Spacetime topology from the tomographic histories approach I: Non-relativistic Case

TL;DR

This paper introduces a method to determine the effective topology of a non-relativistic system's configuration space through experimental data, using a histories approach rooted in quantum mechanics, with future work planned for relativistic systems.

Contribution

It presents an inverse problem framework to recover the topology of a system's configuration space from experimental histories, extending the consistent histories approach.

Findings

Successfully deduces the topology from experimental data

Clarifies the difference between effective and actual topology

Provides groundwork for relativistic case analysis

Abstract

The tomographic histories approach is presented. As an inverse problem, we recover in an operational way the effective topology of the extended configuration space of a system. This means that from a series of experiments we get a set of points corresponding to events. The difference between effective and actual topology is drawn. We deduce the topology of the extended configuration space of a non-relativistic system, using certain concepts from the consistent histories approach to Quantum Mechanics, such as the notion of a record. A few remarks about the case of a relativistic system, preparing the ground for a forthcoming paper sequel to this, are made in the end.