  We propose to realize mechanical parity-time PT symmetry in two coupled
optomechanical systems. To provide gain to one mechanical resonator and the
same amount of damping to the other, the two optical cavities should be driven
by blue- and red-detuned laser fields, respectively. After adiabatically
eliminating the degrees of freedom of the cavity modes, we derive a formula to
describe the PT symmetry of two coupled mechanical resonators. Mechanical
PT-symmetric phase transition is demonstrated by the dynamical behavior of the
mechanical resonators. Moreover, we study the effect of the quantum noises on
the dynamical behavior of the mechanical resonators when the system is in the
quantum regime.
