Supersymmetry and the Philosophy of Space and Time

Abstract: Some areas of physics are heavily discussed by philosophers; others are engaged with more sparsely. Despite its being a central component of many attempts to go beyond the standard model of particle physics, supersymmetry (SUSY) is an example of the latter. This talk is part of an ongoing project to establish a discussion in the philosophy of SUSY.

SUSY is a proposed dynamical symmetry between bosons (broadly speaking, force carriers) and fermions (matter). As a result of being a transformation between particles of different spin, the algebra of its generators has an interesting feature---it appears to allow for an interpretation as a (generalisation of a) spacetime symmetry. Construing SUSY as such, it is possible to re-express the theory in a new setting---superspace, in which ordinary Minkowski spacetime is augmented with a number of anticommuting ‘dimensions’. These are dimensions along which, counter-intuitively, coordinate values are sensitive to the order in which they are multiplied---they cannot, therefore, be visualised in the way that ordinary spatial or temporal dimensions are, as lines extending in some direction. Even though superspace is not a geometry in the familiar point-set sense, it manifests geometric structure in a more general, algebraic way: objects with the algebraic properties of vectors, tensors, derivative operators and so on are well-defined. Thus metrical and inertial structures exist in superspace, but algebraically. In this talk, I address the question of what difference this generalisation makes to our understanding of the roles of the metric and inertial structure in constituting spacetime.

(No prior familiarity with supersymmetry or quantum field theory will be assumed)