Noncommuting quantum observables, if considered asunsharp observables, are simultaneously measurable. This fact is exemplified for complementary observables in two-dimensional state spaces. Two proposals of experimentally feasible joint measurements are presented for pairs of photon or neutron polarization observables and for path and interference observables in a photon split-beam experiment. A recent experiment proposed and performed by Mittelstaedt, Prieur, and Schieder in Cologne is interpreted as a partial version of the latter example.

Summary The question underlying this article is whether the Kantian transcendental philosophy is wide enough to constitute the objects of quantum physics as objects of possible experience and consequently to found the objectivity of quantum physical knowledge. It is shown that the Kantian determinations of the categories (quality, substance, causality) can be interpreted and elaborated in such a way that the quantum physical concept of an object characterized by nonobjectivity of properties is conceived. Therefore the categories are valid in quantum (...) mechanics and warrant the objectivity of quantum physical experience. By the interpretation of the Kantian infinite judgement as an indefinite proposition it is possible to define the non-objectivity of properties categorially as indefiniteness of qualities. In particular by the indefiniteness of the position-quality the non-permanent localizability of quantum mechanical objects can be understood a priori. However the object of possible experience, especially the quantum mechanical object is underdetermined by the categories of substance and causality: If the object is determined to be a substance it is not yet conceived to be an individual; its characterization by means of probability laws is categorially indeterminate. In so far the significance of transcendental philosophy for the foundation of quantum physics is limited. (shrink)

The determination of the past and the future of a physical system are complementary aims of measurements. An optimal determination of the past of a system can be achieved by an informationally complete set of physical quantities. Such a set is always strongly noncommutative. An optimal determination of the future of a physical system can be obtained by a Boolean complete set of quantities. The two aims can be reconciled to a reasonable degree with using unsharp measurements.