  A possible electric-magnetic duality suggests that the confinement of
non-Abelian electric charges manifests itself as a perturbative quantum effect
for the dual magnetic charges. Motivated by this possibility, we study vacuum
fluctuations around a non-Abelian monopole-antimonopole pair treated as point
objects with charges g=\pm n/2 (n=1,2,...), and placed on the antipodes of a
three sphere of radius R. We explicitly find all the fluctuation modes by
linearizing and solving the Yang-Mills equations about this background field on
a three sphere. We recover, generalize and extend earlier results, including
those on the stability analysis of non-Abelian magnetic monopoles. We find that
for g \ge 1 monopoles there is an unstable mode that tends to squeeze magnetic
flux in the angular directions. We sum the vacuum energy contributions of the
fluctuation modes for the g=1/2 case and find oscillatory dependence on the
cutoff scale. Subject to certain assumptions, we find that the contribution of
the fluctuation modes to the quantum zero point energy behaves as -R^{-2/3} and
hence decays more slowly than the classical -R^{-1} Coulomb potential for large
R. However, this correction to the zero point energy does not agree with the
linear growth expected if the monopoles are confined.
