Decoherent Histories Quantum Mechanics and Copenhagen Quantum Mechanics

Abstract

We discuss the relation between our approach to quantum mechanics, based on coarsegrained decoherent histories of a closed system, and the approximate quantum mechanics of measured subsystems, as in the “Copenhagen interpretation.” The latter formulation postulates (implicitly for most authors or explicitly in the case of Landau and Lifshitz [1]) a classical world and a quantum world, with a movable boundary between the two. Observers and their measuring apparatus make use of the classical world, so that the results of a “measurement” are ultimately expressed in one or more “c-numbers”. We have emphasized that this widely taught interpretation, although successful, cannot be the fundamental one because it seems to require a physicist outside the system making measurements (often repeated ones) of it. That would seem to rule out any application to the universe, so that quantum cosmology would be excluded. Also billions of years went by with no physicist in the offing. Are we to believe that quantum mechanics did not apply to those times? In this discussion, we will concentrate on how the Copenhagen approach fits in with ours as a set of special cases and how the “classical world” can be replaced by a quasiclassical realm. Such a realm is not postulated but rather is explained as an emergent feature of the universe characterized by the Hamiltonian H , the quantum state |Ψ〉, and the enormously long sequences of accidents (outcomes of chance events) that constitute the coarse-grained decoherent histories. The material in this paper can be regarded as a discussion of how quasiclassical realms emerge. We say that a ‘measurement situation’ exists if some variables (including such quantummechanical variables as electron spin) come into high correlation with a quasiclassical realm. In this connection we have often referred to fission tracks in mica. Fissionable impurities can undergo radioactive decay and produce fission tracks with randomly distributed definite directions. The tracks are there irrespective of the presence of an “observer”. It makes no difference if a physicist or other human or a chinchilla or a cockroach looks at the tracks. Decoherence of the alternative tracks induced by interaction with the other variables in the universe is what allows the tracks to exist independent of “observation” by an “observer”. All those other variables are effectively doing the “observing”. The same is true of the successive positions of the moon in its orbit not depending on the presence of “observers” and for density fluctuations in the early universe existing when there were no observers around to measure them. The idea of “collapse of the wave function” corresponds to the notion of variables coming into high correlation with a quasiclassical realm, with its decoherent histories that give true