I’m happy to use this bully pulpit to advertise that the following paper has been deemed “probably not terrible”, i.e., published.

Here’s the figure^{a } and caption:

It is my highly unusual opinion that identifying a definition for the branches in the wavefunction is the most conceptually important problem is physics. The reasoning is straightforward: (1) quantum mechanics is the most profound thing we know about the universe, (2) the measurement process is at the heart of the weirdness, and (3) the critical roadblock to analysis is a definition of what we’re talking about. (Each step is of course highly disputed, and I won’t defend the reasoning here.) In my biased opinion, the paper represents the closest yet anyone has gotten to giving a mathematically precise definition.

On the last page of the paper, I speculate on the possibility that branch finding may have practical (!) applications for speeding up numerical simulations of quantum many-body systems using matrix-product states (MPS), or tensor networks in general. The rough idea is this: Generic quantum systems are exponentially hard to simulate, but classical systems (even stochastic ones) are not. A definition of branches would identify *which degrees of freedom* of a quantum system could be accurately simulated classically, and when. Although classical computational transitions are understood in many certain special cases, our macroscopic observations of the real world strongly suggest that *all* systems we study admit classical descriptions on large enough scales. … [continue reading]