as Lorentz invariance can be tested to high precision Liberati (2013).One might also worryabout compatibility with the Wheeler-DeWitt equation of quantum gravity, which takes theformˆH|Ψi= 0. In this case the eigenvalues ofˆHare seemingly irrelevant, since the world isfully described by a zero-energy eigenstate [cf. (Albrecht & Iglesias, 2008)]. But there is alsono fundamental time evolution; that is the well-known “problem of time” (Anderson, 2010).A standard solution is to imagine that time is emergent, which amounts to writing the fullHamiltonian asˆH=ˆHeff-iddτ,(14)whereτis the emergent time parameter. In that case everything we have said thus far still goesthrough, only using the eigenvalues of the effective HamiltonianˆHeff.In addition to spacetime, we still have to show how local quantum fields can emerge in thesame sense as the spacetime metric.Less explicit progress has been made in reconstructingapproximate quantum field theories from the spectrum of the Hamiltonian, but it’s not unrea-sonable to hope that this task is more straightforward than reconstructing spacetime itself. Onepromising route is via “string net condensates,” which have been argued to lead naturally toemergent gauge bosons and fermions (Levin & Wen, 2005).Nothing in this perspective implies that we should think of spacetime or quantum fields asillusory. They are emergent, but none the less real for that. As mentioned, we we may not beforced to invoke these concepts within our most fundamental picture, but the fact that theyplay a role in an emergent description is highly non-trivial. (Most Hamiltonians admit no localdecomposition, most factorizations admit no classical limit, etc.) It is precisely this non-genericcharacteristic of the specific features of the world of our experience that makes it possible to11
contemplate uniquely defining them in terms of the austere ingredients of the deeper theory.They should therefore be thought of as equally real as tables and chairs.This has been an overly concise discussion of an ambitious research program (and one thatmay ultimately fail). But the lesson for fundamental ontology is hopefully clear. Thinking ofthe world as represented by simply a vector in Hilbert space, evolving unitarily according to theSchr¨odinger equation governed by a Hamiltonian specified only by its energy eigenvalues, seemsat first hopelessly far away from the warm, welcoming, richly-structured ontology we are used tothinking about in physics. But recognizing that the latter is plausibly a higher-level emergentdescription, and contemplating the possibility that the more fundamental vocabulary is the onestraightforwardly suggested by our simplest construal of the rules of quantum theory, leads to areconstruction program that appears remarkably plausible. By taking the prospect of emergenceseriously, and acknowledging that our fondness for attributing metaphysical fundamentality tothe spatial arena is more a matter of convenience and convention than one of principle, it ispossible to see how the basic ingredients of the world might be boiled down to a list of energyeigenvalues and the components of a vector in Hilbert space.