  Based on the quasi-local energy definition of Brown and York, we compute the
integral of the trace of the extrinsic curvature over a codimension-2
hypersurface. In particular, we study the difference between the uncompactified
Minkowski spacetime and the toroidal Kaluza-Klein compactification. For the
latter, we find that this quantity interpolates between zero and the value for
the uncompactified spacetime, as the size of the compact dimension increases.
Thus, the quasi-local energy is able to discriminate between the two
spacetimes.
