Indefinite causal order with fixed temporal order for electrons and positrons

TL;DR

This paper explores how indefinite causal orders can be realized in relativistic quantum mechanics with electrons and positrons, especially under extreme electromagnetic fields that permit closed time-like curves, challenging traditional causal structures.

Contribution

It demonstrates the possibility of implementing quantum switches with fixed temporal order that violate causal inequalities in relativistic settings involving electrons and positrons.

Findings

Genuine quantum switch implementations are possible under certain relativistic conditions.

Violations of causal inequalities can occur with fixed temporal order in extreme electromagnetic fields.

Closed time-like curves enable novel causal structures in relativistic quantum mechanics.

Abstract

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.