Massive Unruh particles cannot be directly observed

We show that massive particles created in a relativistically accelerated reference frame, as predicted by the Unruh effect, can only be found in a tiny layer above the Rindler horizon, whose thickness corresponds to a single Compton wavelength. This is beyond the reach of any detector and suggests that the Unruh effect may not ever be directly observed for massive fields. The case of massless particles is also examined, for which qualitatively different behavior is observed in a low-acceleration regime, suggesting that an observation of the Unruh effect for massless particles is more promising.