[Kristine1975]

There's always Wikipedia:

In mathematical physics, a closed timelike curve (CTC) is a world line of a material particle in spacetime that is "closed", returning to its starting point.

So it's essentially like in the movie Groundhog Day I guess.

[p1mrx]

In Groundhog Day, there is no material particle that returns to its starting point, only information (Phil's memory in particular.)

Although, intuitively it seems that a time machine for information should be easier to build than one for matter, because information is so much easier to teleport.

[logfromblammo]

If you had a tiny wormhole and put one end of it into a high-speed centrifuge for a while, until there was a meaningful time differential between the two ends, you might not be able to send even an entire photon through it, but you might be able to do something like bounce a laser off each end such that if you modulate the input polarization at one end, the polarization of light reflected from the other end changes at the appropriate time. No mass or energy travels through the hole itself, but information is transmitted.

[vog]

An even better (although quite contrived) example is given in the movie "Predestination":

http://www.imdb.com/title/tt2397535/

Alternatively, read the short story "All you Zombies" by Robert A. Heinlein, on which most of the movie is based:

http://emilkirkegaard.dk/en/wp-content/uploads/Robert-A.-Hei...