The multiple realizability of general relativity in quantum gravity
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Must a theory of quantum gravity have some truth to it if it can recover general relativity in some limit of the theory? This paper answers this question in the negative by indicating that general relativity is multiply realizable in quantum gravity. The argument is inspired by spacetime functionalism—multiple realizability being a central tenet of functionalism—and proceeds via three case studies: induced gravity, thermodynamic gravity, and entanglement gravity. In these, general relativity in the form of the Einstein field equations can be recovered from elements that are either manifestly multiply realizable or at least of the generic nature that is suggestive of functions. If general relativity, as argued here, can inherit this multiple realizability, then a theory of quantum gravity can recover general relativity while being completely wrong about the posited microstructure. As a consequence, the recovery of general relativity cannot serve as the ultimate arbiter that decides which theory of quantum gravity that is worthy of pursuit, even though it is of course not irrelevant either qua quantum gravity. Thus, the recovery of general relativity in string theory, for instance, does not guarantee that the stringy account of the world is on the right track; despite sentiments to the contrary among string theorists.
KeywordsQuantum gravity General relativity Spacetime functionalism Entanglement Emergent gravity Multiple realizability String theory
I would like to express my gratitude to Niels Linnemann, Kian Salimkhani, Astrid Rasch, Richard Dawid, Sorin Bangu, and two anonymous reviewers of Synthese for valuable feedback on and helpful discussion of earlier drafts of this paper. I also send my thanks for constructing comments to the participants at the Spacetime Functionalism Workshop (University of Geneva) and 1st Scandinavian Workshop on the Metaphysics of Science (NTNU) where earlier versions of this paper was presented.
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