Interacting vector fields in Relativity without Relativity

TL;DR

This paper completes the 3-space approach framework by demonstrating that interacting 3-vector fields naturally emerge as Yang–Mills fields coupled to gravity, all without presupposing relativity.

Contribution

It shows that within the 3-space approach, vector fields interact only as Yang–Mills fields coupled to gravity, completing the bosonic sector's formulation without assuming relativity.

Findings

Vector fields interact as Yang–Mills fields

Gravity and relativity emerge from geodesic dynamics

Framework unifies bosonic interactions without presupposing relativity

Abstract

Barbour, Foster and \'{O} Murchadha have recently developed a new framework, called here {\it{the 3-space approach}}, for the formulation of classical bosonic dynamics. Neither time nor a locally Minkowskian structure of spacetime are presupposed. Both arise as emergent features of the world from geodesic-type dynamics on a space of 3-dimensional metric--matter configurations. In fact gravity, the universal light cone and Abelian gauge theory minimally coupled to gravity all arise naturally through a single common mechanism. It yields relativity -- and more -- without presupposing relativity. This paper completes the recovery of the presently known bosonic sector within the 3-space approach. We show, for a rather general ansatz, that 3-vector fields can interact among themselves only as Yang--Mills fields minimally coupled to gravity.