  Finding a physically consistent approach to modelling interactions between
classical and quantum systems is a highly nontrivial task. While many proposals
based on various mathematical formalisms have been made, most of these efforts
run into difficulties of one sort or another. One of the first detailed
descriptions was given by Sudarshan and his collaborators who, motivated by the
measurement problem in quantum mechanics, proposed a Hilbert space formulation
of classical-quantum interactions which made use of the Koopman-von Neumann
description of classical systems. Here we use the approach of ensembles on
configurations space to give a detailed account of a classical apparatus
measuring the position of a quantum particle that is prepared in a
superposition of two localized states. We show that the probability of the
pointer of the classical apparatus is left in a state that corresponds to the
probability of the quantum particle. A subsequent observation of the pointer
leads to an update of its probability density. From this we can obtain
information about the position of the quantum particle, leading to an update of
its wave function. Since this formalism incorporates uncertainties and finite
measurement precision, it is well suited for metrological applications.
Furthermore, it resolves fundamental issues that appear in the case of a
quantum description of the apparatus.
