Often for this I have heard, the longer the lifetime of the energy state, the uncertainty in the energy state decreases as a result of heisenberg's uncertainty principle. However doesn't that look at uncertainty in time rather than the actual time?
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It does partly, the discussion is quite complicated but it doesn't reflect why the lifetime of the state is a representation of the uncertainty in the time – Mudit Tulsianey Apr 22 '20 at 14:09
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1From the link talking about $\Delta t$ "It tells you the approximate amount of time it takes for the expectation value of an observable to change by a standard deviation provided the system is in a pure state." In order to get the Energy-time relation that is exactly what you have to define $\Delta t$ to be. If you want to use some other idea of a time interval you can; you will just get some other sort of relation. – BioPhysicist Apr 22 '20 at 14:12