Transmission of information in nonlocal field theories

The signaling between two observers in $3+1$ dimensional flat spacetime coupled locally to a nonlocal 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 nonlocality scale. Furthermore, we consider the case in which the two observers are lightlike related and show that the nonlocal modification to the local result is polynomially suppressed in the nonlocality scale. This may have implications for phenomenological tests of nonlocal theories.

Figure 1

Left, spacetime diagram sketching the configuration of the two detectors in which Bob is in the “light band” of Alice and has a delta-switching detector. Right, same configuration as before with Bob detector “on” for a finite amount of time.

Figure 2

Numerical integration of $S^{nl}$ [when $S^{(\ell )}$ is given by Eq. (29)] vs nonlocality scale $\ell$. Here we neglected the coupling constants ${\lambda }_{\nu }$, ${\alpha }_{\nu }$, ${\beta }_{\nu }$ as well as multiplicative numerical factors. We chose $R=7$, $a=8$, $b=8.1$, $\mathrm{\Omega }=1$. $\ell$ goes from ${10}^{-3}$ to ${10}^{-1}$. The (red) points represents the numerical values of ${\mathcal{S}}_2$ whereas the continuum (blue) line is their interpolation with a curve quadratic in $\ell$.

Figure 3

Spacetime diagram sketching the configuration of the two detectors in which Bob is timelike to Alice and has a delta-switching detector.