  In the Ashtekar-Barbero formulation of canonical general relativity based on
an SU(2) connection, Lorentz covariance is a subtle issue which has been the
focus of some debate. Here we present a Lorentz covariant formulation
generalising the notion of a foliation of spacetime to a field of local
observers which specify a time direction only locally. This field spontaneously
breaks the local SO(3,1) symmetry down to a subgroup SO(3); we show that the
apparent symmetry breaking to SO(3) is not in conflict with Lorentz covariance.
We give a geometric picture of our construction as Cartan geometrodynamics and
outline further applications of the formalism of local observers, motivating
the idea that observer space, instead of spacetime, should serve as the
fundamental arena for gravitational physics.
