Uniformly accelerated classical sources as limits of Unruh-DeWitt detectors

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.

arXiv comment10 pages, 2 figures

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• Classical Larmor formula through the Unruh effect for uniformly accelerated electrons
• Thermal Larmor radiation
• Quantum power: a Lorentz invariant approach to Hawking radiation
• Acceleration-induced radiation from a qudit particle detector model
• Vacuum Zero Point Energy and its Statistical Correlations in dS Background
• Electron-mirror duality and thermality
• Physical significance of generalized boundary conditions: an Unruh-DeWitt detector viewpoint on ${\text{AdS}}_2\times {\mathbb{S}}^2$
• Vacuum zero point energy of self-interacting quantum fields in dS background
• Dual-temperature acceleration radiation
• Gravitational radiation with kinetic recoil