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This paper concerns the spacetime locations of massive spinning particles in relativistic quantum mechanics. Using techniques from twistor theory and the unitary representations of the Lorentz group, it is shown that, for a particle of mass m and spin j, the radial distance from the particle to the observer is bounded below by ffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ð1C jÞ p m K1 . If the particle is the source of a Kerr-Minkowski field, the analogue of a Kerr field in general relativity,doi:10.1098/rspa.2007.1853 fatcat:dzu243gbfvchbcdkpoeuatouee