Energy Conservation and the Unruh Effect

In this paper it is explicitly demonstrated that the energy conservation law is kept when a detector uniformly accelerated in the Minkowski vacuum is excited and emits a particle. This fact had been hidden in conventional approaches in which detectors were considered to be forced on trajectories. To lift the veil we suggest the transition amplitude written in terms of the Minkowski coordinates. In this amplitude the Hamiltonian of the detector involves a classical potential term instead of the detector’s fixed trajectory. This amplitude agrees with the corresponding conventional one in the limit of an infinite mass detector though even then the recoil remains. PACS: 03.65.Bz, 04.20.Cv, 03.70.+k