Bootstrap paradox

A causal loop, in the context of time travel or retrocausality, is a sequence of events (actions, information, objects, people) in which an event is among the causes of another event, which in turn is among the causes of the first-mentioned event. Such causally-looped events then exist in spacetime, but their origin cannot be determined. A hypothetical example of a causality loop is given of a billiard ball striking its past self: the billiard ball moves in a path towards a time machine, and the future self of the billiard ball emerges from the time machine before its past self enters it, giving its past self a glancing blow, altering the past ball's path and causing it to enter the time machine at an angle that would cause its future self to strike its past self the very glancing blow that altered its path.

Backwards time travel would allow for causal loops involving events, information, people or objects whose histories form a closed loop, and thus seem to "come from nowhere." The notion of objects or information which are "self-existing" in this way is often viewed as paradoxical, with several authors referring to a causal loop involving information or objects without origin as a bootstrap paradox, an information paradox, or an ontological paradox. The use of "bootstrap" in this context refers to the expression "pulling yourself up by your bootstraps" and to Robert A. Heinlein's time travel story "By His Bootstraps". The term "time loop" is sometimes used to refer to a causal loop, but although they appear similar, causal loops are unchanging and self-originating, whereas time loops are constantly resetting.

An example of a causal loop paradox involving information is given by Everett: suppose a time traveler copies a mathematical proof from a textbook, then travels back in time to meet the mathematician who first published the proof, at a date prior to publication, and allows the mathematician to simply copy the proof. In this case, the information in the proof has no origin. A similar example is given in the television series Doctor Who of a time-traveler who copies Beethoven's music from the future and publishes it in Beethoven's time in Beethoven's name. Everett gives the movie Somewhere in Time as an example involving an object with no origin: an old woman gives a watch to a playwright who later travels back in time and meets the same woman when she was young, and gives her the same watch that she will later give to him.

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