Vasco Gil Gomes | Searcharxiv

arXiv2025

Quantum Spacetime Leaps: Higher Dimensional Energetic Causal Sets

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.

gr-qc↗

arXiv2023

Higher Dimensional Energetic Causal Sets

The energetic causal set (ECS) program of Cortês and Smolin, whose distinguishing feature is the foundational time irreversibility of the evolution equations of quantum gravity, was initiated ten years ago. The model showed the emergence of a time-reversible phase from the time-irreversible foundational regime, but originally only had one spatial dimension. The extension to two and more spatial dimensions has posed a substantial challenge, the higher-dimensional set of solutions having measure zero (requiring infinitely-specified initial conditions). This challenge is overcome here with the extension of the ECS to 2+1 dimensions, invoking a finite interaction cross-section to determine generation of new events and including an adjustable fundamental stochasticity. As in the 1+1 dimensional case, we successfully observe a phase transition into a time-symmetric phase, here through the emergence of crystal-like structures. Due to the irreversible evolution we also witness the discrete dynamical systems behaviour of the 1d+1 case explored in later articles of the ECS program, in which the model is captured in and out of the limit cycles which here take the form of lattice crystals. In a companion paper we carry out a detailed parameter investigation and study the causal network underlying the set, explaining the emergence of the time-symmetric phase. In a final section we propose a view of science as a (potential) unifier of threads, and present one such perspective unifying aspects of quantum gravity, biology, and artificial general intelligence (AGI).

gr-qc↗