  We revisit the question addressed in recent papers by Garriga et al: What
determines the rest frame of pair nucleation in a constant electric field? The
conclusion reached in these papers is that pairs are observed to nucleate at
rest in the rest frame of the detector which is used to detect the pairs. A
similar conclusion should apply to bubble nucleation in a false vacuum. This
conclusion however is subject to doubt due to the unphysical nature of the
model of a constant eternal electric field that was used by Garriga et al. The
number density of pairs in such a field would be infinite at any finite time.
Here we address the same question in a more realistic model where the electric
field is turned on at a finite time $t_0$ in the past. The process of turning
on the field breaks the Lorentz invariance of the model and could in principle
influence the frame of pair nucleation. We find however that the conclusion of
Garriga et al still holds in the limit $t_0 \to -\infty$. This shows that the
setup process of the electric field does not have a lasting effect on the
observed rest frame of pair nucleation. {On the other hand, the electric
current and charge density due to the pairs are determined by the way in which
the electric field was turned on.
