  After a synoptic panorama about some still unsolved foundational problems
involving time-reversal, we show that the \emph{double time-reversal
superselection rule} of Nonrelativistic Quantum Mechanics is redundant. We then
analyze which, among the symmetries of the Clebsch-Gordan coefficients, may be
inferred through time-reversal considerations. Finally, we show how Coupling
Theory allows to improve our comprehension of the fact that, in presence of
hidden symmetries, Wigner's Theorem concerning Kramers degeneration cannot be
applied, by analyzing a set of Z uncoupled massive particles, both in the case
in which they are bosons of spin zero and in the case in which they are
fermions of spin 1/2, subjected to a Keplerian force's field and considering
the coupling of the 2Z quantum angular momenta resulting by the hidden SO(4)
symmetry owed to the fact that, apart from the rotational SO(3) symmetry
responsible of the conservation of the angular momentum, the Laplace-Runge-Lenz
vector is also conserved.
