Grasshopper jumping on a sphere gives new quantum insights
Members of the FoCS group, Dr Dmitry Chistikov and Professor Mike Paterson, together with physicists Olga Goulko (Boise State University) and Adrian Kent (Cambridge), have published an interdisciplinary paper Globe-hopping, solving a probabilistic puzzle on the sphere that has applications to quantum information theory.
Suppose a lawn must cover exactly half the area of a sphere. A grasshopper starts from a random position on the lawn and jumps a fixed distance in a random direction. What shape of lawn maximizes the chance that the grasshopper lands back on the lawn? A natural guess would be that a hemispherical lawn is best. It turns out, however, that this is nearly never the case — there are only a few exceptional jump sizes.
This work involving spherical geometry, probability theory, basic number theory, and theoretical physics appears in the Proceedings of the Royal Society A and shows, apart from concern for the well-being of grasshoppers, that there are previously unknown types of Bell inequalities. The Bell inequality, devised by physicist John Stewart Bell in 1964, demonstrated that no combination of classical theories with Einstein's special relativity is able to explain the predictions (and later actual experimental observations) of quantum theory.
A University press release can be found here.