On the causality and $K$-causality between measures
Mathematical Physics
2017-02-03 v1 General Relativity and Quantum Cosmology
math.MP
Abstract
Drawing from our earlier works on the notion of causality for nonlocal phenomena, we propose and study the extension of the Sorkin--Woolgar relation onto the space of Borel probability measures on a given spacetime. We show that it retains its fundamental properties of transitivity and closedness. Furthermore, we list and prove several characterizations of this relation, including the `nonlocal' analogue of the characterization of in terms of time functions. This generalizes and casts new light on our earlier results concerning the causal precedence relation between measures.
Keywords
Cite
@article{arxiv.1702.00702,
title = {On the causality and $K$-causality between measures},
author = {Tomasz Miller},
journal= {arXiv preprint arXiv:1702.00702},
year = {2017}
}
Comments
10 pages, contribution to the proceedings of the conference "Varying Constants and Fundamental Cosmology - VARCOSMOFUN'16", 12-17 September 2016, Szczecin, Poland