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Tel-Aviv University demonstrates quantum levitation using superconductors locked in a magnetic field.
Short explanation: It is cooled with liquid nitrogen. The core is a super conducting material which conducts electric current without any resistance at temperatures below minus 180 degrees Celsius (minus 292 degrees Fahrenheit). In this state it can trap magnetic fields. The resulting magnetic forces cause not only the levitation but precision control above (or below) the rail, which is made of conventional magnetic material.
Also see these earlier Flixxy videos: How Superconducting Levitation Works Superconducting Magnetic Levitation Model Train Superconductor MagLev Train
Definitions: Superconductivity: A phenomenon of zero electrical resistance occurring in certain materials below a characteristic temperature.
Meissner Effect: The expulsion of a magnetic field from a superconductor during its transition to the superconducting state.
Flux Trapping Effect: The phenomenon that magnetic flux lines do not move (become trapped) inside a superconductor.