Interacting vector fields in Relativity without Relativity

Barbour, Foster and Ó Murchadha have recently developed a new framework, called here 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. Electronic addresses: [email protected], [email protected]