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arXiv:quant-ph/0506141

Quantum mechanics and the time travel paradox

David Thomas Pegg

Published Jun 17, 2005• 5 citations
arXivHTMLPDF

Abstract

The closed causal chains arising from backward time travel do not lead to paradoxes if they are self consistent. This raises the question as to how physics ensures that only self-consistent loops are possible. We show that, for one particular case at least, the condition of self consistency is ensured by the interference of quantum mechanical amplitudes associated with the loop. If this can be applied to all loops then we have a mechanism by which inconsistent loops eliminate themselves.

DOI
10.48550/arxiv.quant-ph/0506141

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The closed causal chains arising from backward time travel do not lead to paradoxes if they are self consistent. This raises the question as to how physics ensures that only self-consistent loops are possible. We show that, for one particular case at least, the condition of self consistency is ensured by the interference of quantum mechanical amplitudes associated with the loop. If this can be applied to all loops then we have a mechanism by which inconsistent loops eliminate themselves.
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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.
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.