A brief remark on Unruh effect and causality

TL;DR

This paper discusses how the Unruh effect can be adapted for non-eternal observers without violating causality by using the time-energy uncertainty principle, focusing on the causally acceptable diamonds's temperature approach.

Contribution

It demonstrates that the diamonds's temperature adaptation of the Unruh effect respects causality through the time-energy uncertainty relation.

Findings

The Unruh effect can be adapted for finite-lifetime observers.

Diamonds's temperature approach is causally acceptable.

The adaptation aligns with the principles of quantum field theory and causality.

Abstract

Unruh effect states that the vacuum of a quantum field theory on Minkovski space-time looks like a thermal state for an eternal uniformly accelerated observer. Adaptation to the non eternal case causes a serious problem: if the thermalization of the vacuum depends on the lifetime of the observer, then in principle the latest is able to deduce its lifetime from the measurement of the temperature. This short note aims at underlining that time-energy uncertainty relation allows to adapt Unruh effect to non-eternal observers without breaking causality. In particular we show that our adaptation - the diamonds's temperature- of Bisognano-Wichman approach to Unruh effect is causally acceptable. This note is self-contained but it is fully meaningful as a complement to gr-qc/0212074 as well as a comment on gr-qc/0306022.