  A model for two entangled systems in an EPR setting is shown to reproduce the
quantum-mechanical outcomes and expectation values. Each system is represented
by a small sphere containing a point-like particle embedded in a field. A
quantum state appears as an equivalence class of several possible
particle-field configurations. Contrarily to Bell-type hidden variables models,
the fields account for the non-commutative aspects of the measurements and deny
the simultaneous reality of incompatible physical quantities, thereby allowing
to escape EPR's ``completeness or locality'' dilemma.
