The Hawking-Unruh Temperature and Quantum Fluctuations in Particle Accelerators

Abstract

We wish to draw attention to a novel view of the effect of the quantum fluctuations during the radiation of accelerated particles, particularly those in storage rings. This view is inspired by the remarkable insight of Hawking that the effect of the strong gravitational field of a black hole on the quantum fluctuations of the surrounding space is to cause the black hole to radiate with a temperature T = hbar g / 2 pi c k, where g is the acceleration due to gravity at the surface of the black hole, c is the speed of light, and k is Boltzmann's constant. Shortly thereafter Unruh argued that an accelerated observer should become excited by quantum fluctuations to a temperature T = hbar a* / 2 pi c k, where a* is the acceleration of the observer in its instantaneous rest frame. In a series of papers Bell and co-workers have noted that electron storage rings provide a demonstration of the utility of the Hawking-Unruh temperature, with emphasis on the question of the incomplete polarization of the electrons due to quantum fluctuations of synchrotron radiation. Here we expand slightly on the results of Bell et al., and encourage the reader to consult the literature for more detailed understanding.