  Inspired by previous work in 2+1 dimensional quantum gravity, which found
evidence for a discretization of time in the quantum theory, we reexamine the
issue for the case of pure Lorentzian gravity with vanishing cosmological
constant and spatially compact universes of genus larger than 1. Taking as our
starting point the Chern-Simons formulation with Poincare gauge group, we
identify a set of length variables corresponding to space- and timelike
distances along geodesics in three-dimensional Minkowski space. These are Dirac
observables, that is, functions on the reduced phase space, whose quantization
is essentially unique. For both space- and timelike distance operators, the
spectrum is continuous and not bounded away from zero.
