  We study a non-supersymmetric $E_8\times\bar E_8$ compactification of
M-theory on $S^1/Z_2$, related to the supersymmetric $E_8\times E_8$ theory by
a chirality flip at one of the boundaries. This system represents an M-theory
analog of the D-brane anti-D-brane systems of string theory. Alternatively,
this compactification can be viewed as a model of supersymmetry breaking in the
``brane-world'' approach to phenomenology. We calculate the Casimir energy of
the system at large separations, and show that there is an attractive Casimir
force between the $E_8$ and $\bar E_8$ boundary. We predict that a tachyonic
instability develops at separations of order the Planck scale, and discuss the
possibility that the M-theory fivebrane might appear as a topological defect
supported by the $E_8\times\bar E_8$ system. Finally, we analyze the eventual
fate of the configuration, in the semiclassical approximation at large
separations: the two ends of the world annihilate by nucleating wormholes
between the two boundaries.
