Temporal paradox

From Wikipedia, the free encyclopedia

A temporal paradox, time paradox, or time travel paradox is a paradox, an apparent contradiction, or logical contradiction associated with the idea of time and time travel. The notion of time travel to the future complies with current understanding of physics via relativistic time dilation, temporal paradoxes arise from circumstances involving hypothetical time travel to the past and are often used to demonstrate its impossibility. In physics, temporal paradoxes fall into two broad groups: consistency paradoxes exemplified by the grandfather paradox; and causal loops.[1] Other paradoxes associated with time travel are a variation of the Fermi paradox and paradoxes of free will that stem from causal loops such as Newcomb's paradox.[2]

Causal loop[edit]

Top: original billiard ball trajectory. Middle: the billiard ball emerges from the future, and delivers its past self a strike that averts the past ball from entering the time machine. Bottom: the billiard ball never enters the time machine, giving rise to the paradox, putting into question how its older self could ever emerge from the time machine and divert its course.

A causal loop is a paradox of time travel that occurs when a future event is the cause of a past event, which in turn is the cause of the future event. Both events then exist in spacetime, but their origin cannot be determined. A causal loop may involve an event, a person or object, or information.[1][3] The terms boot-strap paradox, predestination paradox or ontological paradox are sometimes used in fiction to refer to a causal loop.[4][5]

Grandfather paradox[edit]

The consistency paradox or grandfather paradox occurs when the past is changed in any way, thus creating a contradiction. A common example given is travelling to the past and intervening with the conception of one's ancestors (such as causing the death of the parent beforehand), thus affecting the conception of oneself. If the time traveller were not born, then it would not be possible for them to undertake such an act in the first place. Therefore, the ancestor lives to offspring the time traveller's next-generation ancestor, and eventually the time traveller. There is thus no predicted outcome to this.[3] Consistency paradoxes occur whenever changing the past is possible.[1]

A possible resolution is that a time traveller can do anything that did happen, but cannot do anything that did not happen. Doing something that did not happen results in a contradiction.[3] This is referred to as the Novikov self-consistency principle.

Early examples[edit]

A form of the paradox is described in a letter printed in the July 1927 issue of Amazing Stories, which suggests that a time traveller could shoot and kill his younger self.[6]: 252–253 [7] A similar scenario is presented in Charles Cloukey's "Paradox" (Amazing Stories Quarterly, Summer 1929), wherein the protagonist has the opportunity to avert the events that sent him back in time. Relating this predicament to other characters, the time traveller offers a hypothetical example in which he might have travelled to his grandfather's childhood to kill him.[6]: 254, 286 [8]: 392  One of the listeners remarks that he has heard "that grandfather argument" previously.[8]: 397  Later that year, an editorial note in Science Wonder Stories invited readers to discuss the problem of travelling back 200 years to shoot one's great-great-great-grandfather.[6]: 254–255 [9]

By the early 1930s, the topic was frequently discussed in the lettercolumns of various American science fiction magazines.[6]: 255, 286  [10]: 70–71  A 1931 Amazing Stories letter characterizes the matter as "the age-old argument of preventing your birth by killing your grandparents"[6]: 255  Early science-fiction stories dealing with the paradox are the short story Ancestral Voices by Nathaniel Schachner, published in 1933,[11] and the 1944 book Future Times Three by René Barjavel, although a number of other works from the 1930s and 1940s touched upon the topic in various degrees of detail.[6]: 286–288 


The grandfather paradox encompasses any change to the past,[12] and it is presented in many variations. Physicist John Garrison et al. give a variation of the paradox of an electronic circuit that sends a signal through a time machine to shut itself off, and receives the signal before it sends it.[13][14] An equivalent paradox is known in philosophy as the "retro-suicide paradox" or "autoinfanticide", going back in time and killing a younger version of oneself (such as a baby).[15][16] Another variant of the grandfather paradox is the "Hitler paradox" or "Hitler's murder paradox",[17] a fairly frequent trope in science fiction, in which the protagonist travels back in time to murder Adolf Hitler before he can instigate World War II and the Holocaust. Rather than necessarily physically preventing time travel, the action removes any reason for the travel, along with any knowledge that the reason ever existed.[18] Additionally, the consequences of Hitler's existence are so monumental and all-encompassing that for anyone born after the war, it is likely that their birth was influenced in some way by its effects, and thus the lineage aspect of the paradox would directly apply in some way.[19]

Some advocate a parallel universe approach to the grandfather paradox. When the time traveller kills their grandfather, the traveller is actually killing a parallel universe version of the grandfather, and the time traveller's original universe is unaltered; it has been argued that since the traveller arrives in a different universe's history and not their own history, this is not "genuine" time travel.[20] In other variants, the actions of time travellers have no effects outside of their own personal experience, as depicted in Alfred Bester's short story The Men Who Murdered Mohammed.[importance of example(s)?]

