Birth and Death in Lineland or A Purely Geometric model of Creation and Annihilation of Particles in Low Dimension

TL;DR

This paper presents a geometric model of particle creation and annihilation in a one-dimensional universe, illustrating how inhabitants might interpret such phenomena and how curvature affects their understanding.

Contribution

It introduces a simple geometric model of particle dynamics in Lineland and explores the implications of curvature on inhabitants' interpretations.

Findings

Particles are modeled as intersections of a moving circle with a line.

In a curved Lineland, inhabitants' geometric interpretations are challenged.

The model demonstrates how curvature influences perceived particle behavior.

Abstract

We consider a simple model of a one dimensional universe embedded in the Euclidean plane. In this model, a circle travelling at constant speed intersects the line in a pair of points which first separate and then rejoin. We interpret this as the creation and annihilation of a pair of particles, and describe the trajectories as seen by inhabitants of the one dimensional universe. In our final scenario, considering Lineland as curved, we show how sufficiently accurate measurements will push inhabitants of Lineland to reject their theory for a purely geometric interpretation.