  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.
