Abstract  Arno Bohm and Ilya Prigogine''s Brussels–Austin Group have been working on the quantum mechanical arrow of time and irreversibility in rigged Hilbert space quantum mechanics. A crucial notion in Bohm''s approach is the so-called preparation/registration arrow. An analysis of this arrow and its role in Bohm''s theory of scattering is given. Similarly, the Brussels–Austin Group uses an excitation/de-excitation arrow for ordering events, which is also analyzed. The relationship between the two approaches is initially discussed focusing on their semi-group operators and time arrows. Finally a possible realist interpretation of the rigged Hilbert space formulation of quantum mechanics is considered.