Shape dynamics and Mach's principles: Gravity from conformal geometrodynamics

Understand

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 relativity but differs in an important respect: shape dynamics is a theory of dynamic conformal 3-geometry, not a theory of spacetime.
• Equivalence is achieved by trading foliation invariance for local conformal invariance (up to a global scale).
• After the trading, what is left is a gauge theory invariant under 3d diffeomorphisms and conformal transformations that preserve the volume of space.