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arXiv:quant-ph/0507052

Comment on 'Quantum Theory Looks at Time Travel' by D.Greenberger & K.Svozil

J.S. Wykes

Published Jul 6, 2005• 0 citations

Abstract

It is claimed in the above paper that, if time travel were possible, quantum propagation would prevent classic time travel paradoxes by establishing consistent loops; an example circuit is used to demonstrate such a loop. It is argued here that established loops are not the framework in which the classic paradoxes arise; rather they arise via the establishment of a concrete initial history in which no disturbing time travel is allowed and then disturbing that history via the launch of the time traveller. It is shown that, operated in this two-pass fashion, if the first forward evolution of their circuit produces a definite triggering of a backwards time travelling state, the re-evolution thereby engendered may be organised so as to prohibit the triggering of this state, thereby creating a classic time travel paradox.

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It is claimed in the above paper that, if time travel were possible, quantum propagation would prevent classic time travel paradoxes by establishing consistent loops; an example circuit is used to demonstrate such a loop. It is argued here that established loops are not the framework in which the classic paradoxes arise; rather they arise via the establishment of a concrete initial history in which no disturbing time travel is allowed and then disturbing that history via the launch of the time traveller. It is shown that, operated in this two-pass fashion, if the first forward evolution of their circuit produces a definite triggering of a backwards time travelling state, the re-evolution thereby engendered may be organised so as to prohibit the triggering of this state, thereby creating a classic time travel paradox.

We extend the theory of quantum time loops introduced by Greenberger and Svozil [1] from the scalar situation (where paths have just an associated complex amplitude) to the general situation where the time traveling system has multidimensional underlying Hilbert space. The main mathematical tool that emerges is the noncommutative Möbius Transformation and this affords a formalism similar to the modular structure well known to feedback control problems. The self-consistency issues that plague other approaches do not arise here, as we do not consider completely closed time loops. We argue that a sum-over-all-paths approach may be carried out in the scalar case but quickly becomes unwieldy in the general case. It is natural to replace the beam splitters of [1] with more general components having their own quantum structure, in which case the theory starts to resemble the quantum feedback network theory for open quantum optical models and indeed we exploit this to look at more realistic physical models of time loops. We analyze some Grandfather paradoxes in the new setting. DOI 10.1134/S1061920824601691

For time travel to be consistent with the known laws of physics, the resulting paradoxes must be resolved. It has been suggested that parallel timelines (a.k.a. multiple histories) may provide a resolution. However, so far, a concrete mechanism by which parallel timelines can be created has never been satisfactorily formulated. In this paper we propose such a mechanism based on the Everett (many-worlds) interpretation of quantum mechanics, together with a linear pure-state CTC consistency condition. The timelines in our model are emergent, like the "worlds" of the Everett interpretation; they are created by the entanglement of the time machine with the environment and the resulting decoherence. Therefore, we call them "entangled timelines" or E-CTCs. As the entanglement gradually spreads out to additional systems, the timelines spread out as well, providing a local and well-defined alternative to the naive "branching timelines" picture often presented in the literature. The E-CTC model is similar to Deutsch's familiar D-CTC model, but differs from it mainly by keeping the entangled state explicit and imposing a different consistency condition. These differences allow us to create a clearer practical definition of the resulting parallel timelines.

A time machine that sends information back to the past may, in principle, be built using closed time-like curves. However, the realization of a time machine must be congruent with apparent paradoxes that arise from traveling back in time. Using a simple model to analyze the consequences of time travel, we show that several paradoxes, including the grandfather paradox and Deutsch's unproven theorem paradox, are precluded by basic axioms of probability. However, our model does not prohibit traveling back in time to affect past events in a self-consistent manner.