A senior colleague asked me for thoughts on this paper describing a single-preferred-branch flavor of quantum mechanics, and I thought I’d copy them here. **Tl;dr**: I did not find an important new idea in it, but this paper nicely illustrates the appeal of Finkelstein’s partial-trace decoherence and the ambiguity inherent in connecting a many-worlds wavefunction to our direct observations.

We start by assuming that a precise wavefunction branch structure has been specified. The idea, basically, is to randomly draw a branch at late times according to the Born probability, then to evolve it backwards in time to the beginning of the universe and take *that* as your initial condition. The main motivating observation is that, if we assume that all branch splittings are defined by a projective decomposition of some subsystem (‘the system’) which is recorded faithfully elsewhere (‘the environment’), then the lone preferred branch — time-evolving by itself — is an eigenstate of each of the projectors defining the splits. In a sense, Weingarten lays claim to *ordered consistency* [arxiv:gr-qc/9607073] by assuming partial-trace decoherence^{ a } [arXiv:gr-qc/9301004]. In this way, the macrostate states stay the same as normal quantum mechanics but the microstates secretly conspire to confine the universe to a single branch.

I put proposals like this in the same category as Bohmian mechanics. They take as assumptions the initial state and unitary evolution of the universe, along with the conventional decoherence/amplification story that argues for (but never fully specifies from first principles) a fuzzy, time-dependent decomposition of the wavefunction into branches. To this they add something that “picks out” one of the branches as preferred. By Bell’s theorem, the added thing has to have at least one very unattractive quality (e.g., non-locality, superdeterminism, etc.), and then the game is to try to convince oneself that something else about it makes it attractive enough to choose on aesthetic grounds over normal quantum mechanics.^{ b }

Weingarten is refreshingly clear about this and correctly characterizes his proposal as a hidden variable theory. I’d say its virtue is that, on its face, it doesn’t introduce new mathematical objects like the Bohm particle. However, if we try and quantify theory elegance with something like algorithmic complexity, then the bit string *b* used to specify the preferred branch (which is necessary to write down the complete theory, unlike normal quantum mechanics) is an equivalently inelegant structure.

Weingarten argues (in the paragraph beginning “Each |Ψ(h_{j},t)> may be viewed…”) that this proposal solves most of the fuzziness problems associated with the decoherence story, but I’d say it just repackages them. You need to help yourself to a precise choice of splitting events (when exactly they happen, etc.) to even define the ensemble of branches |Ψ(h_{j},t)⟩, but if you assume you already have that precision, then what’s the problem? Why not just declare that the set of branches is nothing but an ensemble of potential outcomes, exactly one of which is chosen at random (according to the Born probability), thereby reducing quantum mechanics to a classical non-local stochastic theory?

Perhaps Weingarten’s issue is that Many-Worlders like Davide Wallace often embrace a fuzzy/emergent nature of branches, likening them to the fuzzy/emergent nature of a tiger, and refuse to specify an arbitrary precise definition. But then it seems Weingarten would be happy with a consistent histories interpretation, where the branches are specified precisely with projectors…whose precision, insofar as it exceeds the fuzziness inherent to the decoherence story, is just picked arbitrarily.

Indeed, despite the marked inelegance of Bohmian mechanics, it has at least one advantage over Weingarten’s proposal: the Bohm particle path is automatically precise and this requires only an initial random sample from a well-defined probability distribution (to be compared with an arbitrary and still unspecified choice of branch structure). This means that, if we accept the Bohm story, branches can be fuzzy for the same reason that we’re OK with tigers being fuzzy in a universe where we understand atomic physics precisely.

Finally, note that, in the far future, this single-branch theory shares a problem with all theories that take branches as fundamental: eventually, the universe will thermalize and branch structure must break down.

### Footnotes

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- Note on terminology: What Finkelstein called “partial-trace decoherence” is really a specialized form of
*consistency*(i.e., a mathematical criterion for sets of consistent histories) that captures some, but not all, of the properties of the physical and dynamical process of decoherence. That’s why I’ve called it “partial-trace consistency” here and here.↵ - In addition to Bohmian mechanics, see important examples like Kent’s late-time photodetection [arXiv:1608.04805] and the “Many Interacting Worlds” [PRX 4, 041013 (2014)].↵

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