Back in December Gell-Mann and Hartle (G&H) posted their latest paper on consistent histories, “Adaptive Coarse Graining, Environment, Strong Decoherence, and Quasiclassical Realms”. Here are my thoughts.

The discussion of adaptive coarse graining was brief and very much in agreement with previous work.

G&H then give a name and formal description to the idea, long part of the intuitive lore, of a history being defined by the values taken by a particular variable over many time step. (This might be the position of an object, which is being recorded to some accuracy by a environment that decoheres it.) The key idea is that all the Schrödinger-picture projectors at different times defining the history commute:

(1)

This they call the *narrative condition*. From it, one is able to define a smallest set of maximal projectors (which they call a *common framework*) that obey either or for all . For instance, if the ‘s are onto spatial volumes of position, then the ‘s are just the minimal partition of position space such that the region associated with each is fully contained in the regions corresponding to some of the , and is completely disjoint from the regions corresponding to the others.

For times steps , the history projectors at a given time project into subspaces which disjointly span Hilbert space. The narrative condition states that all history projectors commute, which means we can think of them as projecting onto disjoint subsets forming a partition of the range of some variable (e.g. position). The common framework is just the set of smaller projectors that also partitions the range of the variable and which obey or for each and .