We have examined the effect of Time Reversal Symmetry (TRS) on vibrational modes and on the electronic band structure of Si and Ge. Most of the primary non-interacting modes are not affected by TRS. Only phonons originating from high symmetry lines S and A of the Brillouin Zone (BZ) indicate extra degeneracy. Selection rules for some two and three phonons originating from high symmetry lines are determined. The states of electrons and holes described by electronic band structure due to spin-inclusion are assigned by spinor representations of the double space group. Inclusion of the TRS into the band structure results in extra
degeneracy of electrons and holes, and therefore optical selection rules suppose to be modified.