Interpretation of "The Wave Function of the Universe"

Hawking and Hartle interpreted their wave function of the universe as giving the probability for the universe to appear from nothing. However, this i correct interpretation, since the normalization presupposes a universe, not noth ing. Transition probabilities require a measure on the initial state and a physical result requires a physical initial state. Hawking and Hartle have, by a path integral approach, derived a formula they call "the wave function of the Universe. " Since there are no boundary conditions involved, Hawking and Hartle (1983) propose the following interpretation: One can interpret the functional integral over all compact four-geometries bounded by a given three-geometry as giving the amplitude for that three-geometry to arise from a zero three-geometry, i.e., a single point. In other words, the ground state is the amplitude for the Universe to appear from nothing. This article questions the interpretation that they calculate the ampli-tude for the universe to appear from nothing. Before interpreting a wave function as an amplitude for probabilities, the normalization must be clear. In the case of a single particle, without creation or destruction, the wave function is normalized by requiring that the integral of the probabilities over the whole space must yield one at any moment; the particle must be somewhere. In the case of quantum fields, normalization of the wave function, describing the probability amplitude °f different field configurations in space at a certain moment, is achieved by requiring that there is one field configuration at any moment. (This might be a vacuum configuration.) In the case of the wave function of the universe