  We show how two Unruh-DeWitt detectors that do not couple to the zero mode of
a quantum field can exchange information faster than the speed of light. We
analyze the specific cases of periodic and Neumann boundary conditions in flat
spacetime with arbitrary spatial dimensions, and we show that the superluminal
signal strength is only polynomially suppressed with the distance to the
lightcone. Therefore, in any relativistic scenario modelling the light-matter
interaction where a zero mode is present, particle detectors should explicitly
couple to the zero mode.