Fermi paradox[edit]

The Fermi paradox can be adapted for time travel, and phrased "if time travel were possible, where are all the visitors from the future?" Answers vary, from time travel not being possible, to the possibility that visitors from the future cannot reach any arbitrary point in the past, or that they disguise themselves to avoid detection.[21]

Newcomb's paradox[edit]

Newcomb's paradox is a thought experiment showing an apparent contradiction between the expected utility principle and the strategic dominance principle.[22] The thought experiment is often extended to explore causality and free will by allowing for "perfect predictors": if perfect predictors of the future exist, for example if time travel exists as a mechanism for making perfect predictions, then perfect predictions appear to contradict free will because decisions apparently made with free will are already known to the perfect predictor.[23][24]

Philosophical analysis[edit]

Even without knowing whether time travel to the past is physically possible, it is possible to show using modal logic that changing the past results in a logical contradiction. If it is necessarily true that the past happened in a certain way, then it is false and impossible for the past to have occurred in any other way. A time traveller would not be able to change the past from the way it is; they would only act in a way that is already consistent with what necessarily happened.[25][26]

Consideration of the grandfather paradox has led some to the idea that time travel is by its very nature paradoxical and therefore logically impossible. For example, the philosopher Bradley Dowden made this sort of argument in the textbook Logical Reasoning, arguing that the possibility of creating a contradiction rules out time travel to the past entirely. However, some philosophers and scientists believe that time travel into the past need not be logically impossible provided that there is no possibility of changing the past,[27] as suggested, for example, by the Novikov self-consistency principle. Dowden revised his view after being convinced of this in an exchange with the philosopher Norman Swartz.[28]

General relativity[edit]

Consideration of the possibility of backward time travel in a hypothetical universe described by a Gödel metric led famed logician Kurt Gödel to assert that time might itself be a sort of illusion.[29][30] He suggests something along the lines of the block time view, in which time is just another dimension like space, with all events at all times being fixed within this four-dimensional "block".[citation needed]

Causal loops[edit]

Backward time travel that does not create a grandfather paradox creates a causal loop. The Novikov self-consistency principle expresses one view as to how backward time travel would be possible without the generation of paradoxes. According to this hypothesis, physics in or near closed timelike curves (time machines) can only be consistent with the universal laws of physics, and thus only self-consistent events can occur. Anything a time traveller does in the past must have been part of history all along, and the time traveller can never do anything to prevent the trip back in time from happening, since this would represent an inconsistency. Novikov et al. used the example given by physicist Joseph Polchinski for the grandfather paradox, that of a billiard ball heading toward a time machine. The ball's older self emerges from the time machine and strikes its younger self so that its younger self never enters the time machine. Novikov et al. showed how this system can be solved in a self-consistent way that avoids the grandfather paradox, though it creates a causal loop.[31][32]: 510–511  Some physicists suggest that causal loops only exist in the quantum scale, in a fashion similar to that of the chronology protection conjecture proposed by Stephen Hawking, so histories over larger scales are not looped.[32]: 517  Another conjecture, the cosmic censorship hypothesis, suggests that every closed timelike curve passes through an event horizon, which prevents such causal loops from being observed.[33]

Seth Lloyd and other researchers at MIT have proposed an expanded version of the Novikov principle by which probability bends to prevent paradoxes from occurring. Outcomes would become stranger as one approaches a forbidden act, as the universe must favor improbable events to prevent impossible ones.[34]

Quantum physics[edit]

Some physicists, such as Daniel Greenberger,[35][36] and David Deutsch, have proposed that quantum theory allows for time travel where the past must be self-consistent. Deutsch argues that quantum computation with a negative delay—backward time travel—produces only self-consistent solutions, and the chronology-violating region imposes constraints that are not apparent through classical reasoning.[37] In 2014, researchers published a simulation validating Deutsch's model with photons.[38] Deutsch uses the terminology of "multiple universes" in his paper in an effort to express the quantum phenomena, but notes that this terminology is unsatisfactory. Others have taken this to mean that "Deutschian" time travel involves the time traveller emerging in a different universe, which avoids the grandfather paradox.[39]

