  There is a common expectation that the big-bang singularity must be resolved
in quantum gravity but it is not clear how this can be achieved. A major
obstacle here is the difficulty of interpreting wave-functions in quantum
gravity. The standard quantum mechanical framework requires a notion of time
evolution and a proper definition of an invariant inner product having a
probability interpretation, both of which are seemingly problematic in quantum
gravity. We show that these two issues can actually be solved by introducing
the embedding coordinates as dynamical variables \`a la Isham and Kuchar. The
extended theory is identical to general relativity but has a larger group of
gauge symmetries. The Wheeler-DeWitt equations describe the change of the
wave-function from one arbitrary spacelike slice to another, however the
constraint algebra makes this evolution purely kinematical and furthermore
enforces the wave-function to be constrained in the subspace of zero-energy
states. An inner product can also be introduced having all the necessary
requirements. In this formalism big-bang appears as a finite field space
boundary on which certain boundary conditions must be imposed for mathematical
consistency. We explicitly illustrate this point both in the full theory and in
the minisuperspace approximation.
