Bootstrap paradox

The bootstrap paradox is a paradox of time travel in which information or objects can exist without having been created. After information or an object is sent back in time, it is recovered in the present and becomes the very object/information that was initially brought back in time in the first place. Numerous science fiction stories are based on this paradox, which has also been the subject of serious physics articles.

The term "bootstrap paradox" refers to the expression "pulling yourself up by your bootstraps"; the use of the term for the time-travel paradox was popularized by Robert A. Heinlein's story By His Bootstraps (see below).

Definition

Because of the possibility of influencing the past while time traveling, one way of explaining why history does not change is to posit that these changes already are contained self-consistently in the past timeline. A time traveler attempting to alter the past in this model, intentionally or not, would only be fulfilling his or her role in creating history, not changing it. The Novikov self-consistency principle proposes that contradictory causal loops cannot form, but that consistent ones can.

However, a scenario can occur where items or information are passed from the future to the past, which then become the same items or information that are subsequently passed back. This not only creates a loop, but a situation where these items have no discernible origin. Physical items are even more problematic than pieces of information, since they should ordinarily age and increase in entropy according to the Second law of thermodynamics. But if they age by any nonzero amount at each cycle, they cannot be the same item to be sent back in time, creating a contradiction.

Another problem is the "reverse grandfather paradox", where whatever is sent to the past allows the time travel in the first place (such as saving your past self's life, or sending vital information about the time travel mechanism).

The paradox raises the ontological questions of where, when and by whom the items were created or the information derived. Time loop logic operates on similar principles, sending the solutions to computation problems back in time to be checked for correctness without ever being computed "originally".

Whether or not a scenario described in this paradox would actually be possible, even if time travel itself were possible, is not presently known.

The bootstrap paradox is similar to, but distinct from, the predestination paradox, in which individuals or information travel back in time and ultimately trigger events they already experienced in their own present. In the latter case, no information or matter 'appears out of thin air'.

Examples

Involving information

• On his 30th birthday, a man who wishes to build a time machine is visited by a future version of himself. This future self explains to him that he should not worry about designing the time machine, as he has done it in the future. The man receives the schematics from his future self and starts building the time machine. Time passes until he finally completes the time machine. He then uses it to travel back in time to his 30th birthday, where he gives the schematics to his past self, closing the loop.
• A professor travels forward in time, and reads in a physics journal about a new equation that was recently derived. She travels back to her own time, and relates it to one of her students who writes it up, and the article is published in the same journal which the professor reads in the future.
• A man builds a time machine. He goes into the future and steals a valuable gadget. He then returns and reveals the gadget to the world, claiming it as his own. Eventually, a copy of the device ends up being the item the man originally steals. In other words, the device is a copy of itself and it is not possible to state where the original came from.
• A young physicist receives an old, disintegrating notebook containing information about future events sent by her future self via a time machine; before the book deteriorates so badly as to be unusable, she copies the information in it into a new notebook. Over the years the predictions of the notebook come true, allowing her to become wealthy enough to fund her own research, which results in the development of a time machine, which she uses to send the now old, tattered, disintegrating notebook back to her former self. The notebook is not a paradox (it has an end and a beginning; the beginning where she receives it and the end where she threw it out after she copied the information), but the information is: it is impossible to state where it came from. The professor has transferred the information that she wrote herself, so there was no original notebook.

Involving physical items

• A woman is locked outside her house because she's lost her keys. Another woman approaches her with the keys. When the woman enters the house five minutes later, she encounters a time machine which transports her and her keys back in time five minutes, allowing her to give them to herself and close the loop. [The woman would have to take the keys she left inside back in time, otherwise the keys given to her would age by a non-zero amount.]

Involving people

• A man travels back in time and falls in love with and marries a woman, who he later learns was his own mother, who then gives birth to him. He is therefore his own father and, because of this, also his own grandfather, great-grandfather, great-great grandfather, great-great-great grandfather and so on, making his ancestry infinite, and also giving him no origin for his paternal genetic material.

Examples from fiction

Main article: Bootstrap paradox in fiction

The term bootstrap paradox comes from Robert A. Heinlein's story "By His Bootstraps", in which the protagonist is asked to go through a time portal by a mysterious stranger, a second stranger tries to stop him, and all three get into a fight which results in the protagonist being pushed through anyway. Ultimately, it is revealed that all three are the same person: the first visitor is his future self and the second an even older future self trying to prevent the loop from occurring. The bootstrap paradox here is in where and how the loop started in the first place. Heinlein's "—All You Zombies—" involves an even more convoluted time loop involving kidnapping, seduction, child abandonment and sex reassignment surgery, resulting in the protagonist creating the circumstances where he becomes his own mother, father, son, daughter, forever-lost lover and kidnapper.

One example is in the American drama, Lost. John Locke is given a compass by Richard Alpert in 2007. He later is sent back in time about 60 years where he gives the compass back to Alpert, telling him to bring him the compass in 2007. The compass is the subject of the paradox here, it goes through this loop infinite times when the island is dislodged from time.

One of the most noted examples of the bootstrap paradox in fiction occurs in the film Somewhere in Time, based on the Richard Matheson novel Bid Time Return. In the film, Christopher Reeve's character is given a pocket watch by an old lady. He then goes back in time and gives the pocket watch to the old lady's younger self, played by Jane Seymour, which prompts her to seek him out years in the future and give him the watch, resulting in the watch having no apparent origin.

The bootstrap paradox occurs several times in the Terminator franchise, perhaps most notably in the creation of the main villain Skynet. In the first film, the Terminator cyborg sent back in time to kill Sarah Connor is destroyed, but its components are salvaged to form the basis of Skynet, the artificially intelligent computer network that will, in the future, send it back in time on its murderous mission. The knowledge of how to create an artificially intelligent machine therefore has no ultimate source.

The current series of Doctor Who features many examples of the bootstrap paradox, most constructed by writer and later showrunner Stephen Moffat. For example, in Moffat's 2007 episode "Blink", the Doctor records a message on film in 1969 in the form of half a conversation. The other half is filled in when Sally Sparrow views the film on DVD in 2007, which her friend Lawrence Nightingale transcribes. The full transcript, including the Doctor's portion, is eventually handed to the Doctor in 2008, but before he is sent back to 1969 from his subjective viewpoint, so he can use it in creating the message later. The contents of the conversation form a bootstrap paradox. The Doctor explains Sally's confusion by revealing that most people think of time like "a swift progression of cause to effect", when it's actually, "like a big ball of wibbly-wobbly, timey-wimey... stuff".

See also

• Grandfather paradox
• Newcomb's paradox
• Predestination paradox
• Self-fulfilling prophecy
• Strange loop
• Temporal paradox
• The chicken or the egg
• Time travel in fiction