Spacetime topology from the tomographic histories approach: Part II

TL;DR

This paper presents a method to recover the topology of an effective spacetime from experimental data by inferring a partial order of events and proposing two approaches for topology reconstruction, extending previous work in the field.

Contribution

It introduces a novel operational approach to determine spacetime topology using experimental event data and partial order inference, building on prior research.

Findings

Partial order of events can be inferred from experimental data.

Two methods for topology recovery are proposed and analyzed.

Ambiguities in the partial order are classified and discussed.

Abstract

As an inverse problem, we recover the topology of the effective spacetime that a system lies in, in an operational way. This means that from a series of experiments we get a set of points corresponding to events. This continues the previous work done by the authors. Here we use the existence of upper bound in the speed of transfer of matter and information to induce a partial order on the set of events. While the actual partial order is not known in our operational set up, the grouping of events to (unordered) subsets corresponding to possible histories, is given. From this we recover the partial order up to certain ambiguities that are then classified. Finally two different ways to recover the topology are sketched and their interpretation is discussed.