Skip to main content
SpringerLink
Log in

Wormhole Time Machines and Multiple Histories

  • Research Article
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

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.

References

  1. Shoshany, B.: Lectures on faster-than-light travel and time travel. SciPost Phys. Lect. Notes 10, 1 (2019). https://doi.org/10.21468/SciPostPhysLectNotes.10. arXiv:1907.04178

    Article  Google Scholar 

  2. Krasnikov, S.: Back-in-Time and Faster-than-Light Travel in General Relativity. Springer (2018). https://doi.org/10.1007/978-3-319-72754-7

  3. Francisco, S.N., Lobo, editor.: Wormholes, Warp Drives and Energy Conditions. Springer (2017). https://doi.org/10.1007/978-3-319-55182-1

  4. Everett, A., Roman, T.: Time Travel and Warp Drives: A Scientific Guide to Shortcuts Through Time and Space. University of Chicago Press (2012). https://press.uchicago.edu/ucp/books/book/chicago/T/bo8447256.html

  5. Morris, M.S., Thorne, K.S.: Wormholes in spacetime and their use for interstellar travel: a tool for teaching general relativity. Am. J. Phys. 56(5), 395–412 (1988). https://doi.org/10.1119/1.15620

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Visser, M.: Lorentzian wormholes—from Einstein to hawking: Matt visser. Springer (1996). https://www.springer.com/gp/book/9781563966538

  7. Morris, M.S., Thorne, K.S., Yurtsever, U.: Wormholes, time machines, and the weak energy condition. Phys. Rev. Lett. 61, 1446–1449 (1988). https://doi.org/10.1103/PhysRevLett.61.1446

    Article  ADS  Google Scholar 

  8. Krasnikov, S.: The Time travel paradox. Phys. Rev. D 65, 064013 (2002). https://doi.org/10.1103/PhysRevD.65.064013. arXiv:gr-qc/0109029

    Article  ADS  MathSciNet  Google Scholar 

  9. Krasnikov, S.V.: Causality violation and paradoxes. Phys. Rev. D 55(6), 3427 (1997). https://doi.org/10.1103/PhysRevD.55.3427

    Article  ADS  MathSciNet  Google Scholar 

  10. Wasserman, R.: Paradoxes of Time Travel. Oxford University Press (2018). https://global.oup.com/academic/product/paradoxes-of-time-travel-9780198793335

  11. Hawking, S.W.: Chronology protection conjecture. Phys. Rev. D 46, 603–611 (1992). https://doi.org/10.1103/PhysRevD.46.603

    Article  ADS  MathSciNet  Google Scholar 

  12. Visser, M.: From wormhole to time machine: comments on Hawking’s chronology protection conjecture. Phys. Rev. D 47, 554–565 (1993). https://doi.org/10.1103/PhysRevD.47.554. arXiv:hep-th/9202090

    Article  ADS  MathSciNet  Google Scholar 

  13. Visser, M.: The Quantum physics of chronology protection. In: The future of theoretical physics and cosmology: Celebrating Stephen Hawking’s 60th birthday. Proceedings, Workshop and Symposium, Cambridge, UK, January 7–10, 2002, pp. 161–176 (2002). arXiv:gr-qc/0204022

  14. Earman, J., Smeenk, C., Wüthrich, C.: Do the laws of physics forbid the operation of time machines? Synthese 169(1), 91–124 (2009). https://doi.org/10.1007/s11229-008-9338-2

    Article  MathSciNet  MATH  Google Scholar 

  15. Kim, S.-W., Thorne, K.S.: Do vacuum fluctuations prevent the creation of closed timelike curves? Phys. Rev. D 43, 3929–3947 (1991). https://doi.org/10.1103/PhysRevD.43.3929

    Article  ADS  MathSciNet  Google Scholar 

  16. Krasnikov, S.V.: Quantum stability of the time machine. Phys. Rev. D 54, 7322–7327 (1996). https://doi.org/10.1103/PhysRevD.54.7322. arXiv:gr-qc/9508038

    Article  ADS  MathSciNet  Google Scholar 

  17. Kay, B.S., Radzikowski, M.J., Wald, R.M.: Quantum field theory on space-times with a compactly generated Cauchy horizon. Commun. Math. Phys. 183, 533–556 (1997). https://doi.org/10.1007/s002200050042. arXiv:gr-qc/9603012

    Article  ADS  MATH  Google Scholar 

  18. Krasnikov, S.: Quantum field theory and time machines. Phys. Rev. D 59, 024010 (1999). https://doi.org/10.1103/PhysRevD.59.024010. arXiv:gr-qc/9802008

