Tushar Menon (University of Oxford)
The dynamical approach to physical geometry, developed by Harvey Brown and Oliver Pooley, has been the subject of a number of papers over the last decade or so. The position asserts, among other things, that facts about physical geometry are grounded in, or explained by, facts about dynamical fields, not the other way round. One critic in particular, John Norton, is taken to have articulated a robust objection to the view. His claim is that the proponent of the dynamical approach is illictly committed to spatiotemporal presuppositions in 'constructing' spacetime from facts about dynamical symmetries. In this paper, I present an abstract, algebraic formulation of field theories, based on the mathematics of non-commutative field theories and demonstrate how to reproduce the ubiquitous model-theoretic picture of a theory like SR in algebraic terms. I then introduce an extension to the dynamical approach that does away with the requirement of a smooth manifold, the 'illicit spatiotemporal presupposition' that Norton identifies. I argue that the extended dynamical approach is thus immune to the charges that Norton levels against it.
