Quantum mereology, reading the structure of the universe from its spectrum.

A quantum Hamiltonian encodes a spectrum and a preferred basis, i.e a preferred tensor structure that gives a natural decomposition of the system into independent smaller subsystems. Quantum mechanics is independent of the basis, so arguably the spectrum is the most fundamental object.

This raises the question : given the spectrum of a system, can we recover its preferred tensor structure? We present a procedure to do quantum mereology i.e to identify a hierarchical decomposition into subsystems from a spectrum. We use this procedure to suggest a possible mechanism for the emergence of geometric locality and classicality from quantum mechanics itself.