Once upon a time in superspace: the diegetic ideal for the interpretation of physical theories

This paper offers a novel argument for superspace substantivalism. Superspace is a modified spacetime represented formally through combining ordinary spatial dimensions with anticommuting dimensions whose coordinates are labelled in Grassmann numbers rather than real numbers. At supersymmetric worlds, physical laws exhibit supersymmetry—viz., a symmetry that transforms bosons into fermions and vice versa. Superspace substantivalism is the thesis that, at supersymmetric worlds, among the most fundamental structures is superspace. Initially, the focus will be on a prevalent doctrine in the philosophy of physics literature which I call the mimetic ideal. On the mimetic ideal, interpreting physical theories aims primarily at specifying their ontology, namely at achieving accurate reference (in natural-language accounts of those theories) or representation (in model-theoretic portrayals of those theories) with respect to aspects of physical reality. However, I show that the mimetic ideal doesn’t seem able to account for important aspects of physics practice (Sect. 2). In Sect. 3, therefore, I articulate and defend a new, diegetic ideal, according to which the interpretation of physical theories should aim at perspectival coordination between interpreters and practising physicists. Perspectival coordination, in the context of interpreting physical theories, means that interpreters and practising physicists share a perspective or a point of view on some aspect of physical reality described by that theory. In Sect. 4, I apply this analysis to the study of supersymmetric quantum field theories (QFTs): reframing the realist framework which underlies Baker’s (2020) agnosticism, I examine the exciting upshot that superspace substantivalism is true. I conclude with some reflections on what perspectival coordination means for realism (Sect. 5).