Must quantum spacetimes be Euclidean?

The Bohm–de Broglie interpretation of quantum mechanics is applied to canonical quantum cosmology. It is shown that, irrespective of any regularization or choice of factor ordering of the Wheeler-DeWitt equation, the unique relevant quantum effect which does not break spacetime is the change of its signature from Lorentzian to Euclidean. The other quantum effects are either trivial or break the four-geometry of spacetime. A Bohm–de Broglie picture of a quantum geometrodynamics is constructed, which allows the investigation of these latter structures. For instance, it is shown that any real solution of the Wheeler-DeWitt equation yields a degenerate four-geometry compatible with the strong gravity limit of general relativity and the Carroll group. Because of the more detailed description of quantum geometrodynamics given by the Bohm–de Broglie interpretation, some new boundary conditions on solutions of the Wheeler-DeWitt equation must be imposed in order to preserve consistency of this finer view.