[**On a realistic interpretation of quantum mechanics**]{}

[**Arnold Neumaier**]{}\
 \
Institut für Mathematik\
Universität Wien\
Strudlhofgasse 4\
A-1090 Wien, Austria\
email: neum@cma.univie.ac.at\
WWW: http://solon.cma.univie.ac.at/neum/\
 \

[**Abstract.**]{} The best mathematical arguments against a realistic interpretation of quantum mechanics – that gives definite but partially unknown values to all observables – are analysed and shown to be based on reasoning that is not compelling.

This opens the door for an interpretation that, while respecting the indeterministic nature of quantum mechanics, allows to speak of definite values for all observables at any time that are, however, only partially measurable.

The analysis also suggests new ways to test the foundations of quantum theory.

[**Keywords**]{}: realistic interpretation, quantum inseparability, probability, projector, measurement, spin, classical model, particle paths, double slit experiment\

[**1991 MSC Classification**]{}: primary 81P10\

[**1990 PACS Classification**]{}: 03.65\

Introduction {#intro}
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Quantum physics is a very successful theory for predicting nature. However, in spite of many attempts, a mathematically and philosophically convincing basis for the interpretation of quantum phenomena has not yet been found.

As stated recently by [Zeilinger]{} [@Zei], there are at least two levels of interpreting quantum mechanics: the statistical interpretation in the narrower sense introduced by [Born]{} [@Bor], on which there 