Title: How to build a unified field theory from one dimension
Abstract: Motivated in part by Kant's work on the a priori nature of space and time, and in part by the conceptual basis of general relativity, a physical theory deriving from a single temporal dimension will be presented. We describe how the basic arithmetic composition of the real line, representing the one dimension of time, itself incorporates structures that can be interpreted as underpinning both the geometrical form of space and the physical form of matter. This unification scheme has a number of features in common with a range of physical theories based on 'extra dimensions' of space, while being heavily constrained in deriving from a single dimension of time. A proposal for combining general relativity with quantum theory in the context of this approach will be summarised, along with the connections made with empirical observations. In addition to extracts from Kant further references to sources in the philosophical literature will be cited, in particular with regard to the relation between mathematical objects and physical structures.
