  The shear-transformation-zone (STZ) theory has been remarkably successful in
accounting for broadly peaked, frequency-dependent, viscoelastic responses of
amorphous systems near their glass temperatures $T_g$. This success is based on
the theory's first-principles prediction of a wide range of internal STZ
transition rates. Here, I show that the STZ rate-distribution causes the
Newtonian viscosity to be strongly temperature dependent; and I propose that it
is this temperature dependence, rather than any heterogeneity-induced
enhancement of diffusion, that is responsible for Stokes-Einstein violations
near $T_g$. I also show that stretched-exponential relaxation of density
fluctuations emerges naturally from the same distribution of STZ transition
rates that predicts the viscoelastic behavior. To be consistent with
observations of Fickian diffusion near $T_g$, however, an STZ-based diffusion
theory somehow must include the cascades of correlated displacement events that
are seen in low-temperature numerical simulations.
