  We discuss the generation of field-induced entanglement between two objects
each in a superposition of two trajectories. The objects have currents coupled
to local quantum fields, and the currents are evaluated by using classical
values associated with each trajectory of the objects. If the fields have only
dynamical degrees of freedom and satisfy the microcausality condition, we show
that the objects initially in a product state cannot be entangled when they are
spacelike separated. This means that such quantum fields do not work as
mediators to generate spacelike entanglement between the two superposed
objects.
