Waiting for Unruh

How long does a uniformly accelerated observer need to interact with a uantum field in order to record thermality in the Unruh temperature? We address this question for a pointlike UnruhDeWitt detector, coupled linearly to a real KleinGordon field of mass m ≥ 0 and treated within first order perturbation theory, in the limit of large detector energy gap E gap. We first show that when the interaction duration DT is fixed, thermality in the sense of detailed balance cannot hold as E gap → ∞, and this property generalises from the Unruh effect to any KuboMartinSchwinger state satisfying certain technical conditions. We then specialise to a massless field in four spacetime dimensions and show that detailed balance does hold when ΔT grows as a power-law in E gap as E gap → ∞, provided the switch-on and switch-off intervals are stretched proportionally to ΔT and the switching function has sufficiently strong Fourier decay. By contrast, if ΔT grows by stretching a plateau in which the interaction remains at constant strength but keeping the duration of the switch-on and switch-off intervals fixed, detailed balance at E gap → ∞ requires ΔT to grow faster than any polynomial in E gap, under mild technical conditions. The results also hold for a static detector in a Minkowski heat bath. The results limit the utility of the large E gap regime as a probe of thermality in time-dependent versions of the Hawking and Unruh effects, such as an observer falling into a radiating black hole. They may also have implications on the design of prospective experimental tests of the Unruh effect.