  Any quantum theory of gravity which treats the gravitational constant as a
dynamical variable has to address the issue of superpositions of states
corresponding to different eigenvalues. We show how the unobservability of such
superpositions can be explained through the interaction with other
gravitational degrees of freedom (decoherence). The formal framework is
canonically quantized Jordan-Brans-Dicke theory. We discuss the concepts of
intrinsic time and semiclassical time as well as the possibility of tunneling
into regions corresponding to a negative gravitational constant. We calculate
the reduced density matrix of the Jordan-Brans-Dicke field and show that the
off-diagonal elements can be sufficiently suppressed to be consistent with
experiments. The possible relevance of this mechanism for structure formation
in extended inflation is briefly discussed.
