Advertisement

Synthese

, Volume 169, Issue 1, pp 91–124 | Cite as

Do the laws of physics forbid the operation of time machines?

  • John Earman
  • Christopher Smeenk
  • Christian Wüthrich
Open Access
Article

Abstract

We address the question of whether it is possible to operate a time machine by manipulating matter and energy so as to manufacture closed timelike curves. This question has received a great deal of attention in the physics literature, with attempts to prove no-go theorems based on classical general relativity and various hybrid theories serving as steps along the way towards quantum gravity. Despite the effort put into these no-go theorems, there is no widely accepted definition of a time machine. We explain the conundrum that must be faced in providing a satisfactory definition and propose a resolution. Roughly, we require that all extensions of the time machine region contain closed timelike curves; the actions of the time machine operator are then sufficiently “potent” to guarantee that closed timelike curves appear. We then review no-go theorems based on classical general relativity, semi-classical quantum gravity, quantum field theory on curved spacetime, and Euclidean quantum gravity. Our verdict on the question of our title is that no result of sufficient generality to underwrite a confident “yes” has been proven. Our review of the no-go results does, however, highlight several foundational problems at the intersection of general relativity and quantum physics that lend substance to the search for an answer.

Keywords

General relativity Time travel Time machines QFT on curved spacetime Causality Closed timelike curves 

