  The Casimir force due to a massless scalar field satisfying Dirichlet
boundary conditions may attract or repel a piston in the neck of a flask-like
container. Using the world-line formalism this behavior is related to the
competing contribution to the interaction energy of two types of Brownian
bridges. It qualitatively is also expected from attractive long-range two-body
forces between constituents of the boundary. A geometric subtraction scheme is
presented that avoids divergent contributions to the interaction energy and
classifies the Brownian bridges that contribute to the force. These are all of
finite length and the Casimir force can be analyzed and in principle accurately
computed without resorting to regularization or analytic continuation. The
world-line analysis is robust with respect to variations in the shape of the
piston and the flask and the analogy with long-range forces suggests that
neutral atoms and particles are also drawn into open-ended pipes (or
nano-tubes) by Casimir forces of electromagnetic origin.
