Abstract

The aim of this paper is to reconcile the two modes of description of macrosystems, i.e., to remove certain inconsistencies between the classical phenomenological and the quantum-theoretical descriptions of a macrosystem. Starting from Ludwig's formulation of a general framework for classical theories and his ansatz for a compatibility condition between the quantum theoretical and the classical mode of description for a macrosystem, we try to make clear what the “classical content” of many-body quantum theory really is. It is shown that this classical content may be described by a certain “observable,” i.e., an operator-valued measure over the Borel sets of the classical trajectory space. There exists a reduced time evolution within this classical content which has the structure of a true semigroup in case of an irreversible classical time evolution