Causality is an effect
Abstract
Using symmetric boundary conditions at separated times, I show analytically that both the time ordering of (macroscopic) causality and the direction of entropy increase follow from these boundary conditions. In particular, when the endpoints have low entropy, these arrows of time point away from the ends and toward the middle. Causality in this context means that when perturbations are applied, the effect of the perturbation---the macroscopic change in the system's behavior---is confined to one temporal side of the perturbations. These results hold for both mixing and integrable systems, although relaxation for integrable systems is incomplete. Simulations are presented for purposes of illustration.
Cite
@article{arxiv.cond-mat/0011507,
title = {Causality is an effect},
author = {L. S. Schulman},
journal= {arXiv preprint arXiv:cond-mat/0011507},
year = {2007}
}
Comments
For the proceedings of the conference, "Time's Arrows, Quantum Measurements and Superluminal Behavior," Naples, Italy, October 2000. To be published by the Italian CNR. Contains two three-part figures