Pattern recognition in molecular quantum mechanics

It is shown that the classical concept of an open system does not encompass quantal systems but has to be replaced by the non-Boolean notion of an entangled system. Molecular, chemical, or biological phenomena can be considered to be reduced to a fundamental theory like quantum mechanics only if the fundamental and the phenomenological theories are formally and interpretatively connected, and if the classifications used in the empirical sciences are shown to follow from a single set of fundamental dynamical laws. These conditions enforce a non-statistical and ontic interpretation of quantum mechanics, hence a non-Boolean calculus of propositions. In this interpretation the notion of a world state is well-defined, its Schmidt-decomposition defines a background-dependent model state for molecular systems and creates the phenomena we can observe. To any molecular system there is associated in an objective way a nonnegative number which we call the integrity. The integrity measures the inherent fuzziness of the system concept in a holistic theory, and is used to define recognizable molecular patterns.