On the controversies of the Unruh effect

Abstract

In the 50 years since it was first proposed, the Unruh effect has been discussed extensively in literature, with many theoretical results supporting its existence and some questioning whether it is actually observed. The Unruh effect states that observers with constant proper acceleration in Minkowski spacetime will respond as if interacting with a thermal bath at a temperature proportional to the acceleration. For common accelerations this temperature is very low, so experimental confirmation has been challenging. To understand the effect and the discussion around it, we review some important results from quantum field theory and work out a detailed derivation of the Unruh effect for massless and massive fields, including the calculation of the Bogoliubov coefficients for these problems. Furthermore, we follow a discussion on the role that the boundary conditions play in this effect, showing that they may lead to an incomplete description of the field in Minkowski spacetime when written in terms of the modes in Rindler spacetime.