Strong-coupled Relativity without Relativity

TL;DR

This paper develops a family of strong gravity theories within the 3-space approach, extending the regime near singularities where quantization is feasible, and finds that these theories restrict matter coupling and prevent gauge theories.

Contribution

It introduces a new one-parameter family of strong gravity theories derived from scalar-tensor frameworks, expanding the understanding of quantum regimes near singularities.

Findings

Strong gravity theories only couple to ultralocal matter fields.

Gauge theories break down near singularities in these models.

The theories extend the quantization regime of general relativity.

Abstract

GR can be interpreted as a theory of evolving 3-geometries. A recent such formulation, the 3-space approach of Barbour, Foster and \'{O} Murchadha, also permits the construction of a limited number of other theories of evolving 3-geometries, including conformal gravity and strong gravity. In this paper, we use the 3-space approach to construct a 1-parameter family of theories which generalize strong gravity. The usual strong gravity is the strong-coupled limit of GR, which is appropriate near singularities and is one of very few regimes of GR which is amenable to quantization. Our new strong gravity theories are similar limits of scalar-tensor theories such as Brans--Dicke theory, and are likewise appropriate near singularities. They represent an extension of the regime amenable to quantization, which furthermore spans two qualitatively different types of inner product. We find that strong gravity theories permit coupling only to ultralocal matter fields and that they prevent gauge theory. Thus in the classical picture, gauge theory breaks down (rather than undergoing unification) as one approaches the GR initial singularity.