Topology measurement within the histories approach

TL;DR

This paper explores methods for measuring spacetime topology using a histories approach in quantum and classical contexts, proposing a combinatorial modeling procedure and establishing links to discretized spacetime models.

Contribution

It introduces a novel procedure for creating combinatorial topology models within the histories framework and connects these models to discretized spacetime representations.

Findings

Established correspondence between combinatorial models and discretized spacetime.

Proposed a new procedure for topology measurement in quantum and classical frameworks.

Demonstrated the applicability of the histories approach to spacetime topology estimation.

Abstract

An idealised experiment estimating the spacetime topology is considered in both classical and quantum frameworks. The latter is described in terms of histories approach to quantum theory. A procedure creating combinatorial models of topology is suggested. The correspondence between these models and discretised spacetime models is established.