experimental consistency, I searched the literature for concise statements of the basic difficulties in terms unrelated to measurement, but given in a clear mathematical context that allows one to analyse the logic of the problems without losing oneself in philosophical speculations.

The outcome was somewhat surprising: The best presented mathematical arguments turned out to have subtle flaws. This becomes apparent when one reduces them to arguments residing completely within the universally accepted statistical interpretation in the narrower sense.

Probably the weaknesses in the arguments escaped previous attention since the arguments were only used for philosophical discussion and justification of foundations, and never subjected to experiment. I therefore suggest below some specific things that one should try to test with suitable experiments.

In the following, I shall present my analysis of some arguments related to a realistic interpretation of quantum mechanics; [*realistic*]{} in the sense that it allows to speak of definite values for [*all*]{} observables at any time that are, however, only partially measurable.

The findings give rise to the hope that a consistent interpretation is possible that respects the stochastic nature of quantum mechanics, but is also realistic, with all the accompanying advantages for our intuition. In a companion 