Pure shape dynamics: General framework

TL;DR

Pure Shape Dynamics (PSD) offers a new relational framework for describing physical systems through intrinsic geometry of shape space, emphasizing ratios of change in geometric degrees of freedom.

Contribution

It introduces a novel approach to relational physics by formulating dynamics entirely in terms of shape space geometry and shape phase space.

Findings

Framework unifies relational descriptions of physical systems.

Mathematical structure involves shape phase space and local sections.

Provides a geometric equation of state for dynamical systems.

Abstract

We put forward a general framework for describing relational physical theories, which we call Pure Shape Dynamics (PSD). Elaborating on the original insights brought about by the Shape Dynamics program, PSD's novel take on relationalism is its insistence on describing any dynamical system by means of the intrinsic geometry of its associated curve in the suitable relational configuration space of the theory, namely shape space, whereby the corresponding equation of state of the curve expresses the ratio of change of one of its geometric degrees of freedom with respect to another one. The mathematical structure underlying the equation of state is a local section over a natural generalization of the unit tangent bundle, which we call shape phase space.