Interpreting the wave function of the universe

Abstract

The Many-Worlds Interpretation of quantum mechanics is used to determine the meaning of the universal wave function of quantum cosmology. More precisely, the Many-Worlds Interpretation is used to distinguish those quantities in quantum cosmology which are measurable, and hence physically meaningful, from those which are not. A number of rather surprising conclusions are drawn from the analysis. First, it is not possible to measure the expectation value of any universal operator and so such expectation values are physically meaningless. Second, it is physically (although not mathematically) meaningless to talk about eigenstates of the Universal Hamiltonian. Third, before a measurement of the radius of the Universe is made it makes no sense to say the Universe has a radius. Fourth, after the first two radius measurements are made, the Universe can be said to have all radii consistent with the support of the universal wave function and the wave function of the measuring apparatus; in effect, the Universe splits into an infinite number of branches, in each of which the time evolution is observed to be very close to the classical evolution. Fifth, any universal wave function which does not violate a Quantum Copernican Cosmological Principle will automatically solve the Flatness Problem without having to invoke inflation. In effect, quantum cosmology allows us to have “inflation without inflation”. All of these conclusions are illustrated with a closed Friedmann universe quantized in conformal time. My quantization procedure allows only one solution to Schrödinger's equation, and this solution solves the Flatness Problem. I show that the ADM quantization method plus the Hartle-Hawking initial foundary condition gives the same result.