Indistinguishability of thermal and quantum fluctuations

TL;DR

This paper demonstrates that in an accelerated frame, quantum and thermal fluctuations are indistinguishable, showing a fundamental symmetry that challenges the ability of thermodynamic experiments to differentiate between thermal and quantum origins of fluctuations.

Contribution

The paper provides an exact calculation showing the symmetry between quantum and thermal fluctuations for an accelerated observer, extending the concept beyond vacuum fluctuations.

Findings

Quantum and thermal fluctuations are indistinguishable in an accelerated frame.

The reduced density matrix symmetry between acceleration temperature and bath temperature.

Thermal phenomena cannot determine whether fluctuations are due to acceleration or thermal bath.

Abstract

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.