This post is (a seed of) a bibliography covering the primordial research area that goes by some of the following names:
- The “preferred-factorization problem”, aka “quantum mereology”, in the context of decoherence.
- The “set-selection problem” in the context of consistent histories.^{a }
- The “problem of defining wavefunction branches” especially in the context of a many-body lattice.
Although the way this problem tends to be formalized varies with context, I don’t think we have confidence in any of the formalizations. The different versions are very tightly related, so that a solution in one context is likely give, or at least strongly point toward, solutions for the others.
As a time-saving device, I will just quote a few paragraphs from existing papers that review the literature, along with the relevant part of their list of references. I hope to update this from time to time, and perhaps turn it into a proper review article of its own one day. If you have a recommendation for this bibliography (either a single citation, or a paper I should quote), please do let me know.
Carroll & Singh
From “Quantum Mereology: Factorizing Hilbert Space into Subsystems with Quasi-Classical Dynamics”, arXiv:2005.12938:
… [continue reading]While this question has not frequently been addressed in the literature on quantum foundations and emergence of classicality, a few works have highlighted its importance and made attempts to understand it better. Brun and Hartle [2] studied the emergence of preferred coarse-grained classical variables in a chain of quantum harmonic oscillators. Efforts to address the closely related question of identifying classical set of histories (also known as the “Set Selection” problem) in the Decoherent Histories formalism [3–7, 10] have also been undertaken.