Heinz-Jürgen Schmidt (Osnabrück) gives a talk at the MCMP Colloquium (27 November, 2013) titled "The Bohmian challenge". Abstract: The Bohmian extension of quantum theory claims to solve the measurement problem by re-establishing, in some sense, the classical ontology of particle trajectories on a microscopic level. In this talk I will not dwell upon the pros and cons to this claim but rather try to explain why this enterprise constitutes a challenge for philosophy of science, especially for those branches striving for rigorous methods. The Bohmian extension is empirically equivalent to standard quantum mechanics and mathematically only an extension by definitions. The main difference to other interpretations of quantum theory seems to be the belief into the reality of the Bohmian trajectories. Are the theory concepts used in philosophy of science rich enough to represent this crucial difference? In particular, I will scrutinize the theory concept of Günther Ludwig that was explicitly developed to foster his statistical interpretation of quantum theory and contains as a central notion the “reality domain” of a physical theory. A partial result will be that the Bohmian trajectories are not “objective properties” of particles in the sense defined by Ludwig, since the velocity of the Bohmian particles is not observable.