Imagine a guy who finds a box buried in his backyard that contains instructions on how to build a time machine. He builds the machine, then goes back in time and buries the book in a box in his backyard. So, where did the information on how to build a time machine come from? More importantly, how old is the book? It seems that the information just came out of nowhere, and the book is infinitely old since it’s stuck in this time loop for all eternity. Does modern science have any answers to this question?
When someone actually builds a working time machine, then science will have try to develop answers. Until then, there’s no need to do so.
The book was of course written by his grandfather, shortly after he killed him, preventing him from being born.
Or, trying to work around causality causes brain cramps! 
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Robert Heinlein has covered this idea in a story called “By his Bootstraps”.
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The book is what time-travel physicists call a “djinn particle”. It is a particle that have closed world lines.
There is a slight problem with djinn particles that deals with entropy. It is possible in some solutions to Einstein’s Field Equations to develop closed world lines. These djinn particles have to, though, obey the second law of thermodynamics. In effect, they have to, in their reference frame, experience a net increase in entropy. This is usually the result of some sort of decay (a scratch on the book, a torn page, coffee spilled, etc.) If there is decay, at some point along the loop that effect has to be erased or the loop isn’t exactly closed.
The time-travel corollary to the “many worlds” hypothesis of quantum mechanics holds that this isn’t a problem because it’s just another “reality” and that time travel takes place on fractured paths that are based on probability. This could be true and would solve some of the “consistancy” problems of grandfather paradoxes and the like. The alternative is that said particle is extremely special and somehow is able to avoid any change to its character at all (a zero increase in entropy as long as there is no energy exchange is allowed, after all). This is a less satisfying resolution in my mind, but it is one that would allow for the self-consistent universe to be true (the orthodox approach).
We aren’t apt to get a resolution anytime soon since time machines seem to be hard to build.
ricksummon - I think modern science will cross that bridge when it gets there, which doesn’t seem to be in the foreseeable future. Apparently you can make a (somewhat limited) time machine with a pair of cosmic superstrings, but I don’t know how you’d get a hold of those.
Your example is a little creepy, though. That book has no author. The existence of a book like that would cause a complete revolution in scientific thinking.
JS Princeton, I understand the point you’re making about the deterioration of the djinn particle being an issue. If the book travels forward in time and you carry it back, the book does not get any younger, and continues to age. If you loop this process, the book’s age keeps increasing, and so the book must deteriorate due to the Second Law of Thermodynamics. But what if it were just information being conveyed back in time? If I went back and whistled Beethoven’s 9th to a yound Ludwig Von, and he proceded to write it because of hearing it from me, then the 9th would be a djinn particle. In effect, the 9th was written by no one. It just exists on its own in the time loop. Does this sort of djinn particle cause any problems, other than the fact that it makes human brains hurt?
This subject has been discussed before:
http://boards.straightdope.com/sdmb/showthread.php?threadid=158729
