While uncertainty relations in quantum mechanics are based on non commuting
operators, the energy-time "uncertainty" is an exception since time is
a (classical) parameter.
There have been many unsuccessful attempts to construct a general "time operator" which would give the energy-time uncertainty the same operator based justification as the other uncertainty relations.
Here, we accept that the energy-time uncertainty is for some reason not as fundamental as the operator based uncertainties and we find a reason by arguing that time is a useful but "man-made" concept which actually arises from separation in space. Without resorting to relativistic arguments we can construct the time-dependent Schroedinger equation from the time-independent one by separation of system and environment in space using a semiclassical approach.
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