Can a person have posterior vitreous detachment on both eyes far apart?

In time? yes.: If you are asking can you have first one eye, and then much later experience a PVD in the other eye, then yes, very possible. Usually pvds occur spontaneously, although they can occur from trauma as well.

Yes: Vitreous detachment, a usually silent event in middle to older age, can occur in one or both eyes with symptoms. Since the transition from gel to dense liquid takes many years to occur, if it is causing symptoms it could be a number of years between each eye.