  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.
