Related papers: Shape dynamics and Mach's principles: Gravity from…
Barbour's formulation of Mach's principle requires a theory of gravity to implement local relativity of clocks, local relativity of rods and spatial covariance. It turns out that relativity of clocks and rods are mutually exclusive. General…
Classical dynamical laws are conventionally formulated as closed evolution equations defined on fixed geometric backgrounds and a global time parameter. We develop a formulation in which neither prescribed evolution laws nor an external…
Shape Dynamics is a theory of gravity that replaces refoliation invariance for spatial Weyl invariance. Those solutions of the Einstein equations that have global, constant mean curvature slicings, are mirrored by solutions in Shape…
This paper is a review of results which have been recently obtained by applying mathematical concepts drawn, in particular, from differential geometry and topology, to the physics of Hamiltonian dynamical systems with many degrees of…
Motivated by well-known obstacles to quantum gravity, I look for the most general geometrodynamical symmetries compatible with a reduced physical configuration space for metric gravity. I argue that they lead either to a completely static…
The general theory of relativity (GR) was proposed with an aim of incorporating Mach's principle mathematically. Despite early hopes, it became evident that GR did not follow Mach's principle. Over time, multiple researchers attempted to…
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 briefly discuss the current status of Mach's principle in general relativity and point out that its last vestige, namely, the gravitomagnetic field associated with rotation, has recently been measured for the earth in the GP-B…
A new and universal method for implementing scale invariance, called best matching, is presented. It extends to scaling the method introduced by Bertotti and the author to create a fully relational dynamics that satisfies Mach's principle.…
General Relativity on closed spatial topologies can be derived, using a technique called "best-matching", as an evolving 3-geometry subject to constraints. These constraints can be thought of as a way of imposing temporal and spatial…
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…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
Relational formulations of classical mechanics and gravity have been developed by Julian Barbour and collaborators. Crucial to these formulations is the notion of shape space. We indicate here that the metric structure of shape space allows…
It is well known that one can parameterize 2-D Riemannian structures by conformal transformations and diffeomorphisms of fiducial constant curvature geometries; and that this construction has a natural setting in general relativity theory…
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…
One of the foremost goals of research in physics is to find the most basic and universal theories that describe our universe. Many theories assume the presence of an absolute space and time in which the physical objects are located and…
The widely known but also somewhat esoteric Mach principle envisages a fully relational formulation of physical theories without any reference to a concept of `absolute space'. When applied to classical mechanics, under the guise of an…
We show that one can construct two equivalent gauge theories from a linking theory and give a general construction principle for linking theories which we use to construct a linking theory that proves the equivalence of General Relativity…
The notion of "reference frame" is a central theoretical construct for interpreting the physical implications of spacetime diffeomorphism invariance in General Relativity. However, the alternative formulation of classical General Relativity…
In recent years, the use of conformal transformation techniques has become widespread in the literature on gravitational theories alternative to general relativity, on cosmology, and on nonminimally coupled scalar fields. Typically, the…