Acceleration without Temperature

TL;DR

This paper demonstrates that non-uniformly accelerating observers see a Bose-Einstein distribution without a corresponding thermal density matrix, challenging the notion of associating temperature with such observations.

Contribution

It shows that non-uniform acceleration leads to non-thermal states despite particle distributions resembling thermal spectra, due to the absence of event horizons.

Findings

Non-uniformly accelerating observers see a Bose-Einstein distribution.

The density matrix is non-thermal, so temperature cannot be defined.

Minkowski vacuum appears as a single-mode squeezed state to these observers.

Abstract

We show that while some non-uniformly accelerating observers (NUAOs) do indeed see a Bose-Einstein distribution of particles for the expectation value of the number operator in the Minkowski vacuum state, the density matrix is non-thermal and therefore a definition of temperature is not warranted. This is due to the fact that our NUAOs do not see event horizons in the spacetime. More specifically, the Minkowski vacuum state is perceived by our NUAOs as a single-mode squeezed state as opposed to the two-mode squeezed state characteristic of uniformly accelerating observers. Both single and two-mode squeezed states are pure quantum states; however, tracing over degrees of freedom in one of the modes of the two-mode squeezed state reduces the pure density matrix to a thermal density matrix. It is this property in the two-mode squeezed state that allows one to consistently define a temperature. In the single-mode case, an equivalent tracing is neither required nor available.