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.
Constructive Axiomatics in Spacetime Physics Part I: Walkthrough to the Ehlers-Pirani-Schild Axiomatisation
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abstract
The Ehlers-Pirani-Schild (EPS) constructive axiomatisation of general relativity, published in 1972, purports to build up the kinematical structure of that theory from only axioms which have indubitable empirical content. It is, therefore, of profound significance both to the epistemology and to the metaphysics of spacetime theories. This axiomatisation is, however, self-consciously terse, rendering it difficult to ascertain whether it succeeds. In this article, we provide a pedagogical walkthrough to the EPS axiomatisation, filling relevant conceptual and mathematical gaps and rendering explicit controversial assumptions. There are two companion papers, in which we discuss the significance of constructive approaches to spacetime structure more generally (Part II), and (with Emily Adlam) consider extensions of the EPS axiomatisation towards quantum general relativity based upon quantum mechanical inputs (Part III).
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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.