Indefinite causal order with fixed temporal order for electrons and positrons

We provide an analysis of indefinite causal orders in relativistic quantum mechanics based on the electron-positron picture of Feynman involving negative energy electrons moving backward in time. We show that genuine implementations of the paradigmatic quantum switch, but here violating some causal inequalities and with a fixed temporal order, become possible in extreme external electromagnetic field conditions allowing the presence of closed time-like curves.