  We study the system of two localized detectors (oscillators) interacting
through a massless quantum field in a vacuum state via an Unruh-DeWitt
coupling. This system admits an exact solution providing a good model for
addressing fundamental issues in particle-field interactions, causality and
locality in quantum field measurements that are relevant to proposed quantum
experiments in space. Our analysis of the exact solution leads to the following
results. (i) Common approximations used in the study of analogous open quantum
systems fail when the distance between the detectors becomes of the order of
the relaxation time. In particular, the creation of correlations between remote
detectors is not well described by ordinary perturbation theory and the Markov
approximation. (ii) There is a unique asymptotic state that is correlated; it
is not entangled unless the detector separation is of the order of magnitude of
the wavelength of the exchanged quanta. (iii) The evolution of seemingly
localized observables is non-causal. The latter is a manifestation of Fermi's
two-atom problem, albeit in an exactly solvable system. We argue that the
problem of causality requires a reexamination of the notion of entanglement in
relativistic systems, in particular, the physical relevance of its extraction
from the quantum vacuum.
