  Interaction of the electron spin with local elastic twists due to transverse
phonons has been studied. Universal dependence of the spin relaxation rate on
the strength and direction of the magnetic field has been obtained in terms of
the electron gyromagnetic tensor and macroscopic elastic constants of the
solid. The theory contains no unknown parameters and it can be easily tested in
experiment. At high magnetic field it provides parameter-free lower bound on
the electron spin relaxation in quantum dots.
