It is not the theory of wave particle duality (which just stands for "we had to use two contradictory theories" before we can find the more precise theory). The more precise theory is that of quantum fields: there are no particles and no waves, just quantum fields that in certain parameter regimes are well approximated by particles or waves.