Emergent spacetime from purely random structures

TL;DR

This paper explores how a simple random graph model can give rise to a continuous, flat 3D spacetime with properties resembling our universe, including emergent geometry, gravity effects, and quantum principles.

Contribution

It introduces a minimal random graph evolution model that results in an emergent 3D flat spacetime and connects discrete structures with general relativity and quantum concepts.

Findings

Emergent 3D flat spacetime from random graphs

Recovery of gravitational effects like time dilation

Quantum uncertainty principles from statistical fluctuations

Abstract

We examine the fundamental question whether a random discrete structure with the minimal number of restrictions can converge to continuous metric space. We study the geometrical properties such as the dimensionality and the curvature emerging out of the connectivity properties of uniform random graphs. In addition we introduce a simple evolution mechanism for the graph by removing one edge per a fundamental quantum of time from an initially complete graph. We show an exponential growth of the radius of the graph, that ends up in a random structure with emergent average spatial dimension $D=3$ and zero curvature $K=0$, resembling a flat 3D manifold, that could describe the observed space in our universe and some of its geometrical properties. In addition, we introduce a generalized action for graphs based on physical quantities on different subgraph structures that helps to recover the well known properties of spacetime as described in general relativity, like time dilation due to gravity. Also, we show how various quantum mechanical concepts such as generalized uncertainty principles based on the statistical fluctuations can emerge from random discrete models. Moreover, our approach leads to a unification of space and matter-energy, for which we propose a mass-energy-space equivalence that leads to a way to transform between empty space and matter-energy via the cosmological constant.