as Lorentz invariance can be tested to high precision Liberati (2013).
One might also worry
about compatibility with the WheelerDeWitt equation of quantum gravity, which takes the
form
ˆ
H

Ψ
i
= 0. In this case the eigenvalues of
ˆ
H
are seemingly irrelevant, since the world is
fully described by a zeroenergy eigenstate [cf. (Albrecht & Iglesias, 2008)]. But there is also
no fundamental time evolution; that is the wellknown “problem of time” (Anderson, 2010).
A standard solution is to imagine that time is emergent, which amounts to writing the full
Hamiltonian as
ˆ
H
=
ˆ
H
eff

i
d
dτ
,
(14)
where
τ
is the emergent time parameter. In that case everything we have said thus far still goes
through, only using the eigenvalues of the effective Hamiltonian
ˆ
H
eff
.
In addition to spacetime, we still have to show how local quantum fields can emerge in the
same sense as the spacetime metric.
Less explicit progress has been made in reconstructing
approximate 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. One
promising route is via “string net condensates,” which have been argued to lead naturally to
emergent gauge bosons and fermions (Levin & Wen, 2005).
Nothing in this perspective implies that we should think of spacetime or quantum fields as
illusory. They are emergent, but none the less real for that. As mentioned, we we may not be
forced to invoke these concepts within our most fundamental picture, but the fact that they
play a role in an emergent description is highly nontrivial. (Most Hamiltonians admit no local
decomposition, most factorizations admit no classical limit, etc.) It is precisely this nongeneric
characteristic of the specific features of the world of our experience that makes it possible to
11
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 that
may ultimately fail). But the lesson for fundamental ontology is hopefully clear. Thinking of
the world as represented by simply a vector in Hilbert space, evolving unitarily according to the
Schr¨
odinger equation governed by a Hamiltonian specified only by its energy eigenvalues, seems
at first hopelessly far away from the warm, welcoming, richlystructured ontology we are used to
thinking about in physics. But recognizing that the latter is plausibly a higherlevel emergent
description, and contemplating the possibility that the more fundamental vocabulary is the one
straightforwardly suggested by our simplest construal of the rules of quantum theory, leads to a
reconstruction program that appears remarkably plausible. By taking the prospect of emergence
seriously, and acknowledging that our fondness for attributing metaphysical fundamentality to
the spatial arena is more a matter of convenience and convention than one of principle, it is
possible to see how the basic ingredients of the world might be boiled down to a list of energy
eigenvalues and the components of a vector in Hilbert space.