One might also worry about compatibility with the

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as Lorentz invariance can be tested to high precision Liberati (2013). One might also worry about compatibility with the Wheeler-DeWitt 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 zero-energy eigenstate [cf. (Albrecht & Iglesias, 2008)]. But there is also no 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 full Hamiltonian as ˆ H = ˆ H eff - i d , (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 non-trivial. (Most Hamiltonians admit no local decomposition, most factorizations admit no classical limit, etc.) It is precisely this non-generic 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, richly-structured ontology we are used to thinking about in physics. But recognizing that the latter is plausibly a higher-level 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.

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