  In center vortex theory, beyond the simplest picture of confinement several
conceptual problems arise that are the subject of this paper. Confinement
arises through averaging of phase factors which are gauge-group center elements
raised to the power of the Gauss linking numbers of vortices. The simplest
approach to confinement counts this link number by counting the number of
vortices, considered in d=3 as infinitely-long closed self-avoiding random
walks on a cubical lattice, piercing any surface spanning the Wilson loop. A
given vortex, however, may pierce the spanning surface multiply with a link
number smaller than the number of piercings. We call such vortices inert
(although they may be only partially-inert). We estimate the dilution factor
from inert vortices that reduces the ratio of fundamental string tension to
vortex areal piercing density as roughly 0.6. Next we show how inert vortices
resolve the old problem that the link number of a given vortex configuration is
the same for any choice of spanning surface, yet only one such surface appears
in the Wilson loop expectation value. Third, we discuss semi- quantitatively a
configuration of two distinct Wilson loops separated by a variable distance,
and show how inert vortices govern the transition between two allowed forms of
the area law, one at small separation and one at large. The result is a
finite-range Van der Waals force between the loops. Finally, in a problem
related to the double-loop problem, we argue that inert vortices do not affect
the fact that in the SU(3) baryonic area law, the mesonic string tension
appears.
