Energy Conservation and the Unruh Effect

TL;DR

This paper demonstrates that energy conservation holds when a uniformly accelerated detector in Minkowski vacuum is excited and emits a particle, using a new detector model that clarifies the underlying physics.

Contribution

It introduces a detector model based on Minkowski coordinates with a classical potential, revealing energy conservation in the Unruh effect.

Findings

Energy conservation is maintained during detector excitation and emission.

The transition rate matches conventional results for large detector mass.

Recoil effects are acknowledged even in the infinite mass limit.

Abstract

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 a detector model written in terms of the Minkowski coordinates. In this model the Hamiltonian of the detector involves a classical potential term instead of the detector's fixed trajectory. The transition rate agrees with the corresponding conventional one in the limit of an infinite mass detector though even then the recoil remains.