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Phys. Scr., 2015, Volume 90, Issue 8, 85101, 14 pages (Mi phscr6)  

Quantum causality in closed timelike curves

S. M. Korotaev, E. O. Kiktenko

Geoelectromagnetic Research Centre of Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, PO 30 Troitsk, Moscow 142190, Russia

Abstract: Although general relativity allows the existence of closed timelike curves (CTCs), self-consistency problems arise (the 'grandfather paradox' among others). It is known that quantum mechanical consideration of the matter formally removes all the paradoxes, but the questions about causal structure remain. On the other hand, the idea of postselected CTCs (P-CTC) in quantum teleportation has know been put forward and experimentally implemented. We consider these problems with the aid of quantum causal analysis, where causality is defined without invoking the time relation. It implements the Cramer principle of weak causality, which admits time reversal in entangled states. We analyze Deutsch CTCs (D-CTC) with different kinds of interactions between the chronology-violating and chronology-respecting particles, with refined inferences about mixedness, quantum/classical correlations, entanglement and thermodynamics in the D-CTC. The main result is that time reversal causality can really exist, however, the final quantum state does not place retrospective constraints on the initial state, instead the final state can influence the state inside the D-CTC. This is effectively the implementation of Novikov self-consistency principle. The P-CTC has radically different properties; in particular, if the initial state was pure, the final state is always pure too. Self-consistency is controlled by the initial state-dependent traversability of the P-CTC.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation SP-961.2013.5
Russian Foundation for Basic Research 12-05-00001
14-05-04053
This work has been supported by RFBR (grants 12-05-00001 and 14-05-04053) and CGPRF (grant SP-961.2013.5).


DOI: https://doi.org/10.1088/0031-8949/90/8/085101


Bibliographic databases:

Document Type: Article
Received: 08.02.2015
Accepted:23.04.2015
Language: English

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