Quantum Cosmology and Quantum Mechanics

Abstract

The interpretative framework of quantum mechanics loosely subsumed under the name “Copenhagen interpretation” contains two central assumptions which seem incompatible with a quantum cosmology built on a covariant quantum theory of spacetime. The first is a distinguished class of classical systems. The second is a distinguished time variable and its associated notion of causality. The first assumption is incompatible with the uniform application of quantum mechanics to the universe as a whole. The second is incompatible with the general covariance of gravitational theory. This paper explores the possibility that both of these distinguished features of our world arise, not as special features of the formalism of quantum mechanics, but rather as consequences of specific initial conditions for cosmology.

The framework of prediction in quantum cosmology is reviewed. Three kinds of information necessary for prediction are identified: the Hamiltonian, the initial conditions, and the historical information about this specific universe. The inescapable need for a theory of initial conditions is emphasized and some proposals for these theories are described. The role of decoherence in measurement and the construction of history is discussed. For the particular initial conditions of our universe, it is proposed that a family of habitually decohering quasi-classical operators are projections on the densities of conserved or approximately conserved quantities. When viewed through these variables the universe exhibits approximately the Copenhagen “classical world.”

The special role played by time in quantum mechanics is reviewed and its incompatibility with covariant quantum theories of spacetime discussed. A generalized sum-over-histories quantum mechanics for cosmological spacetimes is proposed in which no variable plays the special role of time in familiar quantum mechanics. The status of such notions as causality, state, and unitarity in this generalization is discussed. In this generalization the familiar formulation of quantum mechanics with its preferred time emerges as an approximation appropriate to those initial conditions of the universe which lead to classical spacetime when it is large.