  A Hamiltonian formalism is used to describe ensembles of fields in terms of
two canonically conjugate functionals (one being the field probability
density). The postulate that a classical ensemble is subject to nonclassical
fluctuations of the field momentum density, of a strength determined solely by
the field uncertainty, is shown to lead to a unique modification of the
ensemble Hamiltonian. The modified equations of motion are equivalent to the
quantum equations for a bosonic field, and thus this exact uncertainty
principle provides a new approach to deriving and interpreting the properties
of quantum ensembles. The examples of electromagnetic and gravitational fields
are discussed. In the latter case the exact uncertainty approach specifies a
unique operator ordering for the Wheeler-DeWitt and Ashtekar-Wheeler-DeWitt
equations.
