A
comment on one or two of the writeups above:
The Energy-Time uncertainty relation is not a true uncertainty relation, as anyone familiar with P.W. Atkins work on the subject may know. Rather it is a consequence of the fact that the time-dependent schrodinger equation is first order in time.
This fact is best highlighted by noting that in each of the other uncertainty relations, the two observables have readily identifiable operators associated with them. Energy does, of course, that's the hamiltonian. But time has no operator in quantum mechanics. Instead, it is a parameter.
Also think of the odd consequences that such an uncertainty relation would have for relativistic quantum mechanics.