  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.

Quantum Physics;History and Philosophy of Physics