Time-asymmetry of probabilities versus relativistic causal structure: an arrow of time

TL;DR

This paper explores the fundamental incompatibility between relativistic causal structures and probabilistic signaling devices, revealing an intrinsic arrow of time through time-reversal effects on non-signaling systems.

Contribution

It introduces a formal analysis of how time-reversal can turn non-signaling devices into signaling ones, highlighting an inherent temporal asymmetry in probabilistic correlations.

Findings

Time-reversal can convert non-signaling devices into perfect signaling devices.

Popescu-Roerlich boxes behave differently under time-reversal, not always becoming perfect signals.

Time-reversal implemented via post-selection suggests potential for experimental tests.

Abstract

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.