Constraints on Chronologies

TL;DR

This paper analyzes the structure of possible event chronologies in spacetime, providing analytical, algorithmic, and convexity-based criteria, and explores how spacetime metrics relate to event orderings, including in curved spacetimes.

Contribution

It offers a comprehensive analysis of event chronologies in various spacetime dimensions, including new criteria and methods for determining allowed orderings.

Findings

Characterization of event chronologies in flat spacetime

Algorithmic determination of chronologies in general cases

Proposal of convexity-based criteria for allowed chronologies

Abstract

The time ordering of two spacelike separated events is arbitrary, when all inertial frames are taken into account, but for three or more events it is not generally so. We determine the structure of possible time orderings, or chronologies, for multiple events in any number of dimensions, analytically and exhaustively for three events in four space-time dimensions, algorithmically in other cases. We also formulate an alternative criterion, based on convexity, for determining the allowed chronologies of a set of events. We show how the metric of a Lorentz invariant spacetime can be partially reconstructed from a knowledge of the chronologies it supports. Finally, we propose a different but related criterion for allowed chronologies in curved spacetimes.