## I. INTRODUCTION 

In recent years, work on quantum gravity and quantum cosmology, in particular, has made it impossible to avoid the interpretational issues of quantum mechanics. When considering the universe as a whole, there is no longer any clean separation between the observer and the observed system or between the classical and quantum worlds. Further, any complete cosmological theory must be fully relativistic. In this arena, traditional interpretations in terms of wave function collapse are particularly unappealing. 

The consistent or decoherent histories approach provides an attractive “no collapse” inter- pretation of quantum physics [1–4]. The basic idea of the approach is to assign probabilities to histories , which are time-ordered sequences of quantum properties of a system. When a family of histories are chosen in such a way that they are consistent , they decohere , and classical probabilities can be assigned to them as alternative histories of the system. 

Consistent histories can also be linked to path-integral formulations of quantum mechan- ics [5–7]. If the quantum properties under consideration can be expressed in terms of particle positions, then a quantum history can be considered to be a superposition of those paths in which the particle passes through positions with the required properties at the required times. Looked at another way, a particle path can be considered to be a fine-grained history in which the particle position is exactly determined at every time, while a path integral rep- resents a coarse-grained history as a superposition of all paths meeting some more general criteria. When the criteria are properly chosen, the states for these coarse-grained histories decohere and can have classical probabilities assigned to them [8–10]. 

The path-integral formulation can also be readily generalized to the relativistic case by replacing paths in space parameterized by time with paths in spacetime parameterized by an invariant path evolution parameter [10–19]. The same consistent histories interpretation of path integrals can then be carried over from the non-relativistic to the relativistic case, where “position” is now understood to mean four-position in spacetime. (For other approaches to relativistic generalization of the consistent histories approach, see [20–23].) 

In [24] I presented an approach, based on a relativistic spacetime path formalism [25, 26], in which entire coarse-grained histories of the universe decohere for all time. Each coarse- grained history of all of spacetime is represented by a cosmological state that is constrained by correlations introduced by the measurement-like processes that occur within the history of 

