Isometrodynamics and Gravity

TL;DR

This paper explores Isometrodynamics, a gauge theory of volume-preserving diffeomorphisms, as a fundamental framework for gravity, deriving Newton's law from the effective field theory of gauge fields coupled to matter.

Contribution

It introduces a novel interpretation of Isometrodynamics as a fundamental theory of gravity, connecting gauge fields in inner space to gravitational phenomena.

Findings

Derivation of Newton's inverse square law from gauge field interactions.

Identification of the Planck length as a natural scale in the gauge action.

Effective field theory with an expansion parameter related to the Planck length.

Abstract

Isometrodynamics (ID), the gauge theory of the group of volume-preserving diffeomorphisms of an "inner" D-dimensional flat space, is tentatively interpreted as a fundamental theory of gravity. Dimensional analysis shows that the Planck length l_P - and through it \hbar and \Gamma - enters the gauge field action linking ID and gravity in a natural way. Noting that the ID gauge field couples solely through derivatives acting on "inner" space variables all ID fields are Taylor-expanded in "inner" space. Integrating out the "inner" space variables yields an effective field theory for the coefficient fields with l_P^2 emerging as the expansion parameter. For \hbar goint to zero only the leading order field does not vanish. This classical field couples to the matter Noether currents and charges related to the translation invariance in "inner" space. A model coupling this leading order field to a matter point source is established and solved. Interpreting the matter Noether charge in terms of gravitational mass Newton's inverse square law is finally derived for a static gauge field source and a slowly moving test particle. Gravity emerges as potentially related to field variations over "inner" space and might microscopically be described by the ID gauge field or equivalently by an infinite string of coefficient fields only the leading term of which is related to the macroscopical effects of gravity.