  We employ an approach wherein vacuum entanglement is directly probed in a
controlled manner. The approach consists of having a pair of initially
nonentangled detectors locally interact with the field for a finite duration,
such that the two detectors remain causally disconnected, and then analyzing
the resulting detector mixed state. It is demonstrated that the correlations
between arbitrarily far-apart regions of the vacuum of a relativistic free
scalar field cannot be reproduced by a local hidden-variable model, and that as
a function of the distance L between the regions, the entanglement decreases at
a slower rate than exp(-(L/cT)^3).
