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Nocommutative space and QM

  1. Oct 28, 2006 #1


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    I am reading up on the application of noncommutative coordinates to quantum mechanics, and I found this paragraph which I think many here will find interesting.

    From http://arxiv.org/PS_cache/hep-th/pdf/0109/0109162.pdf

    Quantum Field Theory on Noncommutative Spaces, by
    Richard J. Szabo

    Of course a phase space is not spacetime: by definition it's the space spanned by the canonical variables in the Hamiltonian: the Canonical Coordinates and the Canonical Momenta. Nevertheless the coordinates are convertible to spacetime coordinates and the momenta to the observed kind of momenta. So his point about spacetime being non-commutative at short distances is well taken.

    Now this raises a question in my mind. The difference between the quantum world and the macroscopic one is not always one of scale, but rather of coherence. Quantum effects involving noncommutative operators over distances that can be seen with the naked eye have been demonstrated. So does spacetime noncommutativity extend to those visible cases too? Could it be experimentally demostrated?
    Last edited: Oct 28, 2006
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