  We study the dynamics of phase relaxation between a pair of one-dimensional
condensates created by a supersonic unzipping of a single condensate. We use
the Lorentz invariance of the low energy sector of such systems to show that
dephasing results in an unusual prethermal state, in which right- and
left-moving excitations have different, Doppler-shifted temperatures. The
chirality of these modes can be probed experimentally by measuring the
interference fringe contrasts with the release point of the split condensates
moving at another supersonic velocity. Further, an accelerated motion of the
release point can be used to observe a space-like analogue of the Unruh effect.
A concrete experimental realization of the quantum zipper for a BEC of trapped
atoms on a atom chip is outlined. We interpret these results in the context of
the general question of the Lorentz transformation of temperature, and the
close analogy with the dipolar anisotropy of the Cosmic Microwave Background.
