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Mathematical Breakthrough Sets Out Rules For More Effective Teleportation 162

Posted by Soulskill

Mathematical Breakthrough Sets Out Rules For More Effective Teleportation

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  • by Anonymous Coward on Friday January 18, 2013 @07:06PM (#42630289)

    The name "quantum teleportation [wikipedia.org]" is a bit misleading: no particles, mass or energy is teleported. The only thing "teleported" is a quantum state.

    What's remarkable about quantum teleportation is that you can transfer an exact quantum state from one place to another without sending any particle with that state along the way. That's remarkable because quantum states can't, in general, be copied (see the "no-cloning theorem [wikipedia.org]). When you perform a quantum teleportation, you must destroy the state of the originating particle during the teleportation process.

  • by Neil Jacklin (2818845) on Friday January 18, 2013 @07:26PM (#42630433)
  • by martin-boundary (547041) on Friday January 18, 2013 @09:32PM (#42631249)
    Potential energy "exists" inside the gravitational field: It represents the total amount of work you have to do to traverse a certain path while being subjected to the effects of the field. For a conservative field like the gravitational one, the amount of work is independent of the actual path when the end points are fixed, and that's the reason, the only reason, why we can associate a single number, called potential energy, with any given height above ground level.

    In other words, potential energy is a mathematical shortcut, it saves you from having to compute a work path integral for each problem involving a particle traversing some path in a conservative field. Potential energy is literally a table of precomputed answers. If you have a path from 1000 feet down to 0 feet, you can 1) compute the work over that path or 2) look up the answer from the potential energy table, by subtracting the values at 1000 and 0 respectively. This works because of the fundamental theorem of calculus.

    Now onto the question. If you teleport an object from 1000 feet to 0 feet, there is no traversal of the gravitational field by definition. Therefore there is no work being done against the field since there is no continuous path. Therefore there is no energy change experienced by the object since there is no physical work happening that involves it (disregarding whatever mechanism enables the teleportation in the first place).

    Thus: At 1000 feet, the object has zero kinetic energy, and has potential energy V(1000). At 0 feet, the object has zero kinetic energy, and has potential energy V(0).

    This does violate the conservation of (kinetic + potential energy), however that quantity is only a convenient approximation of the truth for non-teleportation cases, where the only way of arriving at 0 from 1000 feet is by traversing a continuous path. The truth is that (kinetic + work-over-path) is conserved, in this case, since the path is not continuous.

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