  The question of whether unobserved short-wavelength modes of the
gravitational field can induce decoherence in the long-wavelength modes (``the
decoherence of spacetime'') is addressed using a simplified model of
perturbative general relativity, related to the Nordstrom-Einstein-Fokker
theory, where the metric is assumed to be conformally flat. For some
long-wavelength coarse grainings, the Feynman-Vernon influence phase is found
to be effective at suppressing the off-diagonal elements of the decoherence
functional. The requirement that the short-wavelength modes be in a
sufficiently high-temperature state places limits on the applicability of this
perturbative approach.
