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Timelike Curves leads to violation of heisenberg uncertainty Relation

  1. Aug 1, 2012 #1
    General Relatitivity predicts Timelike curves and there are nonlinear extensions of mechanics which resolve the paradoxical aspects of CTC's *i.e. Time Travel, on the other hand Hawking proposed a conjeture to rule out CTCs, the Chronology Protection Conjecture*
    there are a class of Timelike Curves, Open Timelike Curvatures, OTCs which leads to violate Heisenberg's Uncertainty Principle


    ...and show that the Heisenberg uncertainty principle between canonical variables, such as position and momentum, can be violated in the presence of interaction-free CTCs....

    ...We refer to the interaction-free case as an 'open time like curve' (OTC) because the disconnected paths of the time-traveller's trajectory appear to form an open loop rather than a closed curve...

    ...We have speculated on the extension of this idea to curved spacetimes in general by conjecturing that gravitational time dilation can be modelled as an OTC effect. This leads to a modied theory of quantum optics that becomes nonlinear in the presence of curvature. This speculation could be testable with current technology via experiments on entangled systems in earth's gravitational feld*...

    *D. Deutsch, Phys. Rev. D, 44, 3197
    J. B. Hartle, Phys. Rev. D, 49, 6543
    H. D. Politzer, Phys. Rev. D, 49, 3981
    S. Lloyd, L. Maccone, R. Garcia-Patron, V. Giovannetti,
    Y. Shikano, S. Pirandola, L. A. Rozema, A. Darabi,
    Y. Soudagar, L. K. Shalm, and A. M. Steinberg, Phys. Rev. Lett., 106, 040403.
    T. C. Ralph and C. R. Myers, Phys. Rev. A 82, 062330

    *Hawking, S.W. Phys. Rev. D46, 603-611.

    *T. C. Ralph, G. J. Milburn, and T. Downes, Phys. Rev.A, 79, 022121
    Last edited: Aug 1, 2012
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  3. Aug 1, 2012 #2


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    As I read it, this paper is more about the discrimination of models. I really wouldn't expect to see a violation of the HUP.
  4. Aug 2, 2012 #3


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    Deutsch avoids time-travel paradoxes in QM by rejecting the superposition principle of QM. In my opinion there is much simpler and more natural way to avoid the paradoxes, by retaining the superposition principle but rejecting the assumption of free will:
    http://xxx.lanl.gov/abs/1006.0338 [accepted for publication in Advanced Science Letters]
  5. Aug 3, 2012 #4
    Phys. Rev. Focus 27, 5. 2011

    ...Oxford University physicist David Deutsch proposed a consistency condition to avoid time-travel paradoxes: a particle that loops back in time in this way should be in the same quantum state when in reappears in the immediate past of the interaction as it was when it departed the interaction for the immediate future.

    To see how this condition works, imagine a quantum particle having states labeled 0 and 1. It travels around a CTC and, on its return, interacts with an “external” particle in such a way that 0 becomes 1 and 1 becomes 0. Such a particle presents a quantum grandfather paradox: when it comes back around the loop, it flips its former self to the opposite state. However, Deutsch showed that consistency is possible if the particle is in a superposition–a state that is equal parts 0 and 1. The interaction exchanges the 0 and the 1, but the state overall remains unchanged. For this to work, the external particle must also be in a superposition that flips back and forth...


    ...the paradox is avoided, but a difficulty arises if the external particle is measured. Then it cannot remain in a superposition but must become definitely either 0 or 1–which means that the CTC particle cannot remain in a superposition, either. To preserve consistency, Deutsch argued that the CTC particle must exist in two parallel universes–the “1-universe” and the “0-universe”–and continually switch between them, so that no contradiction occurs in either one....

    Deutsch appeals to the multiverse


    ...Lorenzo Maccone*, of the Massachusetts Institute of Technology and the University of Pavia, Italy, and his colleagues propose a more stringent condition that avoids these difficulties. They require that any measurement of the particle going into the future should yield the same result as measuring it when it returns from the past. So any state that would alter the past when it came around again is disallowed, and no grandfather-type paradoxes can arise.....

    *Phys. Rev. Lett. 106, 040403 (2011)
  6. Aug 3, 2012 #5

    Todd A. Brun, Foundations of Physics
    March 2012, Volume 42, Issue 3, pp 341-361

    ...considering that a D-CTC-assisted quantum computer can violate both the uncertainty principle* ...

    *Phys Rev Lett, 102(21):210402, May 2009.

    ...show how a party with access to CTCs, or a "CTC-assisted" party, can perfectly distin-
    guish among a set of non-orthogonal quantum states....

    T. A. Brun, Phys Rev Lett, 102(21):210402, May 2009.

    ...and can be interacted with in the way described by this simple model, our results confirm
    those of Brun et al that non-orthogonal states can be discriminated...

    ...Our work supports the conclusions of Brun et al that an observer can use interactions with a CTC to allow them to discriminate unknown, non-orthogonal quantum states – in contradiction of the uncertainty principle.

    T. C. Ralph, Phys. Rev. A 82, 062330 2010.
    Last edited: Aug 3, 2012
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