Recent analysis suggests that the classical dynamics of a tachyon on an
unstable D-brane is described by a scalar Born-Infeld type action with a
runaway potential. The classical configurations in this theory at late time are
in one to one correspondence with the configuration of a system of
non-interacting (incoherent), non-rotating dust. We discuss some aspects of
canonical quantization of this field theory coupled to gravity, and explore,
following earlier work on this subject, the possibility of using the scalar
field (tachyon) as the definition of time in quantum cosmology. At late `time'
we can identify a subsector in which the scalar field decouples from gravity
and we recover the usual Wheeler - de Witt equation of quantum gravity.Comment: LaTeX file, 24 page