Transmission of Information in Non-Local Field Theories

TL;DR

This paper investigates how non-local field theories in flat spacetime allow signaling between observers even when on-shell massless quanta cannot be exchanged, due to violations of Huygens' principle, with suppression depending on the non-locality scale.

Contribution

It demonstrates that non-locality enables signaling in scenarios where classical local theories forbid it, revealing new effects and suppression behaviors related to the non-locality scale.

Findings

Signaling is possible between timelike observers due to violation of Huygens' principle.

Signaling is exponentially suppressed by the non-locality scale in timelike cases.

Non-local modifications are polynomially suppressed in light-like cases.

Abstract

The signaling between two observers in 3+1 dimensional flat spacetime coupled locally to a non-local field is considered. We show that in the case where two observers are purely timelike related -- so that an exchange of on-shell massless quanta cannot occur -- signaling is still possible because of a violation of Huygens' principle. In particular, we show that the signaling is exponentially suppressed by the non-locality scale. Furthermore, we consider the case in which the two observers are light-like related and show that the non-local modification to the local result is polynomially suppressed in the non-locality scale. This may have implications for phenomenological tests of non-local theories.