  It is shown that the attempt to extend the notion of ideal measurement to
quantum field theory leads to a conflict with locality, because (for most
observables) the state vector reduction associated with an ideal measurement
acts to transmit information faster than light. Two examples of such
information-transfer are given, first in the quantum mechanics of a pair of
coupled subsystems, and then for the free scalar field in flat spacetime. It is
argued that this problem leaves the Hilbert space formulation of quantum field
theory with no definite measurement theory, removing whatever advantages it may
have seemed to possess vis a vis the sum-over-histories approach, and
reinforcing the view that a sum-over-histories framework is the most promising
one for quantum gravity.
