He turns to: a concrete non-spacetime example of emergence; as prototype for spacetime proposal
He sketches the way that starting from a coherent state in an non-relativistic quantum field theory of bosons, one can derive, for certain parameter values, the Gross-Pitaevski equation for the coherent state’s defining wave-function phi, where phi is now considered as a classical collective variable (and the Gross-Pitaevski equation is classical, albeit non-linear and containing hbar).
This illustrates both the points made above (i): The compatibility of reduction and emergence, since the hydrodynamic Gross-Pitaevskii equation is deduced from the microscopic theory, but exhibits novel behavior relative to that theory. (ii): Maudlin’s objection, i.e. his requirement that a theory postulate local beables, being too strong. Thus he writes: (quoting from the paper, Section V):
Now suppose that we did not have access to the atoms at all, experimentally, but still, because we were so smart, we had managed to guess the microscopic theory [i.e. the non-relativistic quantum field theory of bosons], and then even so smart as to guess the appropriate approximate ground state of the system [i.e. the coherent state] … Suppose that we insisted on the idea that the macroscopic fluid we lived in (yes, we are supposing we are unfortunate but smart fishes swimming in the cold superfluid) was only emergent from something totally different, and unaccessible, and almost unthinkable, the “atoms of the fluid”. Suppose that we had managed even to find an approximate derivation of the hydrodynamic equation from the microscopic theory, and thus to hypothetically explain some features of the fluid in terms of its [postulated] atoms. In such a situation, . . . [the microscopic theory], despite not allowing ‘fluid beables’ to describe the atoms, [would surely] still be “physically salient”.