Uniformly accelerated classical sources as limits of Unruh-DeWitt detectors

TL;DR

This paper demonstrates that classical accelerated charges can be viewed as limits of Unruh-DeWitt detectors with negligible energy gaps, clarifying their relationship and resolving longstanding conceptual issues.

Contribution

It shows that Unruh-DeWitt detectors with unresolved internal structure behave as classical sources, providing a new perspective on the classical-quantum analogy in accelerated systems.

Findings

Unruh-DeWitt detectors act as classical sources when their energy gap is negligible.

Re-derivation of electromagnetic charge radiation results without zero-energy particles.

Analysis of small-frequency modes clarifies the detection of acceleration radiation.

Abstract

Although the thermal and radiative effects associated with a two-level quantum system undergoing acceleration are now widely understood and accepted, a surprising amount of controversy still surrounds the simpler and older problem of an accelerated classical charge. We argue that the analogy between these systems is more than superficial: There is a sense in which a "UD detector" in a quantized scalar field effectively acts as a classical source for that field if the splitting of its energy levels is so small as to be ignored. After showing explicitly that a detector with unresolved inner structure does behave as a structureless scalar source, we use that analysis to rederive the scalar version of a previous analysis of the accelerated electromagnetic charge, without appealing to the troublesome concept of "zero-energy particles." Then we recover these results when the detector energy gap is taken to be zero from the beginning. This vindicates the informal terminology "zero-frequency Rindler modes" as a shorthand for "Rindler modes with arbitrarily small energy." In an appendix, the mathematical behavior of the normal modes in the limit of small frequency is examined in more detail than before. The vexed (and somewhat ambiguous) question of whether coaccelerating observers detect the acceleration radiation can then be studied on a sound basis.