The interacting-multiple-universes approach is a variation of Everett's many-worlds interpretation (MWI) of quantum mechanics. It involves time travellers arriving in a different universe than the one from which they came; it has been argued that, since travellers arrive in a different universe's history and not their own history, this is not "genuine" time travel.[40] Stephen Hawking has argued that even if the MWI is correct, we should expect each time traveller to experience a single self-consistent history, so that time travellers remain within their own world rather than travelling to a different one.[41] Allen Everett argued that Deutsch's approach "involves modifying fundamental principles of quantum mechanics; it certainly goes beyond simply adopting the MWI", and that even if Deutsch's approach is correct, it would imply that any macroscopic object composed of multiple particles would be split apart when traveling back in time, with different particles emerging in different worlds.[42]

However, it was shown in an article by Tolksdorf and Verch that Deutsch's CTC self-consistency condition can be fulfilled to arbitrary precision in any quantum system described according to relativistic quantum field theory on spacetimes where CTCs are excluded, casting doubts on whether Deutsch's condition is really characteristic of quantum processes mimicking CTCs in the sense of general relativity.[43] In a later article,[44] the same authors have shown that Deutsch's CTC fixed point condition can also be fulfilled in any system subject to the laws of classical statistical mechanics, even if it is not built up by quantum systems. The authors conclude that hence, Deutsch's condition is not specific to quantum physics, nor does it depend on the quantum nature of a physical system so that it can be fulfilled. In consequence, Tolksdorf and Verch further conclude that Deutsch's condition isn't sufficiently specific to allow statements about time travel scenarios or their hypothetical realization by quantum physics, and that Deutsch's attempt to explain the possibility of his proposed time-travel scenario using the many-world interpretation of quantum mechanics is misleading.

An alternative proposal was later presented by Seth Lloyd[45][46] based upon post-selection and path integrals. In particular, the path integral is over single-valued fields, leading to self-consistent histories.

See also[edit]


