An interesting thought experiment would be to create a large quantum wave-function describing both a pair of electrons with entangled spins and the equipment needed to measure the electrons' spins. In theory, this wavefunction could be evolved in time and monitored to see if any process mimicking measurement of the electrons' spins occurs.
However, as the QED Lagrangian is local I believe such a system could not violate Bell's inequality. Is that correct?
Does that mean that QED (with measurement) is not a self-consistent theory as it admits two methods of modelling the same physics which produce different results?