Influence of the dispersion relation on the Unruh effect according to the relativistic Doppler shift method

TL;DR

This paper investigates how different dispersion relations affect the Unruh effect, showing that non-linear relations lead to a loss of thermality and depend on observer acceleration and dispersion deviation.

Contribution

It introduces a Lorentz boosting phase method to analyze the impact of arbitrary dispersion relations on the Unruh effect, revealing conditions for thermality loss.

Findings

Thermality is lost for general dispersion relations.

Apparent Unruh temperature varies with acceleration and dispersion deviation.

The approach provides an intuitive understanding of thermality loss.

Abstract

We examine the influence of the dispersion relation on the Unruh effect by Lorentz boosting the phase of Minkowski vacuum fluctuations endowed with an arbitrary dispersion relation. We find that, unlike what happens with a linear dispersion relation exhibited by massless fields, thermality is lost for general dispersion relations. We show that thermality emerges with a varying "apparent" Davies-Unruh temperature depending on the acceleration of the observer and on the degree of departure from linearity of the dispersion relation. The approach has the advantage of being intuitive and able to pinpoint why such a loss of thermality occurs and when such a deviation from thermality becomes significant. We discuss the link of our results with the well-known fundamental difference between the thermalization theorem and the concept of Rindler noise. We examine the possible experimental validation of our results based on a successful setup for testing the classical analogue of the Unruh effect recently described in the literature.