Quasiclassical Domains in a Quantum Universe
In this universe, governed fundamentally by quantum mechanical laws, characterized by indeterminism and distributed probabilities, classical deterministic laws are applicable over a wide range of time, place, and scale. We review the origin of these deterministic laws in the context of the quantum mechanics of closed systems, most generally, the universe as a whole. In this formulation of quantum mechanics, probabilities are predicted for the individual members of sets of alternative histories of the universe that decohere, i.e., for which there is negligible interference between pairs of histories in the set as measured by a decoherence functional. An expansion of the decoherence functional in the separation between histories allows the form of the phenomenological, deterministic equations of motion to be derived for suitable coarse grainings of a class of non-relativistic systems, including ones with general non-linear interactions. More coarse graining is needed to achieve classical predictability than naive arguments based on the uncertainty principle would suggest. Coarse graining is needed to effect decoherence, and coarse graining beyond that to achieve the inertia necessary to resist the noise that mechanisms of decoherence produce. Sets of histories governed largely by deterministic laws constitute the quasiclassical domain of everyday experience which is an emergent feature of the closed system’s initial condition and Hamiltonian. We analyse the question of the sensitivity of the existence of a quasiclassical domain to the particular form of the initial condition. We find that almost any initial condition will exhibit a quasiclassical domain of some sort, but only a small fraction of the total number of possible initial states could reproduce the everyday quasiclassical domain of our universe. ∗ Talk given at the Lanczos Centenary Meeting, North Carolina State University, December 15, 1993. † Department of Physics, University of California, Santa Barbara, CA 93106-9530.