Thu Nov 3, 2011
Tim Maudlin (New York University)
New Foundations for Physical Geometry
Abstract: Accounts of the nature space and time, and hence space-time, are largely specifications of a geometrical structure among events. The usual mathematical tool used to describe the most fundamental geometrical structure of a space is topology. Standard topology is founded on the basic notion of an open set of points in a space. I will argue that this mathematical tool is poorly constructed for understanding physical geometry, and will propose an alternative: the Theory of Linear Structures. I will present the axioms of the new theory, and develop enough of its architecture to allow for direct comparisons with standard topology. Application of the new theory to Relativity reveals a way to reduce physical geometry completely to the temporal structure of events. That is, instead of Relativity spatializing time, as is commonly claimed, it allows us to temporalize space.