Emergence of Minkowski-Spacetime by Simple Deterministic Graph Rewriting

TL;DR

This paper demonstrates how simple deterministic graph rewriting rules can generate a 4D lattice graph that exhibits emergent Minkowski spacetime properties, including Lorentz invariance and accurate physical constants.

Contribution

It introduces a novel set of simple rules for discrete Lorentz boosts and rotations that lead to the emergence of continuous Minkowski spacetime from graph structures.

Findings

Emergence of (3+1)-dimensional Minkowski spacetime from simple rules

Accurate reproduction of the speed of light and proper time intervals

Demonstration of Lorentz invariance in the generated graphs

Abstract

The causal set program as well as the Wolfram physics project leave open the problem of how a graph that is a (3+1)-dimensional Minkowski-spacetime according to its simple geodesic distances, could be generated solely from simple deterministic rules. This paper provides a solution by describing simple rules that characterize discrete Lorentz boosts between 4D lattice graphs, which combine further to form Wigner rotations that produce isotropy and lead to the emergence of the continuous Lorentz group and the (3+1)-dimensional Minkowski-spacetime. On such graphs, the speed of light, the proper time interval, as well as the proper length are all shown to be highly accurate.