So, this is something I've never understood in detail. If an excited system decays and emits a photon, the lifetime of the decay will broaden the spectrum of the photon right? Basically just a Fourier transform of the "shape" of the emission in time to get the frequency components of the emitted light. As this emitted photon is a superposition of a continuous range of frequencies, if it passes trough a spectrometer, I can detect it as having one of those frequencies with respective probability right? But if I detect a photon with 'more' energy than I thought was present in the excited system, where does that energy come from? Was this uncertainty in energy already present in the system? What's wrong with the following thought experiment? 1) I generate a photon in a very good optical cavity. With this single photon, I can associate a very well defined frequency and energy. 2) I now pass an atom (or 2 level system with same energy difference) in ground state trough this optical cavity. It stays inside the optical cavity for half a Rabi cycle and absorbs the photon with 100% certainty. 3) The atom is now out of the cavity and is excited with 100% certainty. 4) The excited atom now starts decaying and emits a photon. But due to the decay the spectrum is "broad". 5) I can now detect the photon with a slightly different energy? At what step did extra energy get in or get out? I'm missing something. I've asked it to people before, but I never got a good answer. (or I didn't get it). Thanks!