  1. ^ a b c Francisco Lobo (2003). "Time, Closed Timelike Curves and Causality". Nato Science Series II. 95: 289–296. arXiv:gr-qc/0206078. Bibcode:2003ntgp.conf..289L.
  2. ^ Jan Faye (November 18, 2015), "Backward Causation", Stanford Encyclopedia of Philosophy, retrieved May 25, 2019
  3. ^ a b c Nicholas J.J. Smith (2013). "Time Travel". Stanford Encyclopedia of Philosophy. Retrieved November 2, 2015.
  4. ^ Leora Morgenstern (2010), Foundations of a Formal Theory of Time Travel (PDF), p. 6, retrieved November 2, 2015
  5. ^ Klosterman, Chuck (2009). Eating the Dinosaur (1st Scribner hardcover ed.). New York: Scribner. p. 60. ISBN 9781439168486. Retrieved 2 February 2013.
  6. ^ a b c d e f Nahin, Paul J. (1999). Time Machines: Time Travel in Physics, Metaphysics, and Science Fiction (2nd ed.). New York: Springer-Verlag. ISBN 0-387-98571-9. Retrieved 2022-02-19.
  7. ^ T.J.D (July 1927). "Flowers First and then Flaws". Discussions. Amazing Stories. Vol. 2, no. 4. New York: Experimenter. p. 410. Retrieved 2022-02-19.
  8. ^ a b Cloukey, Charles (1929-07-20). "Paradox". Amazing Stories Quarterly. Vol. 2, no. 3. Jamaica, NY: Edward Langer. pp. 386–397. Retrieved 2022-02-19.
  9. ^ "The Question of Time-travelling". Science Wonder Stories. Vol. 1, no. 7. Mt. Morris, IL: Stellar. December 1929. p. 610. Retrieved 2022-02-19.
  10. ^ Gleick, James (2016). Time Travel: A History. New York: Pantheon. ISBN 9780307908797.
  11. ^ Ginn, Sherry; Leach, Gillian I. (2015). Time-Travel Television: The Past from the Present, the Future from the Past. London: Rowman & Littlefield. p. 192. ISBN 978-1442255777.
  12. ^ Nicholas J.J. Smith (2013). "Time Travel". Stanford Encyclopedia of Philosophy. Retrieved November 2, 2015.
  13. ^ Garrison, J.C.; Mitchell, M.W.; Chiao, R.Y.; Bolda, E.L. (August 1998). "Superluminal Signals: Causal Loop Paradoxes Revisited". Physics Letters A. 245 (1–2): 19–25. arXiv:quant-ph/9810031. Bibcode:1998PhLA..245...19G. doi:10.1016/S0375-9601(98)00381-8. S2CID 51796022.
  14. ^ Nahin, Paul J. (2016). Time Machine Tales. Springer International Publishing. pp. 335–336. ISBN 9783319488622.
  15. ^ Horwich, Paul (1987). Asymmetries in Time: Problems in the Philosophy of Science (2nd ed.). Cambridge, Massachusetts: MIT Press. p. 116. ISBN 0262580888.
  16. ^ Jan Faye (November 18, 2015), "Backward Causation", Stanford Encyclopedia of Philosophy, retrieved May 25, 2019
  17. ^ Eugenia Williamson (6 April 2013). "Book review: Life after Life' by Kate Atkinson". The Boston Globe. Retrieved 9 August 2013. Google the phrase "go back in time and", and the search engine will suggest completing the phrase with a simple directive: "kill Hitler". The appeal of murdering the Nazi dictator is so great that it has its own subgenre within speculative fiction, a trope known as "Hitler's murder paradox" in which a time traveller journeys back far enough to nip the leader — and World War II — in the bud, typically with unexpected consequences.
  18. ^ Brennan, J.H. (1997). Time Travel: A New Perspective (1st ed.). Minnesota: Llewellyn Publications. p. 23. ISBN 9781567180855. A variation on the grandfather paradox . . . is the Hitler paradox. In this one you travel back in time to murder Hitler before he starts the Second World War, thus saving millions of lives. But if you murder Hitler in, say, 1938, then the Second World War will never come about and you will have no reason to travel back in time to murder Hitler!
  19. ^ Inglis-Arkell, Esther (2012-08-06). "Are we running out of time to kill Hitler via time travel?". io9. Retrieved 2013-08-12.
  20. ^ Frank Arntzenius; Tim Maudlin (December 23, 2009), "Time Travel and Modern Physics", Stanford Encyclopedia of Philosophy, retrieved May 25, 2019
  21. ^ "Carl Sagan Ponders Time Travel". NOVA. PBS. December 10, 1999. Retrieved April 26, 2017.
  22. ^ Wolpert, D. H.; Benford, G. (June 2013). "The lesson of Newcomb's paradox". Synthese. 190 (9): 1637–1646. doi:10.1007/s11229-011-9899-3. JSTOR 41931515. S2CID 113227.
  23. ^ Craig (1987). "Divine Foreknowledge and Newcomb's Paradox". Philosophia. 17 (3): 331–350. doi:10.1007/BF02455055. S2CID 143485859.
  24. ^ Craig, William Lane (1988). "Tachyons, Time Travel, and Divine Omniscience". The Journal of Philosophy. 85 (3): 135–150. doi:10.2307/2027068. JSTOR 2027068.
  25. ^ Norman Swartz (2001), Beyond Experience: Metaphysical Theories and Philosophical Constraints, University of Toronto Press, pp. 226–227
  26. ^ Dummett, Michael (1996). The Seas of Language (New ed.). Oxford: Oxford University Press. pp. 368–369. ISBN 0198236212.