    Article  ADS  MathSciNet  Google Scholar 

  19. Friedman, J., Morris, M.S., Novikov, I.D., Echeverria, F., Klinkhammer, G., Thorne, K.S., Yurtsever, U.: Cauchy problem in spacetimes with closed timelike curves. Phys. Rev. D 42, 1915–1930 (1990). https://doi.org/10.1103/PhysRevD.42.1915

    Article  ADS  MathSciNet  Google Scholar 

  20. Echeverria, F., Klinkhammer, G., Thorne, K.S.: Billiard balls in wormhole spacetimes with closed timelike curves: Classical theory. Phys. Rev. D 44, 1077–1099 (1991). https://doi.org/10.1103/PhysRevD.44.1077

    Article  ADS  MathSciNet  Google Scholar 

  21. Hauser, J., Shoshany, B.: Time travel paradoxes and multiple histories. Phys. Rev. D 102 (2020). https://doi.org/10.1103/PhysRevD.102.064062, arXiv:1911.11590

  22. Everett, A.: Time travel paradoxes, path integrals, and the many worlds interpretation of quantum mechanics. Phys. Rev. D 69, 124023 (2004). https://doi.org/10.1103/PhysRevD.69.124023. arXiv:gr-qc/0410035

    Article  ADS  MathSciNet  Google Scholar 

  23. Deutsch, D.: Quantum mechanics near closed timelike lines. Phys. Rev. D 44, 3197–3217 (1991). https://doi.org/10.1103/PhysRevD.44.3197

    Article  ADS  MathSciNet  Google Scholar 

  24. Deutsch, D., Lockwood, M.: The quantum physics of time travel. Sci. Am. 270(3), 68–74 (1994)

    Article  Google Scholar 

  25. Whyte, C.: Paradox-free time travel. New Sci. 244(3261), 6 (2019). https://doi.org/10.1016/S0262-4079(19)32393-0

    Article  ADS  Google Scholar 

  26. Matt Visser, Carlos Barcelo. Energy Conditions And Their Cosmological Implications. In COSMO-99, pp. 98–112. World Scientific (2000). https://doi.org/10.1142/9789812792129_0014, arXiv:gr-qc/0001099

  27. Curiel, E.: A Primer on Energy Conditions. In: Lehmkuhl, D., Schiemann, G., Scholz, E (Eds.) Towards a Theory of Spacetime Theories, pp. 43–104. Springer New York, New York, NY, 2017. https://doi.org/10.1007/978-1-4939-3210-8_3. arXiv:1405.0403

  28. Armendariz-Picon, C.: On a class of stable, traversable Lorentzian wormholes in classical general relativity. Phys. Rev. D 65, 104010 (2002). https://doi.org/10.1103/PhysRevD.65.104010. arXiv:gr-qc/0201027

    Article  ADS  MathSciNet  Google Scholar 

  29. Kuhfittig, P.K.F.: A note on the stability of Morris–Thorne wormholes. Fund. J. Mod. Phys. 14, 23–31 (2020). arXiv:2009.11179

    Google Scholar 

  30. Placek, T.: Branching for general relativists. In: Nuel Belnap on Indeterminism and Free Action, pp. 191–221. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-01754-9_10

  31. Joanna Luc, Tomasz Placek. Interpreting non-hausdorff (generalized) manifolds in general relativity (2019). http://philsci-archive.pitt.edu/16172/

  32. Joanna Luc. Generalised manifolds as basic objects of general relativity. Found. Phys., pp. 1–23 (2019). https://doi.org/10.1007/s10701-019-00292-w

  33. McCabe, G.: The Topology of Branching Universes. Found. Phys. Lett. 18(7), 665–676 (2005). https://doi.org/10.1007/s10702-005-1319-9. arXiv:gr-qc/0505150

    Article  MathSciNet  MATH  Google Scholar 

  34. Shoshany, B., Stober., Z.: Time travel paradoxes and entangled timelines. In preparation (2023)

  35. Alcubierre, M.: The warp drive: hyper-fast travel within general relativity. Class. Quant. Gravity 11(5), L73–L77 (1994). https://doi.org/10.1088/0264-9381/11/5/001. arXiv:gr-qc/0009013

    Article  ADS  MathSciNet  Google Scholar 

  36. Shoshany, B.: Faster-than-light travel through hyperspace. In preparation (2023)

Download references

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.

Author information

Authors and Affiliations

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

    Barak Shoshany & Jared Wogan

Authors
  1. Barak Shoshany
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jared Wogan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Barak Shoshany.

Ethics declarations

Conflict of Interest

The authors have no conflicts of interest to disclose.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10714-023-03094-8

Search

Navigation