  We consider the energy difference restricted to a finite volume for certain
pairs of incongruent ground states (if they exist) in the d-dimensional
Edwards-Anderson (EA) Ising spin glass at zero temperature. We prove that the
variance of this quantity with respect to the couplings grows at least
proportionally to the volume in any dimension greater than or equal to two. An
essential aspect of our result is the use of the excitation metastate. As an
illustration of potential applications, we use this result to restrict the
possible structure of spin glass ground states in two dimensions.