  27. ^ Nicholas J.J. Smith (2013). "Time Travel". Stanford Encyclopedia of Philosophy. Retrieved November 2, 2015.
  28. ^ Norman Swartz (1993). "Time Travel - Visiting the Past". SFU.ca. Retrieved 2016-04-21.
  29. ^ Yourgrau, Palle (4 March 2009). A World Without Time: The Forgotten Legacy of Godel and Einstein. New York: Basic Books. p. 134. ISBN 9780786737000. Retrieved December 18, 2017.
  30. ^ Holt, Jim (2005-02-21). "Time Bandits". The New Yorker. Retrieved 2017-12-13.
  31. ^ Lossev, Andrei; Novikov, Igor (15 May 1992). "The Jinn of the time machine: non-trivial self-consistent solutions" (PDF). Class. Quantum Gravity. 9 (10): 2309–2321. Bibcode:1992CQGra...9.2309L. doi:10.1088/0264-9381/9/10/014. S2CID 250912686. Archived from the original (PDF) on 17 November 2015. Retrieved 16 November 2015.
  32. ^ a b Thorne, Kip S. (1995). Black Holes & Time Warps: Einstein's Outrageous Legacy. New York: W.W. Norton. ISBN 0393312763.
  33. ^ Visser, Matt (15 April 1997). "Traversable wormholes: The Roman ring". Physical Review D. 55 (8): 5212–5214. arXiv:gr-qc/9702043. Bibcode:1997PhRvD..55.5212V. doi:10.1103/PhysRevD.55.5212. S2CID 2869291.
  34. ^ Sanders, Laura (2010-07-20). "Physicists Tame Time Travel by Forbidding You to Kill Your Grandfather". WIRED. Retrieved 2017-01-02. But this dictum against paradoxical events causes possible unlikely events to happen more frequently. 'If you make a slight change in the initial conditions, the paradoxical situation won't happen. That looks like a good thing, but what it means is that if you're very near the paradoxical condition, then slight differences will be extremely amplified,' says Charles Bennett of IBM's Watson Research Center in Yorktown Heights, New York.
  35. ^ Greenberger, Daniel M.; Svozil, Karl (2005). "Quantum Theory Looks at Time Travel". Quo Vadis Quantum Mechanics?. The Frontiers Collection. p. 63. arXiv:quant-ph/0506027. Bibcode:2005qvqm.book...63G. doi:10.1007/3-540-26669-0_4. ISBN 3-540-22188-3. S2CID 119468684.
  36. ^ Kettlewell, Julianna (June 17, 2005). "New model 'permits time travel'". BBC News. Retrieved April 26, 2017.
  37. ^ Deutsch, David (15 November 1991). "Quantum mechanics near closed timelike lines". Physical Review D. 44 (10): 3197–3217. Bibcode:1991PhRvD..44.3197D. doi:10.1103/PhysRevD.44.3197. PMID 10013776.
  38. ^ Ringbauer, Martin; Broome, Matthew A.; Myers, Casey R.; White, Andrew G.; Ralph, Timothy C. (19 June 2014). "Experimental simulation of closed timelike curves". Nature Communications. 5: 4145. arXiv:1501.05014. Bibcode:2014NatCo...5.4145R. doi:10.1038/ncomms5145. PMID 24942489. S2CID 12779043.
  39. ^ Lee Billings (2 Sep 2014). "Time Travel Simulation Resolves 'Grandfather Paradox'". Scientific American. Retrieved 24 September 2014.
  40. ^ Frank Arntzenius; Tim Maudlin (December 23, 2009), "Time Travel and Modern Physics", Stanford Encyclopedia of Philosophy, retrieved May 25, 2019
  41. ^ Hawking, Stephen (1999). "Space and Time Warps". Archived from the original on February 10, 2012. Retrieved February 25, 2012.
  42. ^ Everett, Allen (2004). "Time travel paradoxes, path integrals, and the many worlds interpretation of quantum mechanics". Physical Review D. 69 (124023): 124023. arXiv:gr-qc/0410035. Bibcode:2004PhRvD..69l4023E. doi:10.1103/PhysRevD.69.124023. S2CID 18597824.
  43. ^ Tolksdorf, Juergen; Verch, Rainer (2018). "Quantum physics, fields and closed timelike curves: The D-CTC condition in quantum field theory". Communications in Mathematical Physics. 357 (1): 319–351. arXiv:1609.01496. Bibcode:2018CMaPh.357..319T. doi:10.1007/s00220-017-2943-5. S2CID 55346710.
  44. ^ Tolksdorf, Juergen; Verch, Rainer (2021). "The D-CTC condition is generically fulfilled in classical (non-quantum) statistical systems". Foundations of Physics. 51 (93): 93. arXiv:1912.02301. Bibcode:2021FoPh...51...93T. doi:10.1007/s10701-021-00496-z. S2CID 208637445.
  45. ^ Lloyd, Seth; Maccone, Lorenzo; Garcia-Patron, Raul; Giovannetti, Vittorio; Shikano, Yutaka; Pirandola, Stefano; Rozema, Lee A.; Darabi, Ardavan; Soudagar, Yasaman; Shalm, Lynden K.; Steinberg, Aephraim M. (27 January 2011). "Closed Timelike Curves via Postselection: Theory and Experimental Test of Consistency". Physical Review Letters. 106 (4): 040403. arXiv:1005.2219. Bibcode:2011PhRvL.106d0403L. doi:10.1103/PhysRevLett.106.040403. PMID 21405310. S2CID 18442086.
  46. ^ Lloyd, Seth; Maccone, Lorenzo; Garcia-Patron, Raul; Giovannetti, Vittorio; Shikano, Yutaka (2011). "The quantum mechanics of time travel through post-selected teleportation". Physical Review D. 84 (2): 025007. arXiv:1007.2615. Bibcode:2011PhRvD..84b5007L. doi:10.1103/PhysRevD.84.025007. S2CID 15972766.