Decoherence and Branching in a Mixed-State Everettian Multiverse

Table of Links

Abstract & Introduction

Decoherence and Branching

The Born Rule

Discussion

Conclusion and References

2 Decoherence and Branching

2.1 Decoherence for Wave Function Realism

In other words, any measurement on the system S, entangled with E, effectively ignores the quantum interference between the macroscopically superposed component states. Notice that the interference terms show up only at the subsystem level (3) and not explicitly at the universal level (2). In §2.2 we shall see that although the story of decoherence applies the same way in DMR, “interference terms” also show up at the universal level, even though, as it is still the case, they make almost no contribution to the evolution of the component states.

2.2 Decoherence for Density Matrix Realism – Pure States

2.3 Decoherence for Density Matrix Realism – Mixed States

In this case, we can say that there are not four branches for the universal density matrix (23), but three:

Compared to the two multiverses (17 and 18) considered in the previous section, this multiverse is more expansive. It contains all the branches of the previous two.

Decoherence is approximate, and so is branching of the Everettian multiverse. They both somewhat depend on how we define macrostates and what counts as macroscopically indistinguishable. For example, with a more fine-grained partition of macrostates, we may as well count the multiverse (23) as having four branches instead of three. While this example is a toy model, we believe it’s representative of how branching occurs in a mixed-state multiverse, and is in line with the general Everettian stance on branching and decoherence.