The Rotating Detector and Vacuum Fluctuations

TL;DR

This paper investigates how a massless scalar field behaves in rotating frames versus inertial frames, revealing differences in vacuum states and detector responses through exact solutions and Bogolubov transformations.

Contribution

It provides an exact solution to the Klein-Gordon equation in rotating coordinates and analyzes the vacuum state differences using Bogolubov transformations and detector response functions.

Findings

Rotating observer's vacuum differs from Minkowski vacuum.

Detector response varies with the vacuum state of the field.

Explicit Bogolubov transformation between inertial and rotating modes.

Abstract

In this work we compare the quantization of a massless scalar field in an inertial frame with the quantization in a rotating frame. We used the Trocheries-Takeno mapping to relate measurements in the inertial and the rotating frames. An exact solution of the Klein-Gordon equation in the rotating coordinate system is found and the Bogolubov transformation between the inertial and rotating modes is calculated, showing that the rotating observer defines a vacuum state different from the Minkowski one. We also obtain the response function of an Unruh-De Witt detector coupled with the scalar field travelling in a uniformly rotating world-line. The response function is obtained for two different situations: when the quantum field is prepared in the usual Minkowski vacuum state and when it is prepared in the Trocheries-Takeno vacuum state. We also consider the case of an inertial detector interacting with the field in the rotating vacuum.