The Unruh effect and its applications

TL;DR

The paper surveys the Unruh effect, emphasizing that uniformly accelerated observers perceive the Minkowski vacuum as a thermal bath of Rindler particles, with the temperature set by the acceleration. It systematizes the standard derivations via Bogoliubov transformations and the Bisognano-Wichmann/KMS framework, and extends the discussion to massive fields, curved spacetimes, and classical analogs. It then illustrates a broad set of applications, including Unruh-DeWitt detectors, proton decay and bremsstrahlung from accelerated sources, and the interplay between inertial and Rindler descriptions. The review also covers experimental proposals, recent developments in entanglement/decoherence, and thermodynamic implications, highlighting the Unruh effect as a powerful conceptual and calculational tool for black hole, cosmological, and quantum-information contexts.

Abstract

It has been thirty years since the discovery of the Unruh effect. It has played a crucial role in our understanding that the particle content of a field theory is observer dependent. This effect is important in its own right and as a way to understand the phenomenon of particle emission from black holes and cosmological horizons. Here, we review the Unruh effect with particular emphasis to its applications. We also comment on a number of recent developments and discuss some controversies. Effort is also made to clarify what seems to be common misconceptions.

Figures (11)

• Figure 1: Part of Feynman's blackboard at California Institute of Technology at the time of his death in 1988. At the right-hand side one can find "accel. temp." as one of the issues "to learn".
• Figure 2: Histogram depicting the number of citations of Unruh76 over the years.
• Figure 3: The regions with $|t|<z$, $|t| < -z$, $t>|z|$ and $t< -|z|$, denoted RR, LR, EDK and CDK, respectively, are the left Rindler wedge, right Rindler wedge, expanding degenerate Kasner universe and contracting degenerate Kasner universe, respectively. The curves with arrows are integral curves of the boost Killing vector $z(\partial/\partial t) + t(\partial/\partial z)$. The direction of increasing $U=t-z$ and that of increasing $V=t+z$ are also indicated.
• Figure 4: The world line of a uniformly accelerated detector moving along the $z$-axis in the Minkowski spacetime covered with Cartesian coordinates is shown.
• Figure 5: The world line of a uniformly accelerated detector moving along the $z$-axis in Minkowski spacetime covered with Rindler coordinates is shown.