Tim Koslowski -- A geometric approach to Shape Dynamics

"Observers in the Cosmos" conference at the University of Bristol. Recorded: 23 May 2018 Funded by FQXi. Title: A geometric approach to Shape Dynamics Abstract: Shape dynamics is a framework that builds up fundamental physics from simple relational first principles, which do not allow for any non-dynamical reference structures. In particular there are no non-dynamical rods and clocks, there are only evolving ratios of physical quantities. This can be formalized as the statement that shape dynamics describes the dynamics of the universe as a pure curve (without parametrization) in relational configuration space (shape space). I formalize this by the mathematical statement: "The dynamics of the universe is described as an equation of state of the local differential geometry of a pure curve on shape space." The local geometric properties are a point in the unit tangent bundle over shape space and curvature degrees of freedom. The space of these geometric properties is the shape phase space and the equations of motion are a section in the unit tangent bundle over this shape phase space.