We consider the possibility that as a result of interactions between an elementary particle and a suitably designed classical system, the particle may be divided into two or more pieces that act as though they are fractions of the original particle. We work out in detail the mechanics of this process for an electron interacting with liquid helium. It is known that when an electron is injected into liquid helium, the lowest energy configuration is with the electron localized in a 1s state inside a spherical cavity from which helium atoms are excluded. These electron bubbles have been studied in many experiments. We show that if the electron is optically excited from the 1s to the 1p state, the bubble wall will be set into motion, and that the inertia of the liquid surrounding the bubble can be sufficient to lead to the break-up of the bubble into two pieces. We call the electron fragments “electrinos.” We then show that there is a substantial amount of experimental data in the published literature that gives support to these theoretical ideas. The electrino bubble theory provides a natural explanation for the photoconductivity experiments of Northby, Zipfel, Sanders, Grimes and Adams, and possibly also the ionic mobility measurements of Ihas, Sanders, Eden and McClintock. Previously, these experimental results have not had a satisfactory explanation. In a final section, we describe some further experiments that could test our theory and consider the broader implications of these results on fractional particles.