  Here we describe the quantum limit to measurement of the classical
gravitational field. Specifically, we write down the optimal quantum Cramer-Rao
lower bound, for any single parameter describing a metric for spacetime. The
standard time-energy and Heisenberg uncertainty relations are shown to be
special cases of the uncertainty relation for the spacetime metric. Four key
examples are given, describing quantum limited estimation for: acceleration,
black holes, gravitational waves and cosmology. We employ the locally covariant
formulation of quantum field theory in curved spacetime, which allows for a
manifestly spacetime independent derivation. The result is an uncertainty
relation applicable to all causal spacetime manifolds.
