This manuscript is meant to support secondary school teachers in their constant effort to find novel ways to engage students. Adolescents seem particularly stimulated by time-travelling scenarios, like the famous "wormhole billiard ball paradox" proposed by J. Polchinski in 1990, which are usually solved through closed time-like curves (CTCs). The concept of "causal loop" has been popularized by a vast sci-fi literature, so that it sounds familiar to high school pupils. We present an adaptation of the Polchinski's puzzle to the possible scatterings (Møller or Bhabha) of an electron entering a time-travel tunnel so that it can collide with its earlier self at low energy. In order to avoid a discouraging mathematical formulation, our analysis is based merely on graph isomorphism and can be viewed, in educational terms, as an introduction to quantum electrodynamics at undergraduate level. In fact, all the electron interactions along the CTCs result in Feynman exchange diagrams (s-channel, t-channel, u-channel).