Cartography of the space of theories: An interpretational chart for fields that are both (dark) matter and spacetime

This paper pushes back against the Democritean-Newtonian tradition of assuming a strict conceptual dichotomy between spacetime and matter. Our approach proceeds via the more narrow distinction between modified gravity/spacetime (MG) and dark matter (DM). A prequel paper argued that the novel field $\text{Φ}$ postulated by Berezhiani and Khoury’s ‘superfluid dark matter theory’ is as much (dark) matter as anything could possibly be, but also—below the critical temperature for superfluidity—as much (of a modification of) spacetime as anything could possibly be. Here we introduce and critically evaluate three groups of interpretations that one should consider for such Janus-faced theories. The consubstantiality interpretation holds that $\text{Φ}$ is both (dark) matter and a modification of spacetime, analogously to the sense in which Jesus (according to catholicism) is both human and god. The fundamendalist interpretations consider for each of these roles whether they are instantiated fundamentally or emergently. The breakdown interpretations focus on the question of whether $\text{Φ}$ signals the breakdown, in some sense to be specified, of the MG-DM dichotomy and perhaps even the broader spacetime–matter distinction. More generally, it is argued that hybrid theories urge a move towards a single space of theories, rather than two separate spaces of spacetime theories and matter theories, respectively.