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.

The grandfather paradox is a paradox of time travel in which inconsistencies emerge through changing the past.[1] The name comes from the paradox's common description: a person travels to the past and kills their own grandfather before the conception of their father or mother, which prevents the time traveler's existence,[2] despite its title, the grandfather paradox does not exclusively regard the contradiction of killing one's own grandfather to prevent one's birth. Rather, the paradox regards any action that alters the past,[3] since there is a contradiction whenever the past becomes different from the way it was.[4]

## Early examples

The grandfather paradox was alluded to in written stories as early as 1929, and in 1931 it was described as "the age-old argument of preventing your birth by killing your grandparents" in a letter to American science fiction magazine Amazing Stories.[5] Early science fiction stories dealing with the paradox are the short story Ancestral Voices by Nathaniel Schachner, published in 1933,[6] and the 1944 book Future Times Three by René Barjavel, although a number of other works have touched upon the topic in the 1930s and 1940s in various degrees of detail.[5]

## Variants

The grandfather paradox encompasses any change to the past,[4] and it's presented in many variations. Physicist John Garrison et al. give a variation of the paradox of an electronic circuit which sends a signal through a time machine to shut itself off, and receives the signal before it sends it.[7][8] An equivalent paradox is known in philosophy as autoinfanticide, going back in time and killing oneself as a baby.[9]

Another variant of the grandfather paradox is the "Hitler paradox" or "Hitler's murder paradox",[10] 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, thus removing any point in travelling in time in the first place.[11] 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.[12]

Some advocate a parallel universe approach to the grandfather paradox. When the time traveller kills their grandfather, they are actually killing a parallel universe version of their grandfather, and the time traveller's original universe is unaltered; it's been argued that since the traveler arrives in a different universe's history and not their own history, this is not "genuine" time travel.[13] In other variants, the actions of the time traveller have no effect outside of their own personal experience, as depicted in Alfred Bester's short story The Men Who Murdered Mohammed.[citation needed]

## Philosophical analysis

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.[3][14]

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,[4] as suggested, for example, by the Novikov self-consistency principle. Bradley Dowden himself revised the view above after being convinced of this in an exchange with the philosopher Norman Swartz.[15]

Consideration of the possibility of backwards 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,[16][17] 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 4-dimensional "block".[citation needed]

Hugh Everett's 1957 Many-minds interpretation (then called Many-worlds interpretation) suggest a tree-like, rather than linear, time, in which for any observer there is only one past, but an infinite (and that Everett later showed greater than ${\displaystyle \aleph _{0},}$) number of futures. It allowed science-fiction writers to imagine lateral time travel, as in Keith Laumer's Worlds of the Imperium and the TV series Sliders.

## Causal loops

Backwards time travel that does not create a grandfather paradox creates a causal loop, the Novikov self-consistency principle expresses one view on how backwards 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, of a billiard ball heading towards a time machine: the ball's older self emerges from the time machine and strikes its younger self so its younger self never enters the time machine. Novikov et al. showed how this system can be solved in a self-consistent way which avoids the grandfather paradox, though it creates a causal loop.[18][19]:510–511 Some physicists suggest that causal loops only exist in the quantum scale, in a fashion similar to the chronology protection conjecture proposed by Stephen Hawking, so histories over larger scales are not looped.[19]: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.[20]

Seth Lloyd and other researchers at MIT have proposed an expanded version of the Novikov principle, according to 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.[21]

### Quantum physics

Physicist David Deutsch has argued that quantum computation with a negative delay—backwards time travel—produces only self-consistent solutions, and the chronology-violating region imposes constraints that are not apparent through classical reasoning.[22] In 2014, researchers published a simulation validating Deutsch's model with photons.[23] 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 multiple universes in order to resolve the grandfather paradox.[24] However, it was shown in an article by Tolksdorf and Verch that Deutsch's CTC (closed timelike curve) fixed point 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.[25]

## References

1. ^ Francisco Lobo (2002). "Time, Closed Timelike Curves and Causality" (PDF). p. 2. Retrieved November 2, 2015.
2. ^ "Carl Sagan Ponders Time Travel". NOVA. PBS. December 10, 1999. Retrieved 2016-05-21.
3. ^ a b Norman Swartz (2001), Beyond Experience: Metaphysical Theories and Philosophical Constraints, University of Toronto Press, pp. 226—227
4. ^ a b c Nicholas J.J. Smith (2013). "Time Travel". Stanford Encyclopedia of Philosophy. Retrieved November 2, 2015.
5. ^ a b Nahin, Paul J. (1999). Time Machines: Time Travel in Physics, Metaphysics, and Science Fiction (2nd ed.). New York: Springer. pp. 255, 286. ISBN 0387985719.
6. ^ 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 1442255773.
7. ^ 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:. Bibcode:1998PhLA..245...19G. doi:10.1016/S0375-9601(98)00381-8.
8. ^ Nahin, Paul J. (2016). Time Machine Tales. Springer International Publishing. pp. 335–336. ISBN 9783319488622.
9. ^ Horwich, Paul (1987). Asymmetries in Time: Problems in the Philosophy of Science (2nd ed.). Cambridge, Massachusetts: MIT Press. p. 116. ISBN 0262580888.
10. ^ 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.
11. ^ 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!
12. ^ Inglis-Arkell, Esther (2012-08-06). "Are we running out of time to kill Hitler via time travel?". io9. Retrieved 2013-08-12.
13. ^ Frank Arntzenius; Tim Maudlin (December 23, 2009), "Time Travel and Modern Physics", Stanford Encyclopedia of Philosophy
14. ^ Dummett, Michael (1996). The Seas of Language (New ed.). Oxford: Oxford University Press. pp. 368–369. ISBN 0198236212.
15. ^ Norman Swartz (1993). "Time Travel - Visiting the Past". SFU.ca. Retrieved 2016-04-21.
16. ^ 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.
17. ^ Holt, Jim (2005-02-21). "Time Bandits". The New Yorker. Retrieved 2017-12-13.
18. ^ Lossev, Andrei; Novikov, Igor (15 May 1992). "The Jinn of the time machine: non-trivial self-consistent solutions" (PDF). Class. Quantum Gravity. 9: 2309–2321. Bibcode:1992CQGra...9.2309L. doi:10.1088/0264-9381/9/10/014. Retrieved 16 November 2015.
19. ^ a b Thorne, Kip S. (1995). Black Holes & Time Warps: Einstein's Outrageous Legacy. New York: W.W. Norton. ISBN 0393312763.
20. ^ Visser, Matt (15 April 1997). "Traversable wormholes: The Roman ring". Physical Review D. 55 (8): 5212–5214. arXiv:. Bibcode:1997PhRvD..55.5212V. doi:10.1103/PhysRevD.55.5212.
21. ^ 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.
22. ^ 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.
23. ^ 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:. Bibcode:2014NatCo...5E4145R. doi:10.1038/ncomms5145. PMID 24942489.
24. ^ Lee Billings (2 Sep 2014). "Time Travel Simulation Resolves 'Grandfather Paradox'". Scientific American. Retrieved 24 September 2014.
25. ^ 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:. Bibcode:2018CMaPh.357..319T. doi:10.1007/s00220-017-2943-5.