Grandfather paradox

For the character in the Doctor Who and Faction Paradox franchises, see Grandfather Paradox (Doctor Who).
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 proposed paradox of time travel which results in an inconsistency through changing the past. The paradox was described as early as 1931, and even then it was described as "the age-old argument of preventing your birth by killing your grandparents".[1]:vi:173 Early science fiction stories dealing with the paradox are the short story Ancestral Voices by Nathaniel Schachner, published in 1933,[2] and the 1943 book by René Barjavel Future Times Three.[3] The paradox is described as follows: the time traveller goes back in time and kills his grandfather before his grandfather meets his grandmother. As a result, the time traveller is never born. But, if he was never born, then he is unable to travel through time and kill his grandfather, which means the traveller would be born after all, and so on.

Despite the name, the grandfather paradox does not exclusively regard the impossibility of one's own birth. Rather, it regards any action that eliminates the cause or means of traveling back in time. The paradox's namesake example is merely the most commonly thought of when one considers the whole range of possible actions. Another example would be using scientific knowledge to invent a time machine, then going back in time and (whether through murder or otherwise) impeding a scientist's work that would eventually lead to the invention of the time machine. An equivalent paradox is known (in philosophy) as autoinfanticide, going back in time and killing oneself as a baby.[4]

Assuming the causal link between the time traveller's present and future, the grandfather paradox that disrupts that link may be regarded as impossible (thus precluding the arbitrary alteration of one's fate). However, a number of hypotheses have been postulated to avoid the paradox, such as the idea that the past is unchangeable, so the grandfather must have already survived the attempted killing (as stated earlier); or the time traveller creates—or joins—an alternate timeline or parallel universe[5] in which the traveller was never born.

A variant of the grandfather paradox is the Hitler paradox or Hitler's murder paradox,[6] 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. 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.[7] 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 grandfather paradox would directly apply in some way.[8]

Scientific theories

Novikov self-consistency principle

The Novikov self-consistency principle expresses one view on how backwards time travel could be possible without a danger 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.[9][10]:510–511

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.[11][12]

Parallel universes

One variant of the grandfather paradox is that when the traveller kills the grandfather, the act took place in (or resulted in the creation of) a parallel universe where the traveller's counterpart never exists as a result. However, his prior existence in the original universe is unaltered. Succinctly, this explanation states that if time travel is possible, then multiple versions of the future exist in parallel universes. This theory would also apply if a person went back in time to shoot himself, because in the past he would be dead as in the future he would be alive and well.

Examples of parallel universes postulated in physics are:

Other considerations

Consideration of the grandfather paradox has led some to the idea that time travel is by its very nature paradoxical and therefore logically impossible, on the same order as round squares. For example, the philosopher Bradley Dowden made this sort of argument in the textbook Logical Reasoning, where he wrote:

Nobody has ever built a time machine that could take a person back to an earlier time. Nobody should be seriously trying to build one, either, because a good argument exists for why the machine can never be built. The argument goes like this: suppose you did have a time machine right now, and you could step into it and travel back to some earlier time. Your actions in that time might then prevent your grandparents from ever having met one another. This would make you not born, and thus not step into the time machine. So, the claim that there could be a time machine is self-contradictory.

But, 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, 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.[16]

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.[17][18] He seems to have been suggesting something along the lines of the block time view in which time does not really "flow" but is just another dimension like space, with all events at all times being fixed within this 4-dimensional "block".

See also

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References

  1. ↑ Nahin, Paul J. (1999). Time Machines: Time Travel in Physics, Metaphysics, and Science Fiction. American Institute of Physics. ISBN 0-387-98571-9.
  2. ↑ Schachner, Nathaniel (December 1933), "Ancestral Voices", Astounding Stories (Street & Smith Publications, Inc.), vol. VOLUME XII, NUMBER 4; the story refers to an ancestor of the time traveller not his grandfather.
  3. ↑ Barjavel, René (1943). Le voyageur imprudent ("The imprudent traveller").; actually, the book refers to an ancestor of the time traveller not his grandfather.
  4. ↑ Horwich, Paul (1987). Asymmetries in Time. Cambridge, MIT Press. p. 116.
    When the term was coined by Paul Horwich, he used the term autofanticide.
  5. ↑ See also Alfred Bester, The Men Who Murdered Mohammed, published in 1958, just the year following Everett's Ph.D thesis
  6. ↑ 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.
  7. ↑ Brennan, J. (2002). Time Travel: A New Perspective. 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!
  8. ↑ Esther Inglis-Arkell (2012). "Are we running out of time to kill Hitler via time travel?". io9. Retrieved 2013-08-12.
  9. ↑ 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.
  10. ↑ Thorne, Kip S. (1994). Black Holes and Time Warps. W. W. Norton. ISBN 0-393-31276-3.
  11. ↑ Laura Sanders, "Physicists Tame Time Travel by Forbidding You to Kill Your Grandfather", Wired, 20 July 2010. "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."
  12. ↑
  13. ↑ Deutsch, David (1991). "Quantum mechanics near closed timeline curves". Physical Review D 44 (10): 3197–3217. Bibcode:1991PhRvD..44.3197D. doi:10.1103/PhysRevD.44.3197.
  14. ↑ Martin Ringbauer; Matthew A. Broome; Casey R. Myers; Andrew G. White; Timothy C. Ralph (19 Jun 2014). "Experimental simulation of closed timelike curves". Nature Communications 5. arXiv:1501.05014. Bibcode:2014NatCo...5E4145R. doi:10.1038/ncomms5145.
  15. ↑ Lee Billings (2 Sep 2014). "Time Travel Simulation Resolves 'Grandfather Paradox'". Scientific American. Retrieved 24 September 2014.
  16. ↑ "Time Travel - Visiting the Past". Sfu.ca. Retrieved 2016-04-21.
  17. ↑ Yourgrau, Palle (2004). A World Without Time: The Forgotten Legacy Of Godel And Einstein. Basic Books. ISBN 0-465-09293-4.
  18. ↑ Holt, Jim (2005-02-21). "Time Bandits". The New Yorker. Retrieved 2006-10-19.
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