  Despite the fact that the fundamental physical laws are symmetric in time,
most observed processes do not show this symmetry. Especially the phenomenon of
decay seems to involve a kind of irreversibility that makes the definition of a
microscopic arrow of time possible. Such an intrinsic irreversibility is
incorporated within the Rigged Hilbert Space quantum mechanics of the Brussels
School, contrasting to the statements of standard quantum mechanics. As shown
in this paper, the formalism bears significant advantages in the description of
decaying systems, however the breaking of time symmetry can be avoided.
