Proposal for observing the Unruh effect with classical electrodynamics

The Unruh effect -- according to which linearly accelerated observers with proper acceleration a= constant in the (no-particle) vacuum state of inertial observers experience a thermal bath of particles with temperature $T_U = a \hbar / (2 \pi k_B c)$ -- has just completed its 40$^{th}$ anniversary. A 'direct' experimental confirmation of the Unruh effect has been seen with concern because the linear acceleration needed to reach a temperature $1 K$ is of order $10^{20} m/s^2$. Although the Unruh effect can be rigorously considered as well tested as free quantum field theory itself, it would be satisfying to observe some lab phenomenon which could evidence its existence. Here, we propose a simple experiment reachable under present technology whose result may be directly interpreted in terms of the Unruh thermal bath. Then, instead of waiting for experimentalists to perform the experiment, we use standard classical electrodynamics to anticipate its output and show that it reveals the presence of a thermal bath with temperature $T_U$ in the accelerated frame. Unless one is willing to question the validity of classical electrodynamics, this must be seen as a virtual observation of the Unruh effect. Regardless of doubts still raised by some voices, the Unruh effect lives among us.