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"Quantum" Levitation

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Those of you with backgrounds in materials science, ceramics engineering or graduate-level physics may recognize this phenomenon as something similar to the Meissner-Ochsenfeld effect, though strictly speaking what you're witnessing is not a result of the Meissner effect.
In the Meissner effect, the superconductor that is placed within the magnetic field deflects the field entirely (see the image pictured here), such that none of the field passes through the object itself. But as Hanson points out, the thinness of the superconductive coating featured in the quantum locking video allows for the magnetic field to penetrate it (albeit in discrete quantities) wherever there exist defects in the superconductor's molecular structure. This penetration gives rise to the "flux tubes" (again, pictured alongside Hanson's explanation), which pass through the inert crystal sapphire wafer and "trap" it in midair. This trapping provides the typically wobbly "levitation" characteristic of the Meissner effect a stiffer quality.
http://io9.com/5850729/quantum-locking-will-blow-your-mind--but-how-does-it-work
 
I did notice the difference between the wobbly effect in the CU video you posted compared to the stiffer effect in the "quantum" videos. Are you saying it's just the Miessner effect working on a thinner superconductor?
I guess I should point out that the wobbliness actually means it's a "stronger" superconductor. It means there is a restoring force that physically pushes the superconductor back into the field alignment that was present when the superconducting material was cooled below Tc.

The thin film superconductor appears "stiff" because it doesn't have as strong of a restoring force. In fact the experimenter is able to reposition it by hand, and the field from the superconductor assumes a new orientation. So if it moves, it just stays in the new position instead of snapping back.