emergence unless the metric is absent as a fundamental field.

Gravity as a metric theory \[EPSsec\]
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Before proceeding further, it is worthwhile to review the physical basis for treating gravity as a metric theory. As first discussed by Weyl and later developed by Ehlers, Pirani, and Schild [@EPS], the observations of local Lorentz invariance and the universality of free fall allow one to construct a metric description of gravity. Briefly summarized, the argument goes as follows [@EPS; @Woodhouse] (for a somewhat different approach, see section 2.3 of [@Will]):

1.  [**Local Lorentz invariance**]{} implies the existence of a field of light cones, which establishes a causal structure and a topology. The light cones also determine a conformal structure—an equivalence class of metrics that differ only by local rescalings—for which paths of light rays are null geodesics.

2.  [**The equivalence principle**]{}, specifically the universality of free fall, determines a set of preferred paths in spacetime, the trajectories of freely falling structureless objects. Such a projective structure, in turn, determines an equivalence class of affine connections for which these paths are geodesics.

3.  [**Compatibility**]{} of these two structures—the observation that the trajectories of freely falling massive objects lie within the light cones 