Indistinguishability of thermal and quantum fluctuations

Understand

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 $T^\prime$.