  Some authors have claimed that there exists a minimum size (on the order of
the Compton radius) for electron states composed entirely of positive-frequency
solutions to the free Dirac equation. Other authors have put forward
counterexamples to such claims. This article asks how the counterexamples of A.
J. Bracken and G. F. Melloy [J. Phys. A. 32, 6127 (1999)] bypass two arguments
against their possibility. The first is an old argument that, because of the
prohibition on faster-than-light motion, the electron must be larger than a
certain minimum size if it is to have the correct angular momentum and magnetic
moment. This challenge can be addressed by analyzing the flow of energy and
charge for the counterexample states. The second argument is an explicit proof
(presented in C.-P. Chuu et al., [Solid State Commun. 150, 533 (2010)]) that
there is a minimum size for purely positive-frequency electron states. This
proof hinges on the assumption of a small spread in momentum space, which is
violated by the counterexamples that have been put forward.
