Time Travel Paradoxes, Path Integrals, And The Many Worlds Interpretation Of Quantum Mechanics 04

Time Travel Paradoxes, Path Integrals, And The Many Worlds Interpretation Of Quantum Mechanics 04

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arXiv:gr-qc/0410035 v1 7 Oct 2004 Time Travel Paradoxes, Path Integrals, and the Many Worlds Interpretation of Quantum Mechanics Allen Everett Department of Physics and Astronomy and Institute of Cosmology Tufts University Abstract We consider two approaches to evading paradoxes in quantum mechanics with closed timelike curves (CTCs). In a model similar to Politzer’s, as- suming pure states and using path integrals, we show that the problems of paradoxes and of unitarity violation are related; preserving unitarity avoids paradoxes by modifying the time evolution so that improbable events become certain. Deutsch has argued, using the density matrix, that paradoxes do not occur in the “many worlds interpretation“. We find that in this approach account must be taken of the resolution time of the device that detects ob- jects emerging from a wormhole or other time machine. When this is done one finds that this approach is viable only if macroscopic objects traversing a wormhole interact with it so strongly that they are boken into microscopic fragments. . 1
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I. Introduction There has recently been a good deal of interest in possible spacetimes containing closed timelike curves (CTCs) arising either from the presence of traversable wormholes [1] or from the warping of spacetime in such a way as to allow superluminal travel[2], with the possibility of CTC’s as a consequence[3-5]. A variety of theoretical considerations (e. g., Refs. 6-8), either general or addressed to specific models, have been advanced which suggest that the formation of CTC’s is not possible. However, while some of these considerations are very persuasive, none appear conclusive[9]. In addition to the problems discussed in the references already cited, CTC’s lead to the well known problems with paradoxes arising from the apparent possibility of inconsistent causal loops. This phenomenon is illus- trated by the “grandfather paradox” occurring frequently, in various guises, in science fiction, in which one travels back in time and murders one’s own grandfather, thus preventing one’s self from being born and traveling back in time in the first place. Satisfactory physical theories must avoid giving rise to such self-contradictory predictions. One approach to achieving this is to impose consistency con- straints on the allowable initial conditions on spacelike surfaces prior to the formation of the CTC’s, thus abandoning the principle that initial condi- tions on such surfaces can be chosen at will. For example, in the case of the grandfather paradox we might insist that the initial conditions just before the prospective murder include the presence of a strategically placed banana peel on which the prospective murderer slips as he pulls the trigger, thus spoiling his aim. One might refer to this approach as the “banana peel mechanism”; it leads to a theory free of logical contradictions, but requires occurrences that would seem, a priori , to be highly improbable. This violates strong in- tuitive feelings. These feelings may simply reflect our lack of experience with
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