  In this paper we present a new method to show that a principal homogeneous
space of the Jacobian of a curve of genus two is nontrivial. The idea is to
exhibit a Brauer-Manin obstruction to the existence of rational points on a
quotient of this principal homogeneous space. In an explicit example we apply
the method to show that a specific curve has infinitely many quadratic twists
whose Jacobians have nontrivial Tate-Shafarevich group.
