Dynamics of Pure Shape, Relativity and the Problem of Time

TL;DR

This paper introduces a relational approach to universe dynamics based solely on shape, linking relativity principles and the problem of time, leading to new predictions and a unified view of fundamental physics.

Contribution

It presents a novel shape-based formulation of dynamics that unifies special relativity, general relativity, and gauge principles through a relational framework.

Findings

Stronger predictions than Newtonian theory.

Unified emergence of relativity and gauge principles.

Unique definition of simultaneity in shape dynamics.

Abstract

A new approach to the dynamics of the universe based on work by O Murchadha, Foster, Anderson and the author is presented. The only kinematics presupposed is the spatial geometry needed to define configuration spaces in purely relational terms. A new formulation of the relativity principle based on Poincare's analysis of the problem of absolute and relative motion (Mach's principle) is given. The enire dynamics is based on shape and nothing else. It leads to much stronger predictions than standard Newtonian theory. For the dynamics of Riemannian 3-geometries on which matter fields also evolve, implementation of the new relativity principle establishes unexpected links between special relativity, general relativity and the gauge principle. They all emerge together as a self-consistent complex from a unified and completely relational approach to dynamics. A connection between time and scale invariance is established. In particular, the representation of general relativity as evolution of the shape of space leads to unique definition of simultaneity. This opens up the prospect of a solution of the problem of time in quantum gravity on the basis of a fundamental dynamical principle.