The paper constructs, for any local C^2 Lorentzian metric, six Poincaré-invariant quantum systems whose empirical distance observable reproduces the local geodesic lengths and thus the curvature, but only because the curvature is built into the chosen states.
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Curved spacetimes from quantum mechanics
The paper constructs, for any local C^2 Lorentzian metric, six Poincaré-invariant quantum systems whose empirical distance observable reproduces the local geodesic lengths and thus the curvature, but only because the curvature is built into the chosen states.