The ideas of decoherence (see Ref. 6) were not meant as an interpretation of quantum mechanics but they are sometimes construed that way. In decoherence, the surrounding environment of a multi-quantum-version atomic-level system such as an electron or an atom often causes a system to collapse to just one version. But the environment cannot, in general, cause collapse in macroscopically relevant situations.

To see this, suppose we do a Stern-Gerlach experiment on a spin _ silver atom. As soon as the wave function of the silver atom separates into two non-overlapping parts (as it goes through the magnetic field), the universe is divided into two separate, non-interacting versions (see Separate Universes in Quantum Mechanics). Because the two versions are isolated in separate universes, each will keep its same ‘size’ (same norm, same coefficient). Nothing in the versions of the detectors, or the versions of the environment in general, can change the sizes of the two parts once they separate. Thus there can be no collapse and so there is no singling out mechanism. But a singling out mechanism is required by the probability law (see Probability and Constraints on Interpretations), so the physical process of decoherence cannot provide a satisfactory interpretation of quantum mechanics.

The same is true for Consistent Histories; because it is just quantum mechanics as usual, it provides no singling out mechanism, no means of collapse.