  Two approaches toward the arrow of time for scattering processes have been
proposed in rigged Hilbert space quantum mechanics. One, due to Arno Bohm,
involves preparations and registrations in laboratory operations and results in
two semigroups oriented in the forward direction of time. The other, employed
by the Brussels-Austin group, is more general, involving excitations and
de-excitations of systems, and apparently results in two semigroups oriented in
opposite directions of time. It turns out that these two time arrows can be
related to each other via Wigner's extensions of the spacetime symmetry group.
Furthermore, their are subtle differences in causality as well as the
possibilities for the existence and creation of time-reversed states depending
on which time arrow is chosen.
