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Wormhole Time Machines and Multiple Histories

General Relativity and Gravitation volume 55, Article number: 44 (2023) Cite this article

Abstract

In a previous paper, we showed that a class of time travel paradoxes which cannot be resolved using Novikov’s self-consistency conjecture can be resolved by assuming the existence of multiple histories or parallel timelines. However, our proof was obtained using a simplistic toy model, which was formulated using contrived laws of physics. In the present paper we define and analyze a new model of time travel paradoxes, which is more compatible with known physics. This model consists of a traversable Morris-Thorne wormhole time machine in 3+1 spacetime dimensions. We define the spacetime topology and geometry of the model, calculate the geodesics of objects passing through the time machine, and prove that this model inevitably leads to paradoxes which cannot be resolved using Novikov’s conjecture, but can be resolved using multiple histories. An open-source simulation of our new model using Mathematica is available for download on GitHub. We also provide additional arguments against the Novikov self-consistency conjecture by considering two new paradoxes, the switch paradox and the password paradox, for which assuming self-consistency inevitably leads to counter-intuitive consequences. Our new results provide more substantial support to our claim that if time travel is possible, then multiple histories or parallel timelines must also be possible.

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Data Availability Statement

No data was used in this paper.

Notes

  1. We will discuss in more detail why this is considered a paradox in Sect. 6.2.

  2. One may wonder if perhaps this can be achieved by allowing the time machine to be in a superposition of destroyed and not destroyed. Indeed, we will discuss how quantum mechanics, in the context of the Everett (“many-worlds”) interpretation, can be used to resolve time travel paradoxes in Sect. 7.3.

  3. The Novikov self-consistency conjecture (sometimes also called the Novikov self-consistency principle) is named after physicist Igor Novikov, and should not be confused with another “Novikov conjecture”, named for mathematician Sergei Novikov, which is related to topology.

  4. More precisely, one of us, Barak Shoshany, along with his student Jacob Hauser.

  5. In [21] we also analyzed the case where additional colors and/or particles are allowed, but this will not be relevant to the current discussion.

  6. Defined since 2019 to have the exact value \(\sigma \equiv 2\pi ^{5}k^{4}/15c^{2}h^{3}\) where k is the Boltzmann constant, c is the speed of light, and h is the Planck constant.

  7. Note that \(T<T_{0}\), so we must integrate from T to \(T_{0}\) in order for the integral to be positive.

  8. In fact, Alice changing her mind can also fall into this category. While she is determined to turn off the switch, there is always a small probability that she changes her mind after all. The issue isn’t that she changed her mind, but rather that she had to change her mind regardless of how low the probability for that should have been. Treated this way, we can avoid involving the controversial notion of free will in the discussion.

  9. Interestingly, in [21] we showed that in the case of cyclic histories (there is a “last” history, and it connects back to the first) one may combine Novikov’s conjecture and multiple histories into a “hybrid” method; but this is a special case that will not be relevant to our discussion.

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Acknowledgements

J. W. would like to thank Alicia Savelli for helpful discussions and support, and Carlo Rovelli for his advice and insightful discussions. B. S. would like to thank Thomas A. Roman for his invaluable input. We also thank the two anonymous reviewers for identifying several issues with the original manuscript. This research was supported by funding from the Brock University Match of Minds grant.

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  1. Department of Physics, Brock University, 1812 Sir Isaac Brock Way, St. Catharines, Ontario, L2S 3A1, Canada

    Barak Shoshany & Jared Wogan

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Correspondence to Barak Shoshany.

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Shoshany, B., Wogan, J. Wormhole Time Machines and Multiple Histories. Gen Relativ Gravit 55, 44 (2023). https://doi.org/10.1007/s10714-023-03094-8

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