Related papers: 'Shape Dynamics': Foundations Reassessed
Shape Dynamics (SD) is a theory dynamically equivalent to vacuum General Relativity (GR), which has a different set of symmetries. It trades refoliation invariance, present in GR, for local 3-dimensional conformal invariance. This…
Barbour's interpretation of Mach's principle led him to postulate that gravity should be formulated as a dynamical theory of spatial conformal geometry, or in his terminology, "shapes." Recently, it was shown that the dynamics of General…
Shape dynamics is a completely background-independent universal framework of dynamical theories from which all absolute elements have been eliminated. For particles, only the variables that describe the shapes of the instantaneous particle…
General Relativity can be reformulated as a geometrodynamical theory, called Shape Dynamics, that is not based on spacetime (in particular refoliation) symmetry but on spatial diffeomorphism and local spatial conformal symmetry. This leads…
Shape Dynamics is a metric theory of pure gravity, equivalent to General Relativity, but formulated as a gauge theory of spatial diffeomporphisms and local spatial conformal transformations. In this paper we extend the construction of Shape…
Shape Dynamics (SD) is a new theory of gravity that is based on fewer and more fundamental first principles than General Relativity (GR). The most important feature of SD is the replacement of GR's relativity of simultaneity with a more…
This thesis consists of two parts, connected by one central theme: the dynamics of the "shape of space". The first part of the thesis concerns the construction of a theory of gravity dynamically equivalent to general relativity (GR) in 3+1…
In this PhD thesis, we develop a new approach to classical gravity starting from Mach's principles and the idea that the local shape of spatial configurations is fundamental. This new theory, "shape dynamics", is equivalent to general…
Shape dynamics is a reformulation of general relativity, locally equivalent to Einstein's theory, in which the refoliation invariance of the older theory is traded for local scale invariance. Shape dynamics is here derived in a formulation…
Shape Dynamics is a gauge theory based on spatial diffeomorphism- and Weyl-invariance which is locally indistinguishable form classical General Relativity. If taken seriously, it suggests that the spacetime--geometry picture that underlies…
Shape dynamics is an alternative background-independent approach to classical dynamics that implements Leibnizian philosophy and Mach's Principles. It is a formulation of the dynamics of the universe in terms of the intrinsic and relational…
Shape dynamics is a reframing of canonical general relativity in which time reparametrization invariance is "traded" for a local conformal invariance. We explore the emergence of Lorentz invariance in this model in three contexts: as a…
Shape dynamics is a theory first proposed by Julian Barbour which states that physics happen uniquely in the reduced configuration space of a theory. So far, studies in the area have focused on gravitational systems. Here we first…
We present a scale-invariant theory, conformal gravity, which closely resembles the geometrodynamical formulation of general relativity (GR). While previous attempts to create scale-invariant theories of gravity have been based on Weyl's…
Shape Dynamics is a 3D conformally invariant theory of gravity which possesses a large set of solutions in common with General Relativity. When looked closely, these solutions are found to behave in surprising ways, so in order to probe the…
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…
Classical gravity can be described as a relational dynamical system without ever appealing to spacetime or its geometry. This description is the so-called shape dynamics description of gravity. The existence of relational first principles…
Shape Dynamics is a formulation of General Relativity where refoliation invariance is traded for local spatial conformal invariance. In this paper we explicitly construct Shape Dynamics for a torus universe in 2+1 dimensions through a…
This paper investigates a family of dynamical systems arising from an evolutionary re-interpretation of certain optimal control and optimization problems. We focus particularly on the application in image registration of the theory of…
Mixing, and coherence are fundamental issues at the heart of understanding transport in fluid dynamics and other non-autonomous dynamical systems. Recently, the notion of coherence has come to a more rigorous footing, and particularly…