  Time-reversal invariance places strong constraints on the properties of the
quantum spin Hall edge. One such restriction is the inevitability of
dissipation in a Josephson junction between two superconductors formed on such
an edge without the presence of interaction. Interactions and spin-conservation
breaking are key ingredients for the realization of dissipationless ac
Josephson effect on such quantum spin Hall edges. We present a simple quantum
impurity model that allows to create a dissipationless fractional Josephson
effect on a quantum spin Hall edge. We then use this model to substantiate a
general argument that shows that any such non-dissipative Josephson effect must
necessarily by $8\pi$-periodic.
