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I've been thinking about various time-travel related paradoxes, and have wondered what the name of the paradox is where something doesn't have a cause. Take the following example:

Let's say there is a piece of paper with some informaton on it. Bob is a time traveller, and travels from the year 2010 to 2000 to give this piece of paper to Alice (who is not a time traveller.) This by chance happens to the the first time Alice has met Bob, but the second time Bob has met Alice (relative to their own timeline's.) Alice then meets Bob later on and gives him the piece of paper (Second time Alice meets Bob, First time Bob meets Alice.) This is where Bob get's the piece of paper that he transports back in time to Alice.

This covers 2 things that need a cause which don't seem to have one: the information and the physical paper. This could come up in say, travelling to the future to seek out advance medicine, but it is "invented" by seeing into the future, thus once again removing any proper cause.

I'm unsure as to what the name of this paradox would be. At first I thought it might be covered by the grandfather paradox, but later decided it probably doesn't. The reason I'm thinking it might not is that in the grandfather paradox there is a clearly identified cause and effect (cause: grandfather having children, effect: grandchild exists) and the paradox is that the effect is removing it's own cause rather than there not been any cause. In this paradox though, there isn't an identified cause at all.

I have tried searching for keywords such as "recursive paradox" and "no-cause paradox" but can't seem to find anything.

Any thoughts as to what category it fits into?

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    This question appears to be off-topic because it is about time travel theory and not related to any specific work of science fiction or fantasy. – TGnat Sep 24 '14 at 14:44
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    It's the bootstrap or ontological paradox. A great short story which describes a similar scenario to yours is Robert Heinlein's By His Bootstraps. You can read it at pot.home.xs4all.nl/scifi/byhisbootstraps.pdf. – Null Sep 24 '14 at 15:28
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    In this paradox, specifically with physical objects, entropy is not preserved. What this means is that the object ages by a nonzero amount, then goes back in time and is the same object. This is discussed in the Wikipedia article as well as, I believe, the TVTropes one. – trysis Sep 24 '14 at 16:18
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    Is the only thing this question missing is a direct reference to a sci-fi story containing this paradox? – Ellesedil Sep 24 '14 at 16:20
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    There's a loop like this in Harry Harrison's The Technicolor Time Machine, with a character getting handed a piece of paper by his future self, keeping it to hand to himself. – SQB Sep 24 '14 at 21:06
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I believe that would be a bootstrap paradox. It's a time travel paradox where something is transported from the future to the past and ends up becoming the very thing that is again transported from the future to the past.

Here is the Wikipedia article on it:

http://en.wikipedia.org/wiki/Bootstrap_paradox

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An example with a fabulous mathematical proof playing the role that your information on a piece of paper played:

On the other hand, we have to consider the idea of a consistent causal loop. While equally thought-provoking, this theoretical model of time travel is paradox free. According to physicist Paul Davies, such a loop might play out like this: A math professor travels into the future and steals a groundbreaking math theorem. The professor then gives the theorem to a promising student. Then, that promising student grows up to be the very person from whom the professor stole the theorem to begin with.

From How Time Travel Works, by Kevin Bonsor and Robert Lamb

Heinlein, in the story "By His Bootstraps" also illustrated this kind of causal loop in an "uncaused" or "self-caused" warning that loops through time. From www.fresian.com's Time Travel Paradoxes page:

A paradox of time travel arises in relation to this story. The narrator does indeed set himself up "by his bootstraps" -- his present and future selves all interact with each other to produce the events. The paradoxical nature of this comes down to the case of a notebook that was provided to the narrator by the older man in the future. It contained a vocabulary of the language that was spoken by people in the future. The narrator learns the language and, as the book wears out over the years, copies it over into a notebook he had fetched from the present. This notebook, as it happens, is the very one he, as the older man, then provides to his other self. He is therefore the same person who both learns the knowledge from the notebook and put the knowledge into the notebook in the first place. The vocabulary as a certain list of items arranged in a certain way was thus complied by no one whatsoever. The knowledge exists in a closed temporal loop and is in an important sense uncaused or uncreated. The narrator himself notes that there is something peculiar about this.

There is, of course, a Wikipedia page devoted to time travel paradoxes, and one is the causal loop paradox, or as it is also known the predestination paradox:

A predestination paradox (also called causal loop, causality loop, and, less frequently, closed loop or closed time loop) is a paradox of time travel that is often used as a convention in science fiction. A temporal causality loop is an event whereby a specific moment in time repeats itself continually inside an independent fragment of time. The paradox occurs when a time traveler is caught in a loop of events that "predestines" or "predates" him or her to travel back in time.

In your example the information on the paper is the predestined traveler.

Indeed, there is a Wikipedia page devoted to fiction featuring temporal causal loops (although some of the stories on this list are about such causal loops, some of the stories listed there veer towards self-fulfilling prophecy).

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Another name that I remember seeing for this paradox would be the Free Lunch paradox; in reference to the fact that you are getting something for free without having to pay or work for it.

The same name has also been used frequently in stories to disprove this paradox; ie. by saying that there is no such thing as a Free Lunch in the universe.

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I knew it as extracting information from the void, but googling that gets you close to nothing. It seems to be better known as The Chicken and the Egg Paradox or Closed Time Loops.

Check this. It cites the story of finding the sculptor of Samuel Mines' statue, another example of the paradox you are describing.

I recall this paradox from other works of fiction such as the Anubis Gates by Tim Powers.

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