Birth and death in Lineland or a purely geometric model of creation and annihilation of particles in low dimension

We consider a simple model of a one-dimensional (1D) 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 1D 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.