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We consider a simple model of a one dimensional universe embedded in theEuclidean plane. In this model, a circle travelling at constant speedintersects 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, anddescribe the trajectories as seen by inhabitants of the one dimensionaluniverse. In our final scenario, considering Lineland as curved, we show howsufficiently accurate measurements will push inhabitants of Lineland to rejecttheir theory for a purely geometric interpretation.

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