In the Wheeler-De Witt formalism of quantum gravity, do big bangs act as sources and future singularities as sinks? A finite time ago, existence emerged from the big bang, and existence will fade in a finite time for future singularities. Evolving WDW solutions forward in time leads to no change for parts of the wavefunctional away from singularities, but does it act as a sink for future singularities leading to a reduction in the norm of the wavefunctional? Do big bangs act as a wavefunctional source increasing its norm over time? Then the best we can hope for WDW solutions is a steady state under extended hamiltonian time evolution with "wavefunctional probability density" created at the big bang and ending at future singularities?
reducing the norm of a wavefunction does not affect anything since a physical wavefunction must always be normalized, otherwise it cannot be interpreted as a probability amplitude function, because the probability of anything ocurring is always 1.