  We review connections between the metric of spacetime and the quantum
fluctuations of fields. In particular, we discuss the finding that the
spacetime metric can be expressed entirely in terms of the 2-point correlators
of the fluctuations of quantum fields. We also discuss the open question
whether the knowledge of only the spectra of the quantum fluctuations of fields
suffices to determine the spacetime metric. This question is of interest
because spectra are geometric invariants and their quantization would,
therefore, have the benefit of not requiring the modding out of the
diffeomorphism group. Further, we discuss the fact that spacetime at the Planck
scale need not necessarily be either discrete or continuous. Instead, results
from information theory show that spacetime may be simultaneously discrete and
continuous in the same way that information can. Finally, we review the finding
that a covariant natural ultraviolet cutoff at the Planck scale implies a
signature in the cosmic microwave background (CMB) that may become observable.
