Emergence of Space-Time from Topologically Homogeneous Causal Networks

TL;DR

This paper demonstrates how Minkowski space-time can emerge from a topologically homogeneous causal network through event-counting, operational measurement procedures, and a digital Lorentz transformation analogy in 1+1 dimensions.

Contribution

It introduces a novel approach where space-time arises from pure topology and event-counting in a causal network, emphasizing operational definitions and topological homogeneity.

Findings

Space-time emerges from topologically homogeneous causal networks.

Digital Lorentz transformations can be derived from causal connections.

Operational procedures lead to an indistinguishability of neighboring events.

Abstract

We study the emergence of Minkowski space-time from a causal network. Differently from previous approaches, we require the network to be topologically homogeneous, so that the metric is derived from pure event-counting. Emergence from events has an operational motivation in requiring that every physical quantity---including space-time---be defined through precise measurement procedures. Topological homogeneity is a requirement for having space-time metric emergent from the pure topology of causal connections, whereas physically homogeneity corresponds to the universality of the physical law. We analyze in detail the case of 1+1 dimensions. If we consider the causal connections as an exchange of classical information, we can establish coordinate systems via an Einsteinian protocol, and this leads to a digital version of the Lorentz transformations. In a computational analogy, the foliation construction can be regarded as the synchronization with a global clock of the calls to independent subroutines (corresponding to the causally independent events) in a parallel distributed computation. Thus the Lorentz time-dilation emerges as an increased density of leaves within a single tic-tac of a clock, whereas space-contraction results from the corresponding decrease of density of events per leaf. The operational procedure of building up the coordinate system introduces an in-principle indistinguishability between neighboring events, resulting in a network that is coarse-grained, the thickness of the event being a function of the observer's clock.