Indistinguishability of thermal and quantum fluctuations

The existence of Davies-Unruh temperature in a uniformly accelerated frame shows that quantum fluctuations of the inertial vacuum state appears as thermal fluctuations in the accelerated frame. Hence thermodynamic experiments cannot distinguish between phenomena occurring in a thermal bath of temperature T in the inertial frame from those in a frame accelerating through inertial vacuum with the acceleration $a=2\pi T$. We show that this indisguishability between quantum fluctuations and thermal fluctuations goes far beyond the fluctuations in the vacuum state. We show by an exact calculation, that the reduced density matrix for a uniformly accelerated observer when the quantum field is in a thermal state of temperature $T^\prime$ is symmetric between acceleration temperature $T = a/(2\pi)$ and the thermal bath temperature $T^\prime$. Thus thermal phenomena cannot distinguish whether (i) one is accelerating with $a = 2\pi T$ through a bath of temperature $T^\prime$ or (ii) accelerating with $a=2\pi T^\prime$ through a bath of temperature T. This shows that thermal and quantum fluctuations in an accelerated frame affect the observer in a symmetric manner. The implications are discussed.