The Space Symmetry and the Time Reversal Symmetry of vibrational modes in Si, Ge and diamond are investigated. Using Space Symmetry we have derived the Lattice Mode Representation. Reducing it onto phonon species we obtain the symmetry allowed phonons and their degeneracies. Using reality test for irreducible representations according to those the phonons are classified we determine which modes are
Time Reversal affected. Comparison with experimental data obtained by neutron scattering is made. The effect of Time Reversal Symmetry on electrons in the conduction band and holes in the valence band as well as on excitons is briefly discussed.