  There is an incompatibility between the symmetries of causal structure in
relativity theory and the signaling abilities of probabilistic devices with
inputs and outputs: while time-reversal in relativity will not introduce the
ability to signal between spacelike separated regions, this is not the case for
probabilistic devices with space-like separated input-output pairs. We
explicitly describe a non-signaling device which becomes a perfect signaling
device under time-reversal, where time-reversal can be conceptualized as
playing backwards a videotape of an agent manipulating the device. This leads
to an arrow of time that is identifiable when studying the correlations of
events for spacelike separated regions. Somewhat surprisingly, although
time-reversal of Popuscu-Roerlich boxes also allows agents to signal, it does
not yield a perfect signaling device. Finally, we realize time-reversal using
post-selection, which could lead experimental implementation.
