Multiple-event probability in general-relativistic quantum mechanics: a discrete model

TL;DR

This paper presents a discrete, periodic quantum model to clarify the probabilistic interpretation of generally-covariant quantum systems and tests a new multiple-event probability formalism.

Contribution

It introduces a simple discrete model for general-relativistic quantum mechanics, avoiding infinities, and demonstrates the formalism for multiple-event probability in this context.

Findings

Model avoids complications of continuous spectra and infinite norms.

Illustrates the formalism of general-relativistic quantum mechanics.

Tests multiple-event probability definition with and without unitary evolution.

Abstract

We introduce a simple quantum mechanical model in which time and space are discrete and periodic. These features avoid the complications related to continuous-spectrum operators and infinite-norm states. The model provides a tool for discussing the probabilistic interpretation of generally-covariant quantum systems, without the confusion generated by spurious infinities. We use the model to illustrate the formalism of general-relativistic quantum mechanics, and to test the definition of multiple-event probability introduced in a companion paper. We consider a version of the model with unitary time-evolution and a version without unitary time-evolution