Energy time complementarity from unitary evolution I am looking for a well posed experimental situation that illustrates energy time complementarity. I know of Einsteins box, which is discussed quite nicely in Bohr's article Discussions with Einstein on Epistemological Problems in Atomic Physics. He used time dilation due to gravity, I am looking for examples that do not involve gravitational physics. 
Bohr in his article never applies unitary evolution $e^{-iHt}$ directly to the problem.  This is analogous to $e^{ipx}$ which is at the heart of momentum position uncertainty . It would be nice to see Energy time Complementarity directly from $e^{-iHt}$. What does energy time complementarity imply for energy conservation?
Does such an experiment exist? If not, is there some fundamental impedance preventing it from being done in a gravity-free context?
Please take care to pose the experimental situation completely, as these are subtle issues. I would prefer examples that do not involve QFT, as it would unnecessarily distract us from the main question.
 A: Broadening of spectral lines:
Since a state which exists only for a finite duration can't have a precisely defined energy, you can note that the shorter the lifetime of an excited state of an atom, the greater will be the spread of energies assigned to that state.  So when it transitions to the groundstate, this spread is transferred to the emitted photon, hence the spectral line has an unavoidable broadening from the ideal infinitely thin case.
(Incidentally, not related to examples but there is a good discussion of the general meaning of the energy time uncertainty principle here).
A: In my opinion energy-time uncertainty relation is a historical baggage and has no meaning whatsoever in the sense of position-momentum uncertainty. This is due to the fact that time is not measurable attribute of a particle, correspondingly you don't have a hermitian operator for it. You can't have "wavepacket" in time. Time, like position is a coordinate. However a particle can have a spread in position coordinate and a corresponding spread in momentum at a given time ($[x,p]$ commutator is $i$ when both operators are taken at the same time) . These two quantities are enough to determine the Hamitonian at that time (hence the energy) and unique time evolution of the wave function for infinitesimally later time. Forget everything that is written in QFT textbooks about virtual particles and energy-time uncertainty! Time is certain and energy is conserved. 