References

  1. Arntzenius, F., & Maudlin, T. (2005). Time travel and modern physics. In E. N. Zalta (Ed.), Stanford encyclopedia of philosophy. http://plato.stanford.edu/archives/sum2005/entries/time-travel-phys/.
  2. Bojowald M. (2001) Absence of a singularity in loop quantum cosmology. Physical Review Letters 86: 5227–5230CrossRefGoogle Scholar
  3. Boulware D.G. (1992) Quantum field theory in spacetime with closed timelike curves. Physical Review D 46: 4421–4441CrossRefGoogle Scholar
  4. Brunnemann J., Thiemann T. (2006) On (cosmological) singularity avoidance in loop quantum gravity. Classical and Quantum Gravity 23: 1395–1428CrossRefGoogle Scholar
  5. Carroll J.W. (1994) Laws of nature. Cambridge University Press, New YorkGoogle Scholar
  6. Carroll J.W. (2004) Readings on laws of nature. University of Pittsburgh Press, Pittsburgh, PAGoogle Scholar
  7. Carroll, S. (2004). Why is the universe accelerating? In W. L. Friedman (Ed.), Measuring and Modeling the Universe. Cambridge: Cambridge University Press. astro-ph/0310342.Google Scholar
  8. Cassidy M.J., Hawking S.W. (1998) Models for chronology selection. Physical Review D 57: 2372–2380CrossRefGoogle Scholar
  9. Chrusciel P.T., Isenberg J. (1993) Compact Cauchy horizons and Cauchy surfaces. In: Hu B.L., Jacobson T.A.(eds) Directions in general relativity (vol 2). Cambridge University Press, Cambridge, pp 97–107Google Scholar
  10. Cramer C.R., Kay B.S. (1996) Stress-energy must be singular on the Misner space horizon even for automorphic field. Classical and Quantum Gravity 13: L143–L149CrossRefGoogle Scholar
  11. Davies P. (2002) How to build a time machine. Viking Penguin, New YorkGoogle Scholar
  12. Deutsch D. (1991) Quantum mechanics near closed timelike lines. Physical Review D 44: 3197–3271CrossRefGoogle Scholar
  13. Deutsch D., Lockwood M. (1994) The quantum physics of time travel. Scientific American 270((March): 68–74CrossRefGoogle Scholar
  14. Earman J. (1995) Bangs, crunches, whimpers, and shrieks: Singularities and acausalities in relativistic spacetimes. Oxford University Press, New YorkGoogle Scholar
  15. Earman, J., & Wüthrich, C. (2004). Time machines. In E. N. Zalta (Ed.), Stanford Encyclopedia of Philosophy.http://plato.stanford.edu/archives/win2004/entries/time-machine/.
  16. Everett A. (2004) Time travel paradoxes, path integrals, and the many worlds interpretation of quantum mechanics. Physical Review D 69: 124023CrossRefGoogle Scholar
  17. Fewster, C. J. (2005). Energy inequalities in quantum field theory. math-ph/0501073.Google Scholar
  18. Fewster C.J., Higuchi A. (1996) Quantum field theory on certain non-globally hyperbolic spacetimes. Classical and Quantum Gravity 13: 51–61CrossRefGoogle Scholar
  19. Fewster C.J., Wells C.G. (1995) Unitarity of quantum field theory and closed timelike curves. Physical Review D 52: 5773–5782CrossRefGoogle Scholar
  20. Ford L.H., Roman T.A. (1996) Quantum field theory constrains traversable wormhole geometries. Physical Review D 53: 5496–5507CrossRefGoogle Scholar
  21. Friedman J.L. (1997) Field theory on spacetimes that are not globally hyperbolic. Fields Institute Communications 15: 43–57Google Scholar
  22. Friedman J.L., Papastamatiou N.J., Simon J.Z. (1992) Failure of unitarity for interacting fields on spacetimes with closed timelike curves. Physical Review D 46: 4456–4469CrossRefGoogle Scholar
  23. Friedman J.L., Schleich K., Witt D.M. (1993) Topological censorship. Physical Review Letters 71: 1486–1489CrossRefGoogle Scholar
  24. Frolov V.P. (1991) Vacuum polarization in a locally static multiply connected spacetime and time machine problems. Physical Review D 43: 3878–3894CrossRefGoogle Scholar
  25. Geroch R.P. (1970) Domain of dependence. Journal of Mathematical Physics 11: 437–449CrossRefGoogle Scholar
  26. Geroch R.P. (1977) Prediction in general relativity. In: Earman J., Glymour C., Stachel J.(eds) Foundations of spacetime theories, Minnesota studies in the philosophy of science (vol 8). University of Minnesota Press, Minneapolis, pp 81–93Google Scholar
  27. Gibbons G.W., Hawking S.W. (1993) Euclidean quantum gravity. World Scientific, SingaporeGoogle Scholar
  28. Gott R. (1991) Closed timelike curves produced by pairs of moving cosmic strings: Exact solutions. Physical Review Letters 66: 1126–1129CrossRefGoogle Scholar
  29. Gott R. (2001) Time travel in Einstein’s universe. Houghton Mifflin, New YorkGoogle Scholar
  30. Hartle J., Hawking S.W. (1983) Wave function of the universe. Physical Review D 28: 2960–2975CrossRefGoogle Scholar
  31. Hawking S.W. (1992a) Chronology protection conjecture. Physical Review D 46: 603–611CrossRefGoogle Scholar
  32. Hawking S.W. (1992) The chronology protection conjecture. In: Sato H., Nakamura T.(eds) The sixth Marcel Grossmann meeting. World Scientific, Singapore, pp 3–13Google Scholar
  33. Hawking S.W., Ellis G.F.R. (1973) The large scale structure of spacetime. Cambridge University Press, CambridgeGoogle Scholar
  34. Hawking S.W., Thorne K.S., Novikov I., Ferris T., Lightman A. (2002) The future of spacetime. W. W. Norton, New YorkGoogle Scholar
  35. Hiscock, W. A. (2000). Quantized fields and chronology protection. gr-qc/0009061 v2.Google Scholar
  36. Hochberg D., Visser M. (1997) Geometric structure of the generic traversable wormhole throat. Physical Review D 56: 4745–4755CrossRefGoogle Scholar
