On the possible experimental revelations of Unruh and Sokolov-Ternov effects

In this paper we propose generalizations of the Sokolov-Ternov and Unruh effects, and discuss the possibility to measure them on different experiments.

💡 Research Summary

The manuscript attempts to place the Unruh effect and the Sokolov‑Ternov (ST) effect within a single theoretical framework and to propose experimental tests of their generalized forms in modern circular accelerators. The authors begin by recalling the standard derivation of the Unruh effect: a uniformly accelerated detector couples to a scalar field, and the transition rate per unit proper time is proportional to the Fourier transform of the two‑point Wightman function evaluated along the detector’s world‑line. For constant linear acceleration a, the Wightman function depends only on the proper‑time difference τ, and its analytic structure in the complex τ‑plane contains an infinite ladder of simple poles originating from the light‑cone singularity. Evaluating the contour integral yields the familiar thermal spectrum w∝ΔE/(e^{2πcΔE/ħa}−1), i.e. a temperature T_U=ħa/(2πck_B). The authors stress that this thermal response is a consequence of the pole structure rather than the existence of a horizon, and that the effect persists for finite‑time acceleration provided the observation time greatly exceeds the detector’s equilibration time.

Next, the paper turns to the Sokolov‑Ternov effect, traditionally observed as a partial depolarisation of ultrarelativistic electrons in storage rings due to spin‑flip synchrotron radiation. The authors reinterpret the electron spin as a two‑level detector coupled to the electromagnetic field. For a circular world‑line x(τ)=(cγτ,R cos γωτ,R sin γωτ,0) with γ=1/√(1−v²/c²) and ωR=v, the electromagnetic Wightman function takes the form G∝