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.
Highlights
In 1992, it was shown [1] that the ordinary emission of a photon from a uniformly accelerated classical charge in the Minkowski vacuum corresponds to either the absorption from or the emission to the Unruh thermal bath of a zeroenergy Rindler photon
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
We have shown that uniformly accelerated detectors with some unresolved inner structure emit only Rindler particles with arbitrarily small frequency
Summary
In 1992, it was shown [1] that the ordinary emission of a photon from a uniformly accelerated classical charge in the Minkowski vacuum corresponds to either the absorption from or the emission to the Unruh thermal bath of a zeroenergy Rindler photon (as defined by uniformly accelerated observers). Zero-energy Rindler photon modes concentrate near the horizon, so that localized Rindler observers with finite proper acceleration barely have an opportunity to interact with them These observations are in harmony with classical-electrodynamics results according to which uniformly accelerated charges radiate for inertial observers but do not for coaccelerating ones [4,5]. One reason, which is not our main concern in this paper, is that the calculations in the Rindler frame made use of an extended oscillating dipole regularization, a simple oscillating charge being inconsistent with the charge conservation required by the electromagnetic theory This issue does not arise in the scalar analog. Our two-level scalar system will behave as a structureless source insofar as one does not have enough precision to probe the internal-energy gap It interacts, with field modes of small but nonvanishing energy. We adopt ðþ; −; −; −Þ for the metric signature and natural units, ħ 1⁄4 c 1⁄4 kB 1⁄4 1, unless stated otherwise
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