  37. Hochberg, D. & Visser, M. (1999). General dynamic wormholes and violation of the null energy condition. gr-qc/9901020.Google Scholar
  38. Horwich P. (1987) Asymmetries in time. MIT Press, CambridgeGoogle Scholar
  39. Isenberg J., Moncrief V. (1985) Symmetries of cosmological Cauchy horizons with exceptional orbits. Journal of Mathematical Physics 26: 1024–1027CrossRefGoogle Scholar
  40. Isham C., Butterfield J. (1999) On the emergence of time in quantum gravity. In: Butterfield J.(eds) The arguments of time. Oxford University Press, Oxford, pp 111–168Google Scholar
  41. Kay B.S. (1992) The principle of locality and quantum field theory on (non-globally hyperbolic) curved spacetimes. Reviews in Mathematical Physics, Special Issue 4: 167–195Google Scholar
  42. Kay B.S. et al (1997) Quantum fields in curved spacetime: Non global hyperbolicity and locality. In: Longo R.(eds) Operator algebras and quantum field theory. International Press, Cambridge, MA, pp 578–588Google Scholar
  43. Kay B.S., Radzikowski M.J., Wald R.M. (1997) Quantum field theory on spacetimes with compactly generated cauchy horizons. Communications in Mathematical Physics 183: 533–556CrossRefGoogle Scholar
  44. KimS.-W. Thorne K.S. (1991) Do vacuum fluctuations prevent the creation of closed timelike curves?. Physical Review D: 43(3929–3957): 43, 3929–3957Google Scholar
  45. Krasnikov S.V. (1996) Quantum stability of the time machine. Physical Review D 54: 7322–7327CrossRefGoogle Scholar
  46. Krasnikov S.V. (1997) Causality violation and paradoxes. Physical Review D 55: 3427–3430CrossRefGoogle Scholar
  47. Krasnikov S.V. (1998) A singularity-free WEC-respecting time machine. Classical and Quantum Gravity 15: 997–1003CrossRefGoogle Scholar
  48. Krasnikov S.V. (1999) Quantum field theory and time machines. Physical Review D 59: 024010CrossRefGoogle Scholar
  49. Krasnikov S.V. (2002) No time machines in classical general relativity. Classical and Quantum Gravity 19: 4109–4129CrossRefGoogle Scholar
  50. Lewis D.K. (1973) Counterfactuals. Harvard University Press, Cambridge, MAGoogle Scholar
  51. Lobo F.S.N. (2005) Phantom energy and traversable wormholes. Physical Review D 71: 084011CrossRefGoogle Scholar
  52. Maeda K., Ishibashi A., Narita M. (1998) Chronology protection and non-naked singularities. Classical and Quantum Gravity 15: 1637–1651CrossRefGoogle Scholar
  53. Manchak, J. (2007). On ‘time machines’ in general relativity. Unpublished manuscript.Google Scholar
  54. Nahin P.J. (1999) Time machines (2nd ed). AIP Press, New YorkGoogle Scholar
  55. Ori A. (1993) Must time-machine construction violate the weak energy condition?. Physical Review Letters 71: 2517–2520CrossRefGoogle Scholar
  56. Ori A. (2005) A class of time-machine solutions with a compact vacuum core. Physical Review Letters 95: 021101CrossRefGoogle Scholar
  57. Ori A. (2007) Formation of closed timelike curves in a composite vacuum/dust asymptotically flat spacetime. Physical Review D 76: 044002CrossRefGoogle Scholar
  58. Overbye, D. (2005). Remembrances of things future: The mystery of time. New York Times, June 28 2005.Google Scholar
  59. Penrose R. (1998) The question of cosmic censorship. In: Wald R.M.(eds) Black holes and relativistic stars. University of Chicago Press, Chicago, pp 103–122Google Scholar
  60. Politzer H.D. (1992) Simple quantum systems with closed timelike curves. Physical Review D 46: 4470–4476CrossRefGoogle Scholar
  61. Randles J. (2005) Breaking the time barrier. Paraview Pocketbooks, New YorkGoogle Scholar
  62. Rovelli C. (2004) Quantum gravity. Cambridge University Press, CambridgeGoogle Scholar
  63. Sushkov S.S. (1997) Chronology protection and quantized fields: complex automorphic scalar field in Misner space. Classical and Quantum Gravity 14: 523–533CrossRefGoogle Scholar
  64. Tipler F.J. (1976) Causality violation in asymptotically flat space-times. Physical Review Letters 37: 879–882CrossRefGoogle Scholar
  65. Tipler F.J. (1977) Singularities and causality violation. Annals of Physics 108: 1–36CrossRefGoogle Scholar
  66. Unruh W., Wald R. (1989) Time and the interpretation of canonical quantum gravity. Physical Review D 40: 2598–614CrossRefGoogle Scholar
  67. Visser M. (1997) The reliability horizon for semi-classical quantum gravity: metric fluctuations are often more important than back-reaction. Physics Letters B 415: 8–14CrossRefGoogle Scholar
  68. Visser M. (2003) The quantum physics of chronology protection. In: Gibbons G.W., Shellard E.P.S., Rankin S.J.(eds) The future of theoretical physics and cosmology: celebrating Stephen Hawking’s 60th birthday. Cambridge University Press, Cambridge, pp 161–176Google Scholar
  69. Vollick D.N. (1997) How to produce exotic matter using classical fields. Physical Review D 56: 4720–4723CrossRefGoogle Scholar
  70. Wald R.M. (1984) General relativity. University of Chicago Press, ChicagoGoogle Scholar
  71. Wald R.M. (1994) Quantum field theory in curved spacetime and black hole thermodynamics. University of Chicago Press, ChicagoGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • John Earman
    • 1
  • Christopher Smeenk
    • 2
  • Christian Wüthrich
    • 3
  1. 1.Department of History and Philosophy of ScienceUniversity of PittsburghPittsburghUSA
  2. 2.Department of PhilosophyThe University of Western OntarioLondonCanada
  3. 3.Department of PhilosophyUniversity of CaliforniaSan DiegoUSA

Personalised recommendations