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Unsolvability of the Halting Problem in Quantum Dynamics

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Abstract

It is shown that the halting problem cannot be solved consistently in both the Schrödinger and Heisenberg pictures of quantum dynamics. The existence of the halting machine, which is assumed from quantum theory, leads into a contradiction when we consider the case when the observer’s reference frame is the system that is to be evolved in both pictures. We then show that in order to include the evolution of observer’s reference frame in a physically sensible way, the Heisenberg picture with time going backwards yields a correct description.

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Authors and Affiliations

  1. Korea Institute for Advanced Study, Seoul, 130-722, Korea

    Daegene Song

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  1. Daegene Song
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Correspondence to Daegene Song.

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Song, D. Unsolvability of the Halting Problem in Quantum Dynamics. Int J Theor Phys 47, 1785–1791 (2008). https://doi.org/10.1007/s10773-007-9621-x

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  • DOI: https://doi.org/10.1007/s10773-007-9621-x

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