  We consider notions of physical equivalence of sets of histories in the
quantum mechanics of a closed system. We show first how the same set of
histories can be relabeled in various ways, including the use of the Heisenberg
equations of motion and of passive transformations of field variables. In the
the usual approximate quantum mechanics of a measured subsystem, two
observables re- presented by different Hermitian operators are physically
distinguished by the different apparatus used to measure them. In the quantum
mechanics of a closed system, however, any apparatus is part of the system and
the notion of physically distinct situations has a different character. We show
that a triple consisting of an initial condition, a Hamiltonian, and a set of
histories is physically equivalent to another triple if the operators
representing these initial conditions, Hamiltonians, and histories are related
by any fixed unitary transformation. We apply this result to the question of
whether the universe might exhibit physically inequivalent quasiclassical
realms (which we earlier called quasiclassical domains), not just the one that
includes familiar experience. We describe how the probabilities of alternative
forms, behaviors, and evolutionary histories of information gathering and
utilizing systems (IGUSes) using the usual quasiclassical realm could in
principle be calculated in quantum cosmology, although it is, of course,
impractical to perform the computations. We discuss how, in principle, the
probabilities of occurence of IGUSes could be calculated in realms distinct
from the usual quasiclassical one. We discuss how IGUSes adapted mainly to two
different realms could draw inferences about each other using a hybrid realm
consisting of alternatives drawn from each.
