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I just found this video on Youtube, with the description:

A thin superconductor layer (~1µm thick) is coated on a sapphire wafer. Quantum physics tells us that the magnetic field penetrates into the superconductor in the form of discrete flux tubes. The superconductor strongly pins these tubes, causing it to float in midair.

It looks real, but people can do some pretty impressive magic tricks (especially if they control the camera and can post-process the footage). Unfortunately, I don't know enough about quantum physics to know if this is Star Trek talk or real science.

Related: https://physics.stackexchange.com/questions/16054/how-is-stable-levitation-possible

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Sure, the phenomena is real. It's a nice demonstration of the Meissner effect in which a superconductor resists penetration by a magnetic field. It's become a popular lab demonstration since the discovery of high temperature* superconductors in the mid 80's. At one point, you could even buy home levitation kits.

Resistance to penetration of magnetic field occurs via generation of opposing electromagnetic field, an eddy current: (video demonstration). Eddy current generates a magnetic field to oppose the external field: (Faraday and Lenz's law). Since the object is a supeconductor, the currents, and mag field, don't damp out; hence permanent repulsion between magnet and superconductor. For more, Hyperphysics offers an explanation here.

*High temperature meaning 'near the boiling point of liquid nitrogen', 77°Kelvin (-196 °C; -321 °F).

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    According to another video, youtube.com/watch?v=Ws6AAhTw7RA (and skip to 1:41), the "sapphire wafer" levitation is different from Meissner effect in two ways: (1) some magnetic field is allowed into the superconductor, because the sapphire wafer is too thin; (2) once those magnetic fields enter the wafer, they will be "locked in" due to defects in the wafer, i.e. instead of merely "repelling" the magnetic field, the position of the wafer would be "locked in" so that any movements that change the magnetic field experienced by the wafer would be resisted. – user2547 Jan 6 '12 at 5:01
  • (Disclaimer: I am not a scientist, so I'm not able to judge the correctness of my comment.) – user2547 Jan 6 '12 at 5:02
  • That's called *flux pinning" and allows for "solid" structures to be made with nothing material holding the pieces in place. Some predict this (with higher-temperature superconductors) will be an enabling technology in space construction. – JDługosz May 1 '16 at 5:04

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