(Quantum) Space-Time as a Statistical Geometry of Lumps in Random Networks

TL;DR

This paper proposes a model where macroscopic space-time emerges from a stochastic network of interconnected lumps, using discrete structures like cellular networks to encode quantum non-locality without violating causality.

Contribution

It introduces a novel framework of proto-structures in discrete networks to model the emergence of space-time and quantum phenomena.

Findings

Space-time emerges from entangled network lumps.

Proto-causality is established within the network.

Non-local quantum effects are encoded without violating causality.

Abstract

In the following we undertake to describe how macroscopic space-time (or rather, a microscopic protoform of it) is supposed to emerge as a superstructure of a web of lumps in a stochastic discrete network structure. As in preceding work (mentioned below), our analysis is based on the working philosophy that both physics and the corresponding mathematics have to be genuinely discrete on the primordial (Planck scale) level. This strategy is concretely implemented in the form of \tit{cellular networks} and \tit{random graphs}. One of our main themes is the development of the concept of \tit{physical (proto)points} or \tit{lumps} as densely entangled subcomplexes of the network and their respective web, establishing something like \tit{(proto)causality}. It may perhaps be said that certain parts of our programme are realisations of some early ideas of Menger and more recent ones sketched by Smolin a couple of years ago. We briefly indicate how this \tit{two-story-concept} of \tit{quantum} space-time can be used to encode the (at least in our view) existing non-local aspects of quantum theory without violating macroscopic space-time causality.