ON THE BRUSSELS SCHOOLS ARROW OF TIME IN QUANTUM-THEORY

This paper examines the problem of founding irreversibility on reversi ble equations of motion from the point of view of the Brussels school' s recent developments in the foundations of quantum statistical mechan ics. A detailed critique of both their 'subdynamics' and 'transformati on' theory is given. It is argued that the subdynamics approach involv es a generalized form of 'coarse-graining' description, whereas, trans formation theory cannot lead to truly irreversible processes pointing to a preferred direction of time. It is concluded that the Brussels sc hool's conception of microscopic temporal irreversibility, as such, is tacitly assumed at the macroscopic level. Finally a logical argument is provided which shows, independently of the mathematical formalism o f the theory concerned, that statistical reasoning alone is not suffic ient to explain the arrow of time.