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Closed Timelike Curves—Time and Again

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Abstract

Sixty years ago, in 1949, Kurt Gödel published a paper dedicated to Albert Einstein on the occasion of his 70th birthday. Gödel presented a solution of Einstein’s field equations for a rotating, homogeneous, stationary universe with negative cosmological constant. Among various surprising properties this universe allows closed timelike curves (CTC), i.e. travel into the past and into the future. Until today many papers have been published concerning physical, logical and philosophical consequences of these results and the existence of closed timelike worldlines in the General Theory of Relativity. Starting from a short survey on Gödel’s work we proceed to elucidate more modern interpretations of the existence of CTCs.

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References

  1. Chandrasekhar, S., Wright, J.P.: The geodesics in Gödel’s universe. Proc. Natl. Acad. Sci. USA 47, 341–347 (1961)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  2. de Witt, B.S.: The many universes interpretation of quantum mechanics. In: Foundation of Quantum Mechanics. Academic Press, New York (1971)

    Google Scholar 

  3. Deutsch, D.: Quantum mechanics near closed timelike lines. Phys. Rev. D 44, 3197–3271 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  4. Earman, J., Smeenk, C., Wüthrich, C.: Do the laws of physics forbid the operation of time machines? Synthese 169, 91–124 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  5. Everett, A.: Time travel paradoxes, path integrals, and the many worlds interpretation of quantum mechanics. Phys. Rev. D 69, 124023 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  6. Everett, H. III: ‘Relative state’ formulation of quantum mechanics. Rev. Mod. Phys. 29, 454–461 (1957)

    Article  MathSciNet  ADS  Google Scholar 

  7. Gödel, K.: An example of a new type of cosmological solutions of Einstein’s field equations of gravitation. Rev. Mod. Phys. 21, 447–450 (1949)

    Article  MATH  ADS  Google Scholar 

  8. Gödel, K.: Rotating universes in general relativity theory. In: Graves, L.M., et al. (eds.) Proceedings of the International Congress of Mathematicians, pp. 175–181. American Mathematical Society, Providence (1952)

    Google Scholar 

  9. Gott, R.: Closed timelike curves produced by pairs of moving cosmic strings: exact solutions. Phys. Rev. Lett. 66, 1126–1129 (1991)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  10. Hawking, S.W.: Chronology protection conjecture. Phys. Rev. D 46, 603–611 (1992)

    Article  MathSciNet  ADS  Google Scholar 

  11. Hawking, S.W., Ellis, G.F.R.: The Large Scale Structure of Space-Time. Cambridge University Press, Cambridge (1973)

    Book  MATH  Google Scholar 

  12. Jammer, M.: The Philosophy of Quantum Mechanics, pp. 509–521. Wiley, New York (1974)

    Google Scholar 

  13. Kanitscheider, B.: Vom Absoluten Raum Zur Dynamischen Geometrie. Bibliogr. Inst., Mannheim (1976)

    MATH  Google Scholar 

  14. Kundt, W.: Trägheitsbahnen in einem von Gödel angegebenen kosmologichen Modell. Z. Phys. 145, 611–620 (1956)

    Article  ADS  Google Scholar 

  15. Malament, D.: Minimal acceleration requirements for ‘time-travel’ in Gödel space-time. J. Math. Phys. 26, 774–777 (1985)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  16. Mittelstaedt, P.: Der Zeitbegriff in der Physik, 3th edn. BI-Wissenschaftsverlag, Mannheim (1989)

    MATH  Google Scholar 

  17. Ozsváth, I., Schücking, E.: Finite rotating universe. Nature 193, 1168–1169 (1962)

    Article  MATH  ADS  Google Scholar 

  18. Ozsváth, I., Schücking, E.: Approaches to Gödel’s rotating universe. Class. Quantum Gravity 18, 2243–2252 (2001)

    Article  MATH  ADS  Google Scholar 

  19. Pfarr, J.: Zur wissenschaftstheoretischen Deutung der ‘Many-Words-Interpretation’ der Quantentheorie. In: Mittelstaedt, P., Pfarr, J. (eds.) Grundlagen der Quantentheorie, pp. 111–127. B.I.-Wissenschaftsverlag, Mannheim (1981)

    Google Scholar 

  20. Pfarr, J.: Time-travel in Gödel’s space. Gen. Relativ. Gravit. 13, 1073–1091 (1981)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  21. Rosa, V.M., Letelier, P.S.: Stability of closed timelike curves in the Gödel universe. Gen. Relativ. Gravit. 39, 1419–1435 (2007)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  22. Tipler, F.J.: Rotating cylinders and the possibility of global causality violation. Phys. Rev. D 9, 2203–2206 (1974)

    Article  MathSciNet  ADS  Google Scholar 

  23. van Stockum, W.J.: The gravitational field of a distribution of particles rotating about an axis of symmetry. Proc. R. Soc. Edinb. 57, 135–154 (1937)

    MATH  Google Scholar 

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Correspondence to Joachim Pfarr.

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Pfarr, J. Closed Timelike Curves—Time and Again. Found Phys 40, 1326–1332 (2010). https://doi.org/10.1007/s10701-010-9448-9

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  • DOI: https://doi.org/10.1007/s10701-010-9448-9

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