Ideas

 For any pair of conjugate variables, there is an uncertainty relation. The dE * dt ~ h relation is tricky because it is very different from the standard uncertainty relation. For a standing ice pick, it is correct to identify the arc length (or d\th) as one of the conjugate variables, but the other is the angular momentum conjugate to it. This is a firm ground to stand on and the E-t relation were equivalent it should give the same answer, but that is not so. Vortex crystal in http://journals.aps.org/prb/abstract/10.1103/PhysRevB.85.054515 ?