Quantum Spacetime Leaps: Higher Dimensional Energetic Causal Sets

TL;DR

This paper introduces a 2+1 dimensional simulation of Energetic Causal Sets, exploring how fundamental time-irreversible laws can produce reversible dynamics in higher dimensions.

Contribution

It extends the ECS model to two spatial dimensions, analyzing the interplay of multiple orders and disordered causality in a higher-dimensional setting.

Findings

Initial simulation results show potential for reversible dynamics in 2+1D ECS.

Disordered causality introduces complex interactions affecting energy-momentum flow.

The model provides insights into fundamental time irreversibility and causality structures.

Abstract

We propose a 2+1d simulation of Energetic Causal Sets (ECS). These are a class of Causal Sets where the agency of time and its irreversibility are taken as fundamental. Events are endowed with energy-momentum conservation laws being applied at events dictating the dynamics of the Set. Unlike Causal Sets, ECS have three orders, a birth total order, a partial dynamical order which prescribes the flow of energy-momentum between events and a partial causal order that arises from the embedding of these events in Minkowski spacetime. These orders aren't necessarily in agreement with each other, something we call discausality or disordered causality. We therefore explain our first attempts at expanding to two spatial dimensions the simulations of the Energetic Causal Set model to see if we can still obtain reversible dynamics from fundamental time-irreversible laws like in the 1d case.