On the thermodynamics of moving bodies

TL;DR

This paper investigates the thermodynamic response of a moving photon detector in a heat bath, revealing velocity-dependent effects and discrepancies with classical Doppler predictions, with implications for cosmic microwave background observations.

Contribution

It models an Unruh-DeWitt detector on a brane at non-zero temperature, analyzing angular response and velocity effects, highlighting deviations from classical Doppler shift at relativistic speeds.

Findings

Agreement with Doppler shift at low velocities and high photon energy

Discrepancies at higher velocities and lower photon energy

No detector response within a 'backward' cone at relativistic speeds

Abstract

We model the situation in which a photon detector moves with constant velocity in a Minkowski heat-bath by considering an Unruh-DeWitt detector, with variable energy gap $\hbar \omega$, moving on a brane, at a non-zero (Unruh) temperature $T$ due to acceleration in an orthogonal direction. We compute the angular response for a 2-brane. At low velocity we find agreement with the standard Doppler shift formula in the limit $\hbar\omega \gg T$ in which the photon gas is classical; otherwise there is a discrepancy, which we attribute to angular-dependence of the induced emission rate. At relativistic velocities our result disagrees with the standard formula even when $\hbar\omega \gg T$, and above a critical velocity there is no response from the detector within a `backward' cone. We discuss potential implications for observations of the cosmic microwave background radiation.