Discrete spacetime: classical causality,prediction, retrodiction and the mathematical arrow of time

TL;DR

This paper introduces a background-free mathematical framework for classical causality in discrete spacetime, linking spacetime and dynamics without relying on a background metric, and clarifies concepts like cosmic time and causal flows.

Contribution

It provides a novel, background-free definition of causality in discrete spacetime, connecting spacetime structure with dynamics without assuming a metric.

Findings

Defines classical causality mathematically over discrete spacetime

Introduces background-free notions of cosmic time and spacelike hypersurfaces

Discusses causal propagators and the speed of causality

Abstract

A mathematical definition of classical causality over discrete spacetime dynamics is formulated. The approach is background free and permits a definition of causality in a precise way whenever the spacetime dynamics permits. It gives a natural meaning to the concepts of cosmic time, spacelike hypersurfaces and timelike or lightlike flows without assuming the notion of a background metric. The concepts of causal propagators and the speed of causality are discussed. In this approach the concepts of spacetime and dynamics are linked in an essential and inseparable whole, with no meaning to either on